September 12, 2024 Tom Drucker, University of Wisconsin, Whitewater:
Exploring Felix Klein’s Contested Modernism
ABSTRACT: One of the pleasures of history of mathematics is that it is often free from the jargon that one finds prevalent in much contemporary history of a broader sort. The article about which I'll be speaking has five authors, one from Israel, three from Germany, and one from the United States, and is laden with more jargon than is necessary. The number of directions in which the article sets off suggests that different contributors may have had different points they were trying to make. The primary target is the Marxism of the historian Mehrtens, but another target is Frank Quinn. Among the questions the authors hope to settle is whether Klein was antisemitic in behaviour or writings. There is also the issue of whether Klein was countermodernist, while Hilbert was recognizably modernist.
I
t's clearly impossible to tackle all these matters in one talk, but I'll address a few of those that seem least dependent on jargon. First, there's the issue of Klein's alleged antisemitism. Then there's the question of whether a Marxist historian can address such issues without any historical bias. Finally, there are the roles that Klein and Hilbert played in creating the Gottingen that was to fall victim to the Nazi view that only Deutschemathematik was worth pursuing. There may be time to look at Quinn in the questions that follow the talk.
April 18, 2024 David E. Dunning, History and Sociology of Science, University of Pennsylvania:
From Notations to Neurons: Mathematical Logic, AI, and the Act of Writing
ABSTRACT: In this talk I will discuss two episodes from my current book project, a history of the rise of mathematical logic and its connection to early computer science and AI. I focus on shifting and competing notational practices in order to show how methods of writing have shaped understandings of natural and artificial reasoning alike. After briefly introducing the larger project, I will share two cases. I’ll discuss Victorian self-taught mathematician George Boole’s efforts to rewrite logic in algebraic notation, revealing his specific vision for how and why his system should be learned. Many of his readers were very enthusiastic, but rather than straightforwardly adopting his system, they tended to follow him in taking notation itself as a fruitful arena for innovation. After presenting Boole, I’ll turn to the watershed 1943 paper “A Logical Calculus of the Ideas Immanent in Nervous Activity,” by Warren McCulloch and Walter Pitts. The authors drew on recent mathematical logic and navigated “typographical necessity” in order to present abstract neurons as a system for writing logical propositions. By taking seriously the centrality of writing in the project that launched neural network techniques, I aim to show how modelling the mind mathematically was not simply about understanding or imitating intelligence, but rather reimagining thought as a fundamentally notational phenomenon.
March 21, 2024 Daniel Otero, Xavier University:
Barrow's Sum of the Secants
ABSTRACT: There are a handful of methods used to determine the integral of the secant function. We examine in this session what may be the earliest attempt to handle this challenging integral in the Lectiones Geometricae (1670) of Isaac Barrow (1630—1677). Barrow operated in the days when analysis of curves and their properties were pre-eminent in geometry, a generation before Newton successfully employed these ideas to describe a theory of gravitation and Leibniz clarified the relation between derivative and integral, and about 100 years before Euler recast the calculus as a collection of powerful and versatile techniques for their study. The diagram above comes from the Appendix to Lectio XII of the Lectiones Geometricae. In seventeenth-century geometric language, Barrow provides a derivation of what we would interpret today as the integral of the secant function. This talk will invite the audience into a reading of Barrow’s text (and a wrangling of the nest of curves in the figure above!) to clarify this interpretation. [illustration]
February 15, 2024 Bonita Lawrence, Professor Emerita, Marshall University:
Solving Dynamic Equations: Using Gifts from the Past
The Marshall Differential Analyzer Project developed from an idea sparked by a visit to the London Science Museum’s display of historic differential analyzer machines. The primary goal of the project was to offer an alternative perspective, and hence an enhanced understanding, of the behavior of solutions to dynamic equations. As our study and the construction of our machines progressed, we found that the dynamic motion of the machine’s components and the sounds created offered observers an amazing physical connection to the “programed” mathematical equation. Through the years, our machines have been used to teach students about modeling physical systems with dynamic equations, for research studies, and to offer prospective students an alternative view of our mathematical structure.
This presentation will begin with some discussion of the history of the development of these machines and of our own project. A general overview of the primary components of the machine and the relationship between the mechanics and the mathematics being modeled will follow. The big finale will be a live streaming of a run of the large four integrator machine, complete with a discussion of the link between the physical connections between the components and the differential equation under consideration.
Integrator Machine Known as “Art”,
Mrs. Johnson, and her Calculus Students
from St. Joseph’s High School, Ironton, Ohio
(Marshall Differential Analyzer Lab)
January 18, 2024 Jeffrey Oaks, University of Indianapolis
How to think like a medieval algebraist
There are many seemingly minor yet consistent differences in wording, procedure, and notation between what we read in pre-Vietan algebra and what we practice today. Together with how the earlier authors describe their work, they point to a radically different way of understanding monomials, polynomials, and equations. In this talk I describe this premodern algebra, focusing mainly on medieval Arabic algebra, though what I say applies equally to Diophantus, medieval Latin and Italian algebra, as well as the algebra of sixteenth-century Europe. Some attention will be given to delineating the role of algebra in premodern mathematics and to the concept of number upon which the concept of monomial was based.
December 7, 2023 Maryam Vulis, St. John’s University and Norwalk Community College :
The History of Markov Chains
This presentation will review the origins of Markov chains. Notably, Markov was inspired by poetry in his development of the chain link theory. His 1906 paper was the first to mention the idea of chains in which he stated that the that it was not necessary for “quantities” to be independent for the validity of the Law of Large Numbers. Markov’s interest in studying chain dependence stemmed from a dispute with Pavel Nekrasov from Moscow Mathematical School. Nekrasov, a deeply religious man, believed that the Weak Law of Large numbers was true for pairwise independent events only due to “free will”. Markov intended to refute Nekrasov’s statement and eventually proved that the Law of Large Numbers did not have to apply to independent events only. Why Markov chains or the chains of linked events are of interest now? The insight is that the current event depends only on the immediate previous event, not on the prior events and this process can be used in AI such as chatbots. Thus, 100 years after the Markov Chains were introduced they are used in chatbots which prominently emerged in popular culture. Markov’s work has a great impact on today’s technology.
November 16, 2023 Benjamin B. Olshin, University of the Arts, Bryn Mawr College
Early Circular Maps: An Example of Perspectographic Imaging?
A great deal has been written about map projections, and their development over the many centuries that human beings have engaged in map-making. From the time of Ptolemy, there have been various methods to carry out such projections, with the fundamental goal being the rendering of the globe or part of the globe onto a two-dimensional surface. Traditionally, history tells us that there were crude circular maps in the Middle Ages, and then a marked transition to Ptolemaic (mathematical) projections, followed by increasingly advanced projections, such as Mercator's. However, this lecture will present the conjecture that many of the circular maps from the late medieval and early Renaissance period were created using Albrecht Dürer's simple method of drawing a 3D object in 2D through the use of a device known as a perspectograph. This lecture will show how this method might have worked, and how it might have represented a way of creating 2D maps without formal projective geometry.
October 19, 2023 Benjamin B. Olshin, University of the Arts, Bryn Mawr College:
Leonardo da Vinci and the Deconstruction of Perpetual Motion
The engineering drawings of Leonardo da Vinci are famous for both their ingenuity and aesthetic qualities. But Leonardo used drawing in a rather unique way as a method of “visual thinking” or formal analysis, to investigate and work out problems in fields ranging from anatomy to mechanics to hydraulics. Interestingly, Leonardo used this same method to investigate the possibility ― or impossibility ― of perpetual motion. In many of his notebook folio pages, we find pictures and text dealing with a range of designs for perpetual motion machines powered by weights or water. One can actually find a thorough typology in his renderings of various schemes for perpetual motion machines: a classification scheme based upon the various mechanical elements, and motive forces employed, that Leonardo posited or analyzed in these devices. This presentation shows that these are not random sketches, but rather a systematic and even mathematical "deconstruction" of the myth of perpetual motion.
September 21, 2023 Lawrence D'Antonio, Ramapo College:
Edmond Halley, Samuel Pepys, and the “Historia Piscium”
In this talk, we will look at the remarkable life of Edmond Halley (1656 – 1742). Not just a predictor of comets, Halley produced the first star catalog of stars visible from the Southern Hemisphere. He also discovered an interesting root solving method, became the Savilian Professor of Geometry at Oxford after the death of Wallis, was a sea captain, and was named the second Astronomer Royal (succeeding John Flamsteed). Halley also played a major role in the Royal Society of London. It was a visit by Halley that encouraged Newton to write the Principia Mathematica and Halley used his own funds to publish the first edition. Halley also played a key role in the controversy surrounding the publication of Flamsteed’s star catalog (the controversy ended with a book burning!). Finally, we will discuss Halley’s election as the Clerk of the Royal Society which will help explain the title of this talk.
April 20, 2023 David Richeson, Dickinson College:
A Romance of Many (and Fractional) Dimensions
Dimension seems like an intuitive idea. We are all familiar with zero-dimensional points, one-dimensional curves, two-dimensional surfaces, and three-dimensional solids. Yet dimension is a slippery idea that took mathematicians many years to understand. We will discuss the history of dimension, which includes Cantor’s troubling discovery, the surprise of space-filling curves, the public’s infatuation with the fourth dimension, time as an extra dimension, the meaning of non-integer dimensions, and the unexpected properties of high-dimensional spaces.
March 16, 2023 Annalisa Crannell, Franklin and Marshall College:
Drawing Conclusions from Drawing a Square
The Renaissance famously brought us amazingly realistic perspective art. Creating that art was the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the way we see the world around us, whether we look with our eyes, with our cameras, or with the computer (via our favorite animated movies). One of the surprising results of projective geometry is that it implies that every quadrangle (whether convex or not) is the perspective image of a square. We will describe implications of this result for computer vision, for photogrammetry, for applications of piecewise planar cones, and of course for perspective art and projective geometry.
February 16, 2023 Ezra Brown, Virginia Tech:
A Tour of the Birth and Early Development of Finite Geometries,
Combinatorial Designs, and Normed Algebras
In this tak, we give a brief tour of the birth and early development of finite geometries, combinatorial designs, and normed algebras. Arthur Cayley (1845), Jakob Steiner (1853) and Gino Fano (1892) are credited with the creation of (respectively) the 8-dimensional real normed algebra, certain block designs with block size 3, and the first finite geometry. During our tour, we learn about the truly ground-breaking work of Julius Pl ̈ucker, John Graves (motivated by William Hamilton's quaternions), Wesley Woolhouse and Thomas Kirkman, work that anticipated Cayley, Steiner and Fano by one, 18, and 57 years, respectively.
January 19, 2023 Maryam Vulis, St John's University, Norwalk Community College and CCNY:
Ukrainian Mathematicians in the Soviet Ukraine
Our presentation will discuss the work and life of two Ukrainian mathematicians who lived in worked in the Soviet Ukraine - Mykhaylo Kravchuk and Nina Virchenko. The mathematician Mykhaylo Kravchuk was an important part of Ukrainian mathematics who dedicated his life to promoting Ukrainian culture and education. He was a member of the Ukrainian Academy of Sciences and in fact, his two-volume publication on differential equations was translated into English by the computer pioneer John Atanasoff who found Kravchuk’s results for his computer construction. Kravchuk was well-known in international circles, and perhaps it cost him his life as he met the fate of many members of intelligentsia. One must mention Nina Virchenko, a mathematics researcher and a follower of Kravchuk. She was also persecuted by Soviets, amazingly survived incarceration in a camp, and continued for decades to work on mathematics and to promote the achievements of Kravchuk. Naturally, the recognition of the Ukrainian mathematicians’ achievements came with Ukrainian gaining independence in 1991.
December 8, 2022 Amy Ackerberg-Hastings, Independent Scholar, Editorial Staff of Convergence, MAA:
HoM Toolbox: Historiography and Methodology for Mathematicians
I have been contemplating creating an article series for MAA Convergence that introduces historiography and methodology in ways that are accessible to undergraduate mathematics students and instructors. The current plan is to begin with an overview of the principles for researching and writing history by considering five questions: 1) What is history? Why should readers want to research and write it well? 2) How do we know about the past? 3) How do we create history based on what we know about the past? 4) What is the history of the history of mathematics? 5) How can readers articulate their own philosophies of the history of mathematics?
Then, subsequent installments could provide brief explanations of various approaches to historical interpretation, accompanied by examples of how these approaches have been applied in the history of mathematics—for instance, I might discuss book history and how I have used that method to make sense of the activities and significance of two 18th-century Scottish mathematicians, Robert Simson (1687–1768) and John Playfair (1748–1819). The talk will give an update on my progress with the project and solicit feedback on the two-pronged problem posed by the series concept: a) How can current historians of mathematics best train the next generation for the profession? and b) What do most mathematics instructors and students need to know about the theory and practice of history?
November 17, 2922 Ximena Catepillan, Professor Emeritus,
Millersville University:
Maya Calendar Computations
The civilization of the Maya, which began ca. 1200 BC, had a long history generally divided into three periods: The Pre-Classic period ca. 1200BC - 200AD, the Classic period 200AD - 900AD, and the Post-Classic period 900AD - 519AD. The Maya civilization extended from what it is now Belize, Central and Southern Mexico, Guatemala, El Salvador, and parts of Honduras. About thirty Mayan languages are still spoken in the above-mentioned regions, with a modern Maya population of about 5 million. The Maya developed a glyph writing system, vigesimal and quasi-vigesimal number systems, and they mastered several areas of science, art, and architecture. Based on astronomical observations, the Maya created an elaborate system of calendars. In this talk, their number systems will be discussed, and algorithms for converting among the calendars that are simple enough to do with paper and pencil will be presented. This presentation will be available for incorporating ethnomathematics into mathematics courses and ethnomathematics focused courses.
October 20, 2022 Tom Archibald, Department of Mathematics, Simon
Fraser University:
Justifying abstraction? Examples from Integration Theory to 1940
Making sense of mid-twentieth century abstraction posed problems for both new and ongoing practitioners. To historicize aspects of processes of generalization and abstraction can be tricky as it is easy to be anachronistic. Hilbert's Grundlagen der Geometrie, for example, indicates the recognition of several possible positions on the nature of axioms, for example as ``self-evident'', as idealizations of experience, or as rules. Since the axioms interact with definitions, this variation in ideas about axioms is accompanied by different ideas about definitions, ranging from definitions as descriptions to definitions as prescriptions. Description, though, is an equivocal term, since one can be describing an object one thinks of as existing, or as one that we are in a sense designing.
Historical questions arise: in what ways, and in what terms, do researchers attempt to justify their particular approaches to abstraction and generalization? How do these justifications function? In the first half of the 20th c. they were not merely conventional in my view. In what follows, we discuss some research papers and look at explicit or implicit efforts to explain the value of the approach. Such justifications are so familiar now from textbook and other writing that they are easy to overlook.These various ways of justifying one's approach serve as a kind of guide to how the main models of innovation in twentieth century mathematics became standard. We look in particular at a set of examples around the ``Lebesgue-Nikodym'' Decomposition theorem in analysis.
September 15, 2022 Karen Parshall, Commonwealth Professor of History and Mathematics, University of Virginia:
American Mathematicians and World War II
When the United States entered World War II in December 1941, America’s mathematicians had already been bracing themselves for war. This talk will examine the various venues in which they contributed to the war effort and indicate the sorts of contributions they made.
April 21, 2022 David Derbes, U of Chicago Lab School (retired):
Mark Kac’s First
Publication, On a new way of solving equations of the third
degree
In his autobiography, Mark Kac relates that as a teenager he became obsessed with the problem of deriving the Cardano formula for the roots of a cubic polynomial. He had been told that it was too hard for him. He succeeded, and it led to his becoming a mathematician. The derivation itself has been nearly impossible to locate, but it will be explained in this talk. Interestingly, it has some features in common with Lodovico Ferrari’s solution of the quartic. Additionally, some history of the cubic’s solution, some biographical details concerning Kac, and finally what may be the simplest derivation of the Cardano formula, due to François Viète, will be given in detail. This derivation seems easily within the reach of high school students. If time allows, Viète’s trigonometric solution to the casus irreducibilis (three real roots) will be sketched.
[based on
Convergence article April 2021; PDF talk available upon
request; Zoom recording available for a limited time]
March 17, 2022 William Dunham, Bryn Mawr College:
The Math Matriarchs of Bryn Mawr
Over its first 50 years, Bryn Mawr College boasted three remarkable mathematicians who, one after the other, left deep footprints on the institution and on the U.S. mathematical community. They were Professors Charlotte Angas Scott (British), Anna Pell Wheeler (American), and Emmy Noether (German). In this lecture, we meet these women and flesh out their biographies with plenty of local color … not to mention a real-life assassin in a supporting role. From 1885 to 1935, they gave Bryn Mawr a record of women in mathematics unsurpassed by any college, anywhere. [Zoom recording available upon request.]
February 17, 2022 Julian Gould, University of Pennsylvania:
Nazi regime effect on Mathematics
The founding of the Weimar Republic in Germany at the end of World War One opened the doors of mathematics academia for Jewish people. The rise of the Nazi party in the 1930s closed those doors more tightly than ever before. What happened in math departments in Germany under the Nazi regime? How did the content, teaching, and research of mathematics change? In this talk, we will first dissect the anatomy of mathematics academia and identify key questions about the intersection of mathematics and politics. Next, we will look the history of mathematics under the Third Reich, with an emphasis on the way Nazi politics and culture impacted the anatomy. This important period of history has relevant lessons about how mathematics can be politicized today and in the future.
January 20, 2022 Maryam Vulis, St. John's University:
Sophia Yanovskaya (1896-1966) and Soviet Mathematical Logic
The goal of our discussion is to present the portrait of Sophia Yanovskaya, a mathematician and educator who made invaluable contributions to the development of mathematical logic, history and philosophy of mathematics, and research in the USSR. In 1933 Yanovskaya and Vygodsky started the Seminar on History of Mathematics, and in 1943 Yanovskaya and Novikov organized the Seminar on Mathematical Logic and Philosophy of Mathematics - the center of research in mathematical logic. 1936 saw the first official course in Mathematical Logic taught at Moscow State University by Sophia Yanovskaya. In 1959 Yanovkaya oversaw the creation of the Division of Mathematical Logic at MSU in 1959. Dr. Yanovskaya’s publications included topics on history and philosophy of mathematics, foundations of mathematics, mathematical logic, and applications. There are many stories about Yanovskaya’s dedication to her students and support of young mathematicians. The biography of the Sophia Yanovskaya was complicated and currently many regard her position to be not without a fault. One should remember that the scientists of that era had little choice but to go along with the political climate of the country.
December 9, 2021 Colin McKinney, Wabash College:
Clairaut’s Quatre Problèmes sur de Nouvelles Courbes
In 1726, Alexis Clairaut presented four new families of curves to the Royal Academy of Sciences in Paris, at the age of twelve and a half. He subsequently published an article featuring these curves in 1734. Clairaut gives the algebraic and geometric properties of each curve, and shows how they can be used to solve the ancient problem of finding any number of mean proportionals between two given straight lines. He also finds tangents to his curves, and computes their quadratures. In our presentation, we will motivate Clairaut’s investigations and relate one of his family of curves to those given by Descartes in La Géométrie. We’ll also discuss our process of creating a critical edition of Clairaut’s French text and translating the work into English.
November 18, 2021 Professor Emeritus James T. Smith of San Fransisco State University:
What Specific Contributions of Mario Pieri and Alfred Tarski are
Discernible in Typical Mathematical-logic Textbooks?
Tarski’s are famous, but Pieri’s? I will trace back two themes in axiomatics: selecting primitive concepts and formulating postulates sufficient to develop a familiar informal theory; and deducing its theorems as logical consequences. The modern concept of logical consequence stems from Tarski (1953, 1935), then Ajdukiewicz (1921), Pieri (1898), and Bolzano (1830s). I will sketch Tarski’s and Pieri’s milieux in Warsaw and Turin, and survey Pieri’s pioneering development of postulate systems. This presentation is extracted from three recent books written with coauthors Elena Marchisotto and Francisco Rodríguez-Consuegra and with Andrew and Joanna McFarland.
October 21, 2021 Fred Rickey:
Stanislaw Lesniewski, Logician Extraordinaire
Stanislaw Lesniewski (1886--1939) received his Ph.D. at Lwow University under the direction of Kazimierz Twardowski in 1912. After a few years of teaching in schools for girls he left for Poland and soon joined the codebreaking group that helped Poland win the battle of the Vistual. In 1919 he became Extraordinary Professor of the Foundations of Mathematics at Warsaw University, a position created especially for him. His obsession with the Russell Antinomy led him to create three foundational system for mathematics: Protothetic, Ontology, and Mereology. His concern for rigor led him to formulate the rules of procedure in a precise way that was unmatched. We will discuss the basic ideas of his systems and their fate.
September 16,
2021 Dan Velleman, Amherst College:
The Fundamental Theorem of Algebra: History in Pictures
The fundamental theorem of algebra says that every nonconstant polynomial with complex coefficients has a root in the complex plane. In this talk I will present a method of visualizing functions on the complex plane and use this method illustrate proofs by D'Alembert, Gauss, and Argand. At the end of the talk I will describe recent work on filling a gap in Gauss's proof.
April 15, 2021 Brenda Davidson, Simon Fraser University:
Stokes and the Pendulum
During the first half of the 19th century, the pendulum occupied an important place in experimental physics and in surveying. Precision pendulum measurements were used, for example, to determine accurate values of the gravitational constant and to determine the exact shape of the earth. The desire for exceedingly precise measurement meant that temperature, humidity, altitude, external vibrations, and the medium through which the pendulum swung had to be controlled or corrected for. Simultaneous measurements being made at a variety of locations around the world meant that assurance was needed that what was being compared from one location to the other was actually comparable. Further, theory was needed to support the various experimental results and to predict the effect of changing conditions on the pendulum period. In particular, the computation, from theory, of a vacuum to air correction factor for a given pendulum was important. Sir George Gabriel Stokes provided this theory in 1848 and he used divergent series to do so. This talk will use a portion of the fascinating history of the pendulum during the early 19th century to establish their importance and then will take a close look at the mathematics that Stokes developed in support of this effort.
February 18, 2021 Maria Zack, Mathematics, Information and Computer Science, Point Loma University:
The Cycloid, A Very Popular Curve
January 21, 2021 Maryam Vulis, St. Johns University, NY,
Norwalk Community College, CT
Polish Mathematical School: Zygmunt Janiszewski (1888 -1920)
The Polish mathematician Zygmunt Janiszewski made important mathematical contributions during his life cut short by the 1918 influenza pandemic. Janiszewski studied mathematics in Europe and after defending his dissertation Sur les Continus Irréductibles Entre Deux Points (1911) under Lebesgue’s supervision, continued visiting mathematical centers in Europe and attending conferences. Consequently, his meeting with the Lwow mathematicians Józef Puzyna and Waclaw Sierpinski at the Congress of Polish Scientists and Physicians in Krakow brought Janiszewski to Lwow where he obtained his habilitation in 1913. WWI, however, interrupted his plans of becoming a professor at the Lwow University and Janiszewski joined the Polish Legion to fight in the war. During the war years he came back to Lwow to substitute for Sierpinski, but was not able to stay due to political reasons. Zygmunt Janiszewski went on to become a professor at the University of Warsaw, even one of the Mathematics Chairs. Janiszewski continued his research working alongside with Stefan Mazurkiewicz and Waclaw Sierpinski. Zygmundt Janiszewski published several important articles in pure mathematics and is considered to be one the founders of the Polish Mathematics School. Janiszewski was instrumental in setting the direction of Polish mathematics at the time and establishing the journal “Fundamenta Mathematicae” based on the novel idea of the journal devoted to a single mathematical field. One cannot talk about Zygmunt Janiszewski without adding that he was a Polish patriot and a humanitarian whose liberal views were not easily shared by his colleagues.
December 10, 2020 Larry D'Antonio, Ramapo College :
Newton and his Fudge Factors
Newton remarked to Halley that lunar theory gave him a headache. In particular the calculation of the motion of the lunar apsides frustrated Newton (an apse is an endpoint of the major axis of the ellipse defining the orbit of a body). The lunar apsides rotate approximately 3 degrees per month, but Newton’s calculations only showed half of this amount, leading Newton to say that the problem was “too complicated and cluttered with approximations.” In this talk we will examine Newton’s lunar theory, his failures and successes, and his occasional use of a fudge factor to get the theory to align with observation. Newton’s biographer, Richard Westfall, once commented that “no one can manipulate the fudge factor as the master mathematician himself.”
October 8, 2020 Chris Rorres,
Professor Emeritus of Mathematics
Drexel University:
Olympic Starting Lines, Pistons, and Black Holes
The overall theme of my talk is circularity. It pivots around research I conducted with an archaeologist to find the center of an ancient circular Olympic starting line. I'll begin with some history of the ancient and modern Olympics (hopefully next in Tokyo in 2021) and finish with examples of the importance of measuring the precision of circles in engineering (pistons, shafts, bearings, etc.) and in astronomy (event horizons of black holes, planetary orbits, Ptolemaic epicycles).
[article
website] [Rorres
website]
September 17, 2020 Laura Turner, Monmouth University:
E. V. Huntington
In addition to publishing postulate-theoretic results directed at his research-oriented contemporaries, Harvard mathematician Edward V. Huntington (1874-1952) wrote a number of pedagogical and expository works in which he outlined the principles and aims of postulate theory, and pointed to certain roles it might serve in mathematics and well beyond. In this talk we explore some of these roles, focusing on his arguments for the pedagogical and practical value of postulate theory, and the reasons for which he sought to present this material to non-research and even non-mathematical publics in the first place.
March 18, 2020 Ellen Abrams, Cornell University:
Axiom Systems and American Mathematics: Which Shall
Be Regarded as the Best?
In the early twentieth century, researchers in the United States engaged with foundational studies in mathematics by building and evaluating axiom, otherwise known as postulate, systems. At the same time, their contemporaries were evaluating the meaning and politics of knowledge more broadly. In this talk, I explore the ways in which the study of postulates in the United States was tied to important Progressive Era questions about the nature of knowledge, the status of the knower, and the development of American Pragmatism. While most investigations of postulate studies have considered their implications within mathematical research and education, I look instead to the role of postulate studies in the professionalization of mathematics in the United States and to its cultural status more broadly.
February 20, 2020 Dr. David Richeson, Dickinson College:
Geometric Constructions Using a Compass and Marked Straightedge
It is impossible to trisect an arbitrary angle, to double the cube, and to construct every regular polygon with a compass and straightedge. But Archimedes showed that if a straightedge is marked so it is able to make one measurement, then, by using a technique called a neusis construction, it is possible to trisect any angle. It is also possible to double the cube and to construct additional regular polygons. In this talk, we look at the history of the neusis construction from Archimedes to the present day, and we discuss what additional geometric constructions are possible using these tools.
January 23, 2020 Maryam Vulis, St. Johns University, NY, Norwalk Community College, CT:
The Lvov School of Mathematics
The Lvov School of Mathematics officially existed from 1919 to 1939, when the city of Lvov was part of Poland. The end of the school came with the 1939 annexation of Lvov to the USSR and the German occupation during WWII. We will discuss the works of the Polish mathematicians and the establishment of the Lvov School as a natural outcome of the development of mathematics prior to 1918, when Poland finally regained independence. It is often called the school of functional analysis. We will discuss the contributions of mathematicians who worked with Stefan Banach, Stanislaw Ulam, Marc Kac, Stanislaw Mazur, Hugo Steinhaus, Kazimierz Kuratowski. Sadly, many mathematicians from Lvov did not survive WWII. Research was conducted at the University, which was founded in 1661 and was affiliated with different countries over its long history. Lvov Polytechnic was also a place for mathematical studies Lvov School of Mathematics left invaluable legacy, and contributions various mathematicians are numerous.
December 12, 2019 Karen Parshall, University of Virginia:
Growing Research-Level Mathematics in 1930s America?: An Historical Paradox
World War I had marked a break in business as usual within the American mathematical research community. In its aftermath, there was a strong sense of entering into “a new era in the development of our science.” And then the stock market crashed. Would it be possible in such newly straitened times to sustain into the 1930s the momentum that American mathematicians had managed to build in the 1920s? This talk will explore the contours of an answer to that question.
November 21, 2019 Brittany Shields, University of Pennsylvania:
Engineering Education for “Vital War Industries”: Mathematical Foundations in the US Engineering, Science and Management War Training Program during the Second World War
The US Office of Education trained over 1.8 million citizens during the Second World War in emergency courses through the Engineering, Science and Management War Training Program. Spanning the duration of the war, the program established regional administrators to oversee the development and implementation of courses understood to be of vital importance to defense related industries. Over 200 colleges and universities participated in this robust program. In this talk, I will discuss how the mathematical sciences fit into the larger engineering training program with a focus on the northeastern region of the US.
October 24, 2019 Shelley Costa, Swarthmore College and West Chester University:
The Exchange of Geometrical Problem-Solving in 18th- and 19th-century Japan
The unique cultural traditions we associate with Japan flourished over the century and a half during which Japan’s borders were closed to foreign influence during the Edo period (1603-1867). Among the many practices that were refined during this period, Japanese abstract mathematics is not one of the most familiar. In this talk I give a glimpse of some powerful techniques and problem-solving conventions unique to Japanese mathematics, with a focus on how the ways they were shared were in keeping with ancient Japanese culture. In particular, I summarize the marvelous work done to date on historicizing the practice of sharing geometrical problems via wooden prayer boards — “sangaku” — displayed to the public at shrines and temples. In our discussion I bring to bear my own work on public problem-solving exchange in early 18th-c. Europe and introduce questions about the roles of economics, social expectations, gender, and faith in the mathematical exchanges of each cultural tradition. I offer this talk shortly after having been privileged to spend the first six months of 2019 in Kyoto, Japan, whose thousands of active shrines and temples allow a wonderful ancient wisdom to permeate postmodern urban society. If any would like to explore this elegant and challenging geometry ahead of time, attached are reproductions of two of the more accessible problems.
September 19, 2019 David Perry, National Security Agency:
The Cracking of Enigma
Although most people have heard of Alan Turing and his colleagues at Bletchley Park successfully breaking the Enigma, it is less well known that the Polish Cipher Bureau broke the Enigma during the 1930s, using the mathematics of permutations in a way that had not been anticipated.Because of this story, code making and codebreaking became the purview of mathematicians thereafter.In this talk, we provide the details of what Marian Rejewski and his colleagues did to crack the Enigma.
April 25, 2019 John Dawson, Professor Emeritus, Penn State University:
How Relevant Has Logic Been To Mathematical Practice?
For centuries mathematics has been regarded as the exemplar of rigor us deductive reasoning. Yet for much of its history it has not been, and few universities today require mathematics graduates to have had a course in formal logic. To what extent then have results in formal logic actually affected progress in mathematics? And what accounts for the popular view that deductive logic is central to mathematical practice?
December 13, 2018 Mariya Boyko, Math Circles Instructor, Department of Mathematics, University of Toronto:
Soviet Mathematics Education Reforms of the 1970's
and Their Aftermath
During the 1960's Soviet government initiated major education reform in USSR. Professor of Mathematics at the Moscow State University Andrei Kolmogorov got appointed as the head of the mathematics committee of the Scientific Methodological Council and got heavily involved in restructuring the current mathematics curriculum.He aimed to merge the rigorous and non-rigorous ways of mathematical thinking in the minds of the students.Kolmogorov introduced a collection of pedagogical innovations and emphasized the set theory, deductive logical approach, and pre-calculus in the new curriculum. These changes in the curriculum were influenced by trends in modern mathematical research, such as the emphasis on rigorous and deductive logical approach, as well as, social and ideological tendencies that prevailed in the Soviet society, such as the rise of the Socialist Competition.Soon, however, the community of mathematics educators discovered various shortcomings in the new curriculum, and the decision to conduct counter-reforms were made.We will discuss the intellectual, political and ideological factors that shaped the development of the new Soviet mathematics curriculum, analyze the legacy of the reforms, and explore the reasons for the decline of the reforms.
November, 15, 2018, Professor Emeritus John Dawson,
Pennsylvania State University, York:
Formal Logic
For centuries mathematics has been regarded as the exemplar of rigorous deductive reasoning.Yet for much of its history it has been, and few universities today require mathematics graduates to have had a course in formal logic. To what extent then have results in formal logic actually affected mathematical practice? And what accounts for popular impression that deductive logic is central to mathematical practice?"
October, 11, 2018, Adrian Rice, Professor of Mathematics,
Randolph-Macon College:
Ada Lovelace: The Making of a Computer Scientist
Ada Lovelace is widely regarded as an early pioneer of computer science, due to an 1843 paper about Charles Babbage's Analytical Engine, which, had it been built, would have been a general-purpose computer.Her paper contains an account of the principles of the machine, along with a table often described as 'the first computer program'. However, over the years, there has been considerable disagreement among scholars as to her mathematical proficiency, with opinions ranging from 'genius' to 'charlatan'. This talk presents an analysis of Lovelace's extant mathematical writings and will attempt to convey a more nuanced assessment of her mathematical abilities than has hitherto been the case.
September 20, 2018, Chris Rorres, Professor Emeritus, Drexel University:
The Cattle of the Sun: From Babylonia to Homer to Archimedes
One of the oldest and best known mathematical
puzzles is Archimedes Cattle Problem, which was not completely
solved until 1965. In this talk I will present the long history of
this problem and its influence on number theory, especially on the
Pell Equation. I will also be presenting my own thoughts on this
problem together with some materials that I recently came across.
[article
website] [Rorres
website]
April 19, 2018, John Botzum of Kutztown University of
Pennsylvania:
The Phi-bonacci Sequence
Sometimes innocent questions from students can stir long-forgotten memories and stimulate mathematical investigation.Last year I took over my wife's Discrete Mathematics course for a week.I spent much of the first class working out elementary induction proofs and introducing recurrence relations.At the end of the class, one of the students asked if there was a recurrence relation for the nth term of the Fibonacci sequence.I was in a hurry to teach a class 45 minutes away, so I foolishly replied that I did not think there was.On the drive to my other job, I recalled Binet's formula which prompted me to dig up notes on this subject that I had long since forgotten.This paper will discuss my discovery and re-discovery of the beautiful interplay between Binet's recurrence relation, the Golden Mean, and the Fibonnacci Sequence, as well as, discuss whether Binet was the first to discover the formula.
March 15, 2018 Christopher J. Phillips , Carnegie Mellon University:
The New Math and Mid-Century American Politics
The new math changed the way Americans think about mathematics. The mathematicians and teachers who designed the new math—a novel curriculum lavishly supported by the National Science Foundation in the 1950s and 1960s—believed they were doing more than improving computational ability or producing more mathematicians. The new math embodied a plan to reform American society by revolutionizing the way schoolchildren learned to think. Forged in the crucible of Cold War fears of intellectual inadequacy, deployed in the heyday of the liberal Great Society, and criticized by ascendant conservatives in the 1970s, the new math was fundamentally political. Debates about the math curriculum were debates about how to shape American citizens.
January 18, 2018 V. Fred Rickey, Professor Emeritus, West Point Military Academy:
Professor Bolesław Sobociński and Logic at Notre Dame
Bolesław Sobociński (1906–1980) received his Ph.D. in 1938 under the direction of Jan Łukasiewicz (1878–1960) and then served as assistant to Stanisław Leśniewski (1886–1939). This close contact with the two founders of the Warsaw School of Logic determined the course of his research. He played an important role in the Polish underground during WW II, escaped to Brussels where he worked for several years and then emigrated to the US. After a few years in St. Paul, MN, he joined the faculty at the University of Notre Dame. He founded the Notre Dame Journal of Formal Logic and edited it for 19 years. We will discuss his interesting life and make some remarks about his contributions to logic.
December 14, 2017 Peter Freyd, University of Pennsylvania:
The Stable Marriage Problem
In 2012 the Nobel memorial prize ( for "economics") was awarded to Lloyd Shapley for work on the "stable marriage problem," specifically for the 1962 paper with David Gale "College Admissions and the Stability of Marriage" published in -- of all places -- the MAA Monthly and I'm sure that Gale would have shared the prize if he had been alive. The paper was intended to be -- mostly -- a nice example of mathematics about something other than numbers or geometry. In 1961 Gale and I were both at Brown University for a good part of the summer and my talk will be more of an "oral history" than anything scholarly. But it is a tale I think worth telling.
November 16, 2017 Lindsay Roberts , Prince George’s Community College:
An Antebellum Algebra Textbook: Proofs, Algorithms, and Slavery
In 1857 Daniel Harvey Hill, a professor at Davidson College in North Carolina, published a textbook titled Elements of Algebra, aimed at the college market. A twenty-first century mathematical reader will find in Hill’s book features both familiar and unfamiliar, and will gain insight into the state of the field at the time. Hill is comfortable with well-defined algorithms and symbol manipulation, but he flubs a proof involving the fundamental properties of prime numbers, and he treats imaginary numbers with trepidation. Hill, an ardent southern loyalist who would later serve as a general in the Confederate army, also spices his book with anti-Yankee sentiments and unapologetic references to slavery. This talk will touch on both the mathematical and ideological aspects of Hill’s book, comparing it with some similar books of roughly the same time period.
October 19, 2017 Laura Turner, Monmouth University:
E.V. Huntington's Postulates for the Real Numbers: a Preliminary
Report
In this talk, we consider five texts written by the Harvard mathematician Edward V. Huntington (1874-1952) and attempt to pin down particular mathematical values informing and exemplified within his work. In these texts, published in the first years of the 20th century, Huntington presents a number of different sets of postulates defining the algebra of real quantities and the underlying linear continuum. As we will see, these postulate sets, which initially demonstrate striking parsimony, ultimately reveal a pedagogically-informed classical, analytical perspective, expressed in the logical formulation characteristic of the the modernist transformation of mathematics that took place in the late 19th and early 20th centuries.
September 21, 2017 Marina Vulis, Norwalk Community College and CUNY
The Saint Petersburg Academy of Sciences and Mathematics in the 18th-19th Century Russia
Peter the Great established the Saint Petersburg Academy of Sciences in 1724, and after its first meeting in August of 1725 the Academy quickly became the center of scientific research in Russia. Mathematics education at the University and Gymnasium part of the Academy became vital for preparing research mathematicians and mathematics teachers. Of course, the name of the Academy immediately brings to mind Leonhard Euler; we however will focus on the other mathematicians who made important contributions to mathematics. Our discussion will also include the original papers from the Academy Archives on Vasievskij Ostrov.
April 20, 2017 Amy Ackerberg-Hastings:
John Playfair and His Misnamed Axiom
The term "Playfair's Axiom" is a mainstay of school geometry textbooks as well as one of the few things many mathematicians know about John Playfair (1748–1819), Professor of Mathematics and then of Natural Philosophy at the University of Edinburgh. However, the ubiquity of the phrase masks considerable historical complexity. At least three different versions of the statement circulate among speakers of English—only two of which appeared in the editions of Playfair's Elements of Geometry—while the underlying concept dates back to Proclus. Additionally, the versions are not logically equivalent with each other. I will discuss recent research that has revealed new information about when and why "Playfair's Axiom" became commonplace as a label.
March 16, 2017 Erich H. Reck, University of California, Riverside:
Dedekind and the Structuralist Transformation of Mathematics
In recent history and philosophy of mathematics, “structuralism" has become an important theme. There are two different ways in which this theme is typically approached: (a) by focusing on a structuralist methodology for mathematics (concerning the tools used, the ways in which various parts of mathematics are organized, etc.); (b) in terms of a structuralist semantics for mathematics (a conception, or several related conceptions, of what we talk about when we study “the natural numbers”, “the real numbers”, “the cyclic group with five elements", etc.). In this talk, I will show that Richard Dedekind’s writings from the nineteenth century should be seen as one of the main historical sources for both strands. Moreover, the two strands are intimately connected for him, as I will also try to establish. This will involve comparing his foundational work (on the natural and real numbers) with his contributions to algebra and number theory (his investigation of the notions of algebraic number, group, field, ring, lattice, etc., including his famous theory of ideals). Dedekind built on the work of his teachers and mentors, to be sure, especially Gauss, Dirichlet, and Riemann. But he went significantly beyond them precisely by initiating a structuralist transformation of modern mathematics, one that was later continued by Hilbert, Noether, Bourbaki, and in category theory. Some of the contents of this talk appeared in Professor Reck’s article “Dedekind’s Contributions to the Foundations of Mathematics” in the Stanford Encyclopedia of Philosophy.
February 16, 2017 Shelley Costa, Swarthmore College and West Chester University:September 15, 2016 Fred Rickey, Professor Emeritus, West Point Military Academy:
E228
How's that for the shortest title ever? How can you decide if a number is the sum of two squares? Euler begins with the dumbest possible algorithm you can think of: Take the number, subtract a square, and check if the remainder is a square. If not, repeat, repeat, repeat. But Euler, being Euler, finds a way of converting all those subtractions into additions. He applies this to 1,000,009, and---in less than a page---finds that there are two ways to express this as a sum of squares. Hence, by earlier work in E228, it is not a prime. Amusingly, when he later described how to prepare a table of primes ``ad millionem et ultra'' (E467), he includes this number as prime. So he then feels obliged to write another paper, E699, using another refinement of his method, to show that 1,000,009 is not prime.
February 18, 2016 Lawrence D’Antonio, Ramapo College:
When Mathematicians were Rock Stars: the Academies
of Science in the 18th Century
During the Enlightenment, the university was not the primary center of intellectual activity. Instead, the major institutions for mathematics and natural philosophy were the Academies of Science. The Paris, Berlin, St. Petersburg Academies of Science and the Royal Society of London sponsored research, gave academy members opportunities to present their research in oral and written form, and encouraged communication among the prominent scholars during the Enlightenment. The duty of the scientific academies was to drive out superstition and ignorance by establishing secure knowledge, of which mathematics is the most perfect model. Mathematicians played central roles, both intellectual and political, in these Academies.
January 21, 2016 Chris Rorres, Drexel University:
The Law of the Lever: Archimedes vs. Mach
Over a century ago Ernst Mach, the famous Austrian physicist and philosopher of science, wrote a blistering criticism of Archimedes' celebrated proof of the Law of the Lever. Mach accused Archimedes of overusing his "Grecian mania for demonstration" and succeeding in his proof only "by the help of the very proposition he sought to prove". His attack drew the expected objections from many historians and philosophers of science who, in turn, accused Mach of not understanding the subtleties of Archimedes' proof. I will give my own interpretation of this controversy from a mathematician’s point of view, concluding with my belief that, while Archimedes did indeed prove something, it can hardly be called a proof of the Law of the Lever.
[article
website] [Rorres
website]
In 1646 the 17-year-old Christiaan Huygens proved that the hanging chain did not take the shape of a parabola, as was commonly thought at the time. Forty-four years later, no one had yet described the actual shape of the chain, so Jakob Bernoulli posed the problem publicly in 1690. Huygens then studied several aspects of this curve, which he called the catenary, and published them in a short article one year later. We will quickly review the earlier work of Huygens and concentrate on the work from his notebooks in 1691. This talk is a continuation of the story begun at PASHoM in April 2009, although attendance at that talk is not a prerequisite for this one.
October 5, 2015 (Monday!) Robin Wilson, Open University, UK:
A Century of Graph Theory
This talk covers the period from around 1890, when graph theory was mainly a collection of isolated results, to the 1990s when it had become part of mainstream mathematics. Among many other topics it includes material on the four-colour problem, trees, graph structure, and graph algorithms. No particular knowledge of graph theory is assumed.
March 19, 2015: Robert Naugle, Shepherd University:
Archimedes, Codex C, "The Method of Mechanical Theorem" : Controversy
The only extant copy of "The Method of Mechanical Theorems" in the original Greek has been known to exist in Codex C since Johan Ludvig Heiberg (1854-1928) examined it at the turn of the 20th Century. Heiberg succeeded in deciphering most of its contents using light, a magnifying glass and a camera. Proposition 14, determining the planar cut of a cylinder encased in a cube, a "hoof", had a large gap hidden from Heiberg in the gutter of Codex C. Heiberg wrote in Latin that "I shall not speculate as to what could have been written in such a large gap." This gap was exposed by unbinding and modern imaging during the recovery of the Archimedes palimpset after its sale to a private buyer in 1998. Dr. Reviel Netz, a Classics scholar at Stanford who is fluent in the Doric dialect of Archimedes and who was at the time completing an extensive translation and commentary of Archimedes mathematics was called in to consult after the codex was unbound. Dr. Netz subsequently claimed that information hidden in the gutter of Codex C suggests that Archimedes had considered a 19th century concept of infinity (actual, completed infinity) in Proposition 14 of The Method. We will use this as motivation for examining The Method through Proposition 1 in which Archimedes shows Eratosthenes his heuristic method of realizing that the area of a circumscribing parabola is 4/3 that of the triangle it encloses and move to Proposition 14, show the rudiments of The Method applied again and the Doric Greek hidden in the gutter that led Netz to make his claim.
February 19, 2015, Robert Bradley, Adelphi University:
L’Hôpital’s Synthesis of Calculus and Geometry
Guillaume François Antoine, the Marquis de l’Hôpital, wrote the first differential calculus textbook, which he published in 1696. Leibniz’ calculus, which the Marquis had learned from Johann Bernoulli, was at this time a calculus of algebraic functions only. Nevertheless, by combining the techniques of the new calculus with methods of Euclidean geometry, Leibniz and the Bernoullis were able to investigate the properties of wide a variety of transcendental curves, including the cycloid, the quadratrix, and various spirals. Through his groundbreaking textbook, the Marquis de l’Hôpital shared these new methods with the French mathematical community. In this talk, I will describe l’Hôpital’s calculus, providing a variety of examples drawn from my forthcoming translation of Analyse des infiniment petits, a joint project with Sal Petrilli and Ed Sandifer.
January 22, 2015, William Noel, University of Pennsylvania:
EUREKA! The Archimedes Palimpsest
The Archimedes Palimpsest, a 10th century manuscript, is the unique source for two of Archimedes treatises, The Method and Stomachion, and it is the unique source for the Greek text of ON Floating Bodies. All these texts were erased in the thirteenth century, and written over. In private hands throughout much of the 20th century, the manuscript was sold at auction to a private collector in 1998, and subsequently deposited at The Walters Art Museum in Baltimore, Maryland by the owner a few months later. Since that date the manuscript has been the subject of conservation, imaging, and scholarship. Entirely new texts from the ancient world have been discovered, and transcribed, using many different imaging techniques, including X ray flourescence imaging at SLAC. This lecture will describe the history of the Palimpsest, its imaging, and the recent discoveries.
December 4, 2014, Stephanie Dick, Junior Fellow Harvard Society of Fellows, Harvard University:
After Math: Following Mathemetics into the Digital
Age
The advent of modern digital computing in the mid-twentieth century precipitated many transformations in the practices of mathematical knowledge production. However, early computing practitioners throughout the United States subscribed to complicated and conflicting visions of just how much the computer could contribute to mathematics - each suggesting a different division of mathematical labor between humans and computers and a hierarchization of the tasks involved. Some imagined computers as mere plodding "slaves" who would take over tedious and mechanical elements of mathemtical research. Others imagined them more generously as "mentors" or "collaborators" that could offer novel insight and direction to human mathematicians. Still others believed that computers would eventually become autonomous agents of mathematical reasearch. And computing communities did not simply narrativize the potential of the computer differently; they also built those different visions right in to computer programs that enabled new ways of doing mathematics with computers. With a focus on communities based in the United States in the second half of the twentieth century, this talk will explore different visions of the computer as a mathematical agent, the software that was crafted to animate those imaginings, and the communities and practices of mathematical knowledge-making that emerged in tandem.
November 20, 2014, Shelley Costa, Swarthmore College:
The Ladies' Diary: Society, Gender and Mathematics in early 18th-c. England
Some of you may be familiar with my work on the Ladies' Diary, an 18th- and 19th-c. British annual periodical that contained advanced mathematical problems (see esp. Osiris, 2002). Most of the research contained in my PhD dissertation (Cornell Univ., 2000) has remained unpublished. In this talk I will outline the historical perspectives that informed my approach to this material and report on my present experience of newly revising it for publication nearly 15 years on. From Anne’s reign to Victoria’s, the Ladies’ Diary or Woman’s Almanack hosted an annual mathematical exchange among an enthusiastic readership of men and women. In the dissertation I analyze the social structures that shaped the Diary’s first fifty years, including a feverishly consumerist print culture, genteel expectations of femininity, and the mathematization of early industrial technology.
October 23, 2014, Victor Katz, University of District of Columbia
retired (author of "A History of Mathematics, An Introduction"):
Recreational Problems in Medieval Mathematics
Recreational problems have been a fixture in mathematics problem solving from antiquity. it has long been known that the same problems reappear in cultures all over the world - from ancient Egypt and Babylonia through Greece, medieval China and India, and on into medieval Europe and the Renaissance, as well as into modern times. What is surprising, perhaps, is that often the exact same problems reappear, even with the same numerical values, in cultures separated by many years and many miles. We frequently have no idea of the paths these problems took in moving from civilization to civilization. In this talk, we will look at some appearances of two of these classic recreational problem types and see how different people at different times solved them. Perhaps we can also gain some insight into the methods of travel of these problems.
September 18, 2014, Peggy Kidwell, Smithsonian Institute:
Handheld Electronic Calculators Enter American Life
This talk explores the history of the handheld electronic calculator in American culture, as suggested by an ongoing examination of surviving examples in the collections of the Smithsonian Institution. During the first half of the 1970s, with the advent of inexpensive microprocessors, the electronic calculator became a commonplace. Arithmetic, which had been regarded by nineteenth century mathematicians such as Frederick P. Barnard of Columbia University as "toil of pure intelligence," could be performed routinely by instruments that cost only a few dollars. In the 1980s, with the advent of programming graphing caluclators, the new technology attracted the attention of college and university mathematics teachers, and inspired discussions of curriculum reform.
April 24, 2014, Shelley Costa, Swarthmore College, West Chester University:
Theory of Differences: How and why the most famous science
writer in 19th-century England could not get her mathematical
textbook published
Mary Fairfax Somerville's writings on mathematics and science made her a household name in Victorian England. Her most well-known work was Mechanism of the Heavens (1831), a highly valued exposition of Laplace. While most of her titles were popular expositions, her book on Physical Geography was used as a standard textbook until the 20th century. Her publisher treated her with great deference and her influential writings led her to receive an annual pension from the British government from 1835 until her death in 1872. Yet Mary Somerville could not get her favorite project, a mathematical textbook on the calculus of variations, published. Why??? In answering this question, I will explore the concept of originality in mathematics (and in publishing), and how class and gender might have played a role. The talk will summarize my research on the manuscript and the correspondence between her and her publisher, and how I was led to this topic as part of researching a project currently under contract with Johns Hopkins University Press: The Material of Intellect: A Historical Sourcebook on Women and Mathematics, 1500-1900.
March 20, 2014. V Frederick Rickey, The United States Military Academy at West Point:
Washington and Mathematics
There are many interesting things in the cyphering books that George Washington compiled as a teenager: His study of decimal arithmetic is straightforward, but understanding some of the errors he made can be fun. He had a technique for partitioning a plot of land into two equal pieces, bit it was wrong---and so was his source. Some things are hard to understand for time has passed them by. For example, his pre-Eulerian trigonometry is a mystery today, so we shall elucidate it. We shall present some pages of the cyphering books that the Library of Congress did not digitize because they were at Cornell, Dartmouth and the Historical Society of Pennsylvania.
February 20, 2014. Paul Wolfson, West Chester University:
Planetary Orbits and the Calculus Controversy
The conflict between the Newtonians and the Leibnizians is often portrayed as a dispute over priority for the invention of the calculus. It was that, but it was much more, since the participants differed on matters of substance concerning theology, natural philosophy, and mathematics. The first and second editions of Newton’s Principia were published during this protracted conflict. By examining a few propositions about orbits and some continental reactions to them we can infer some of the differences between the two schools concerning mathematical methods and values.
January 23, 2014 Nicholas Scoville, Ursinus College:
Topology and its History: Must There Be a Separation?
A first course in point-set topology tends to not only be divorced from history, but also divorced from any other branch of mathematics in the minds of many students. This makes continued motivation of new topological concepts difficult. In contrast, the historical development of certain concepts provides automatic motivation and places the concept in its larger mathematical context. In this talk, we will outline a preliminary list of topics which trace the evolution of connectedness. Beginning with Cantor and a problem of Fourier series, we investigate the contributions of Jordan and Schoenflies, culminating in the current definition first given by Lennes. We share pedagogical suggestions to connect the thought of these mathematicians to build a coherent narrative which teaches some of the main properties of connectedness through part of its historical development.
December 12, 2013. Amy Ackerberg-Hastings, Smithsonian Institute:
Themes Observed and Lessons Learned in the NMAH Mathematics Collections
For over a decade, the Smithsonian Institution has gradually been digitizing catalog records for its 137 million objects and making them available to the public viahttp://collections.si.edu. More recently, staff members at the Smithsonian's National Museum of American History (NMAH) have been organizing object records into groups and posting them as mini-exhibits at http://americanhistory.si.edu/collections/object-groups. Thanks to the generosity of slide rule collectors Ed and Diane Straker, I have been able to assist with both efforts for the past 27 months. This talk will provide a tour of the resources available on these websites, particularly as they relate to mathematics. Since my appointment is winding down, I will also utilize this opportunity to reflect on how we might better understand the history of mathematics by looking closely at object groups. These groups include slide rules, planimeters, sectors, protractors, dividers and drawing compasses, scale rules, parallel rules, and sets of drawing instruments—in all, over 650 objects and related documentation from the NMAH mathematics collections. [This is a completely different talk from my presentation at the AMS Eastern Section Meeting at Temple University in October.]
November 21, 2013. David Leep, University of Kentucky, Lexington **
October 10, 2013. David Zitarelli, Temple University **
September 19, 2013. Peggy Kidwell, Smithsonian Institute:
Toys for Drawing Figures: The Polygraph to the Spirograph
From the late nineteenth century, Americans have made and sold special forms of drawing instruments for recreational use. Drawing instruments – unlike playing cards, tangrams, the fifteen puzzle and dissections – were initially made as useful tools for architects, navigators, engineers and craftsmen. A few manufacturers offered special designs for entertainment. Mathematicians and mathematics educators occasionally took an interest in these toys, both as inspiration for research and as classroom novelties. Instruments for drawing geometric figures, sold as the polygraph, the Wondergraph, the Hoot Nanny, and, most successfully, the Spirograph, merit particular attention. Versions of the pantograph, a machine for enlarging and reducing figures, also deserve brief mention.
April 18, 2013. David Lindsay Roberts, Prince George's Community College **
March 14, 2013. Tom Drucker, University of Wisconsin, Whitewater **
February 14, 2013 Chris Rorres:
Correcting an Error in Book I of Archimedes' "On Floating Bodies"
Archimedes is credited with quantifying the concept of the center of gravity of an object and in his works he determined the locations of the centers of gravity of many planar and solid bodies. His calculations, however, implicitly assumed that the body was immersed in a uniform gravitational field, so he was actually determining the location of the body's center of mass (or centroid). He did not realize that the concept of a center of gravity is not applicable in a nonuniform gravitational field, a fact that many are not aware of even today. This led to his incorrectly proving an erroneous theorem at the end of Book 1 of his work "On Floating
Bodies". His theorem states that a truncated sphere floating in a body of water on a spherical earth that attracts objects to its center will float stably with its base horizontally under very general conditions. I'll discuss his error and suggest an alternate
proof of a similar correct result.
[article
website] [Rorres website]
January 17, 2013. William Huber, Haverford College **
December 13, 2012. Steve Weintraub, Lehigh University **
November 15, 2012. Amy Shell-Gellasch, Hood College **
October 25, 2012 William Dunham, Muhlenberg College :
Heron, Newton, Euler, and Barney
Heron's formula, giving the area of a triangle in terms of the lengths of its sides, is one of the great, peculiar results of plane geometry. It is thus to be expected that, over the years, there have been multiple demonstrations of this remarkable formula. Here, I consider four such proofs. Heron's original was a clever if convoluted exercise in Euclidean geometry. Centuries later, Isaac Newton gave a demonstration whose heavy lifting was done by algebra rather than geometry. Leonhard Euler’s proof was geometric and exhibited his characteristic flair. Then in 1990 Barney Oliver, a former recipient of the National Medal of Science, shared with me an elegant trigonometric argument where the symmetry of the formula was mirrored by the symmetry of the proof itself. The first two of these – Heron’s and Newton’s – I’ll mention only briefly. The second pair – Euler’s and Barney’s – I'll prove in detail. Taken together, these should remind us why the history of our discipline is such a fine source for wonderful mathematics.
September 20, 2012. David Richeson, Dickinson College **
April 19, 2012 Francine F. Abeles, Kean University:
Hypotheticals, Conditionals, and Implication in Nineteenth Century Britain
Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different.and their tie to implication unclear. In this paper, I will explore the views of four prominent British logicians of the period, W. E. Johnson, J.N. Keynes, H. MacColl, and J. Venn on these issues.
March 22, 2012 Robert E. Bradley, Adelphi University:
The Origins and Contents of de l’Hôpital’s Analyse
Guillaume François Antoine de l’Hôpital’s Analyse des infiniment petits (1696) was the first ever calculus textbook. It was also something of an enigma. For one thing, it was published anonymously, although de L’Hôpital’s authorship was no secret. Also, it made no mention of the integral calculus: instead, its introduction to the differential calculus was followed by what can only be described as an advanced text on differential geometry, motivated by what were then cutting-edge problems in mechanics and optics. However, the oddest aspect of this book is its genesis. The introductory chapters were based on Johann Bernoulli’s Lectiones de calculo differentialium, lessons that only ever existed in manuscript form and were unknown to the scholarly community until 1921. De l’Hôpital received his copy when he hired Bernoulli to tutor him in 1691-92. Subsequently, he “purchased” the advanced material of the later chapters, in an arrangement under which he supported Bernoulli with a stipend in 1694-95. In this talk, we will consider both the mathematics that was presented in the Analyse and the process by which in came into being. We will compare de l’Hôpital’s exposition of the elements of the differential calculus with that of Bernoulli and examine some of the more advanced results presented in the Analyse.
February 16, 2012 Marina Vulis , Fordham University:
Tales of Nineteenth Century Russian Mathematics
The Moscow Mathematical Society, which grew out of a math circle, had its first meeting on September 27, 1864. It was founded with the purpose of promoting mathematical sciences in Russia. In few years, it started the publication of the “Mathematichekij Sbornik,” the first Russian Mathematics Journal. The Moscow Society reflected the philosophy of the Moscow School of Mathematics which rejected the importance of applied mathematics and emphasized mysticism and spirituality, whereas the St. Petersburg School of Mathematics, influenced by the French school, saw the importance of practical applications in development of mathematical ideas.
January 19, 2012. Thomas L. Bartlow, Villanova University:
A Tentative Look at American Postulate Theory
American postulate theory is the body of work of several American mathematicians in the first few decades of the twentieth century, concerned with studying the structure of established mathematical theories by examining fundamental assumptions. They examined alternative postulational formulations and considered desirable features of a postulate system: consistency, independence, completeness, categoricity, brevity. John Corcoran, “On Definitional Equivalence and Related Topics,” History of Symbolic Logic 1 (1980), 231—234, introduced the term “American postulate theory,” identified some of its practitioners and suggested a need for historical study of their work. Michael Scanlan “Who Were the American Postulate Theorists?,” The Journal of Symbolic Logic 56 (1991), 981—1002 and “American Postulate Theorists and Alfred Tarski,”History and Philosophy of Logic 24 (2003), 307-325 identified others, compared two American postulate theorists to European contemporaries, and analyzed their influence on mathematical logicians. I will undertake a broader review, attempting at least partial answers to the following questions: Who contributed to American Postulate Theory? What were the characteristics of their research? Who or what influenced them? Were there mutual influences or rivalries among them? What influence did they have on other lines of mathematical research? Did a theory of postulation develop?
December 8, 2011 Brittany
Shields of the University of Pennsylvania:
The Architecture of Mathematical Institutes: A Comparative Study of
Göttingen and NYU’s Mathematical Institutes under the Leadership of
Richard Courant
In this study of the cultural history of mathematics, I consider the architecture of mathematical institutes as historical artifacts. The buildings in which mathematical research and teaching take place offer incredible insight into the work practices, as well as social and cultural identities, of the mathematicians who inhabit these spaces. As a case study, I consider the career of the mathematician Richard Courant (1888-1972), who served as director during the construction of two world-class mathematical institutes – the first, in the late 1920s at the University of Göttingen (where he was exiled in 1933), and then in the 1960s at New York University. In both cases, I consider the buildings’ planning, development, construction, and habitation processes, examining blueprints, committee meeting minutes, and correspondence between the mathematicians, university administrators, government officials and philanthropy representatives. Ultimately, I hope to explore how the built environment mattered to those whose work required a certain type of private workspace, desk, and chalkboard –situated in the right relationship to shared workspaces, a mathematics library, classrooms, and other scientific departments. What can the physical environment of mathematical institutes tell the historian about the work practices and social identities of mathematicians?
November 17, 2011 Chris Rorres, University of
Pennsylvania:
The Turn of the Screw: The History and Optimal Design of an
Archimedes Screw
The Archimedes Screw is one of the
oldest machines still in use today. It is now enjoying renewed
popularity because of its proven trouble-free design, its ability to
lift wastewater and debris-laden water effectively, and its gentle
treatment of aquatic life. Within the last decade it has also found
a new application in the generation of electricity by being run
backwards. In this presentation I will give a history of this device
from Archimedes' time (3rd century BC) to the present day and also
discuss my past and proposed research on the design of the Screw
that maximizes the amount of water lifted or lowered in each turn of
the screw.
[article
website] [Rorres
website]
October 20, 2011 Patricia Allaire, Queensborough Community College,
City University of New York:
Yours truly, D. F. Gregory
Duncan F. Gregory (1813-1844) was a proponent of the Calculus of
Operations and a founding editor of the Cambridge Mathematical
Journal. Extant is a series of six letters that Gregory
wrote to a friend in 1839. This correspondence provides a
glimpse into life at early-Victorian Cambridge, reveals something of
the character of Gregory and his dedication to the CMJ, and
shows some of the mathematical problems he pondered.In this
talk, we will look briefly at Cambridge, Gregory and the CMJ,
and will examine several of the problems.
September 15, 2011
V. Frederick Rickey,
United States Military Academy:
Polish Logic from Warsaw to Dublin: The Life and Work of Jan
Lukasiewicz
A few years after earning his Ph.D. in
Lwow under Twardowski, Jan Lukasiewicz (1878-1956) joined the
faculty of the newly reopened University of Warsaw where he became,
along with Lesniewski and his student Tarski, one of the founders of
the Warsaw School of Logic. He did seminal research in many-valued
logics, propositional calculi, modal logic, and the history of
logic, especially concerning Aristotle's syllogistic. He left Warsaw
toward the end of World War II and found a new home at the Royal
Irish Academy in Dublin where he continued his creative work.
April 14, 2011
David Zitarelli,Temple University:
David Hilbert's American Colony
No, David Hilbert never crossed the Atlantic. Yet at Gottingen he produced an outstanding cadre of American doctoral students who played important roles in the development of mathematics in the U.S. during the first half of the twentieth century. In this talk we describe the life and careers of those mathematicians who obtained doctorates under Hilbert 1899-1910, emphasizing the critical role they played in what was then the southwestern part of the country, particularly at the University of Missouri. We end by comparing the schools of American students produced by Felix Klein, Sophus Lie, and David Hilbert<
March 17,
2011 Florence Fasanelli, American Association for the Advancement of
Science:
Andrew Ellicott: Surveyor, Town Planner, Mentor, Teacher
Since ancient times conquerors have sent mathematicians out to survey what has been taken. Andrew Ellicott (1754-1820), surveyor and mathematician, had a profound impact on the shape of this country (and opined about what had been taken), establishing boundaries of states and cities as well as its international boundaries both north and south. In 1785 he set the boundary of western Pennsylvania and in 1791 surveyed the territory now known as the District of Columbia which was my first motivation in studying Ellicott. In 1796, he surveyed the international border between the U.S. and Spanish territories in Florida under the San Lorenzo Treaty. In 1817, he was appointed astronomer for the United States establishing the boundary between the US and Canada concluding the War of 1812. As a teacher his most famous student was Meriwether Lewis (a second motivation) who needed field instruction before Lewis and Clark's great expedition to the west. In 1813, he was appointed by President Monroe as a professor of mathematics at the Military Academy at West Point where he was among the first in the country who taught a class in calculus (a third motivation). I will speak somewhat briefly about each of these events.
February 17, 2011 Alan Gluchoff, Villanova
University:
Status (“Respect”) in
Mathematics: The Case of Nomography
Nomography can be defined as the study and preparation of graphical representations of mathematical equations. These representations usually take the form of charts or diagrams from which the values of certain variables in the relation can be read once others have been given. The subject has a history which goes back several centuries and is closely tied with engineering applications. It was organized as a body of knowledge by Maurice d’Ocagne, a French engineer, at the turn of the twentieth century. Nomography then spread to other countries, including America, in later years, where it became of use to engineers and scientists, and of interest to mathematicians. From an American Nomography text of 1947 used at MIT comes the following quote: “The theory of the nomgraphic chart cannot be dismissed as a simple topic. Mathematicians who do so are unaware that a complete treatment of the subject draws on every aspect of analytic, descriptive, and projective geometries, the several fields of algebra, and other mathematical fields. This suggests a conflict over the status of nomography as a mathematical area: how deep is the mathematics of this subject? Is it more than just a set of techniques for drawing charts? Can nomography give rise to problems of genuine mathematical interest? We will examine these questions as they presented themselves to American mathematicians of the era 1900-1950 and give examples of the connections between nomography and: elementary properties of determinants, the duality principle of projective geometry, classification problems in elementary algebraic forms, finding roots of real polynomials, simple partial differential equations, cubic curves, and Hilbert’s thirteenth problem (number of examples to be limited by time constraints). An attempt will be made to determine how American mathematicians of this era felt about the mathematical status of nomography.
January 20, 2011 Eugene Bowman , Pennsylvania
State University, Harrisburg:
Benjamin Robins' 'Treatise on Fluxions': An Early Response to
Berkeley
In 1734 Bishop George Berkeley published "The Analyst; or A Discourse Addressed to an Infidel Mathematician," wherein he, quite famously and in some cases correctly, criticized Newton's Doctrine of Fluxions. Maclaurin's 1742 book "The Elements of the Method at Fluxions" is usually taken to be the definitive Newtonian response to Berkeley. But there were earlier attempts to clarify and/or rigorize Newton. One was Benjamin Robins' "Treatise on Fluxions" published only one year after Berkeley. In his introduction Robins explains his purpose , "For though Sir Isaac Newton has very distinctly explained... these subjects... yet as the great author's great brevity has made a more diffusive illustration not altogeher unnecessary; (1) have here endeavored to consider more at large each of these methods; whereby, I hope, it will appear that they have all the accuracy of the strictest mathematical demonstration That is, Robins presents his text as simply " filling in the blanks" left by Newton. I will examine some key theorems/proofs from Robins' text.
December
9, 2010 Paul Wolfson of West
Chester University:
Geometry of Relativistic Velocities
Almost immediately after Einstein published his first paper on relativity in 1905, others reworked some of his arguments in a more geometrical language. Minkowski's was, of course, the broadest and most successful effort, but beginning in 1909, Sommerfeld and Varicak developed a geometric representation of relativistic velocities. In this talk I shall discuss these developments and explain the setting in which Felix Klein unified them.
November 18, 2010 J.
W. Dawson, Pennsylvania State University, York:
The Role of Alternative Proofs in Mathematical Practice
I will consider expanding my article "Why do mathematicians re-prove theorems?" into a book-length study of the roles that new proofs of old theorems play in mathematical practice. I will consider alternative proofs of various well-known theorems (the fundamental theorems of arithmetic and algebra, the infinitude of the primes, the Pythagorean theorem, the law of quadratic reciprocity, the prime number theorem, etc.) and solicit suggestions for further examples to study.
October 21, 2010
Betty Mayfield of Hood College:
Women, Mathematics, Euler
and Undergraduates
What happens when two faculty members and four undergraduates spend the summer researching Women and Mathematics in the Time of Euler? In 2007, my colleague Kimber Tysdal and I did just that. I will describe our experienceand what we learned.
September 16, 2010 Karen Parshall, University of
Virginia:
Algebra: Creating New Mathematical Entities in Victorian Britain
Analytic geometry and mathematical physics may have interested a
majority of mathematicians in Victorian Britain, but algebra also
served to focus their mathematical attention.In the century’s
first half, algebraic work centered on the development of the
so-called “symbolical algebra” and the creation of new algebras,
while in its second, the theory of invariants dominated and the
theory of groups witnessed key developments.Underlying much
of this research was the philosophical question of how free
mathematicians were to create new mathematical entities.The
Victorian British response to that question was ultimately, “quite
April 15, 2010
Alan Gluchoff, Villanova University:
The Introduction and Spread of Nomography in America, 1900-1950
Nomography can be roughly defined as the theory and methods by which numerical evaluation of ordinary functional relations can be accomplished geometrically. (The slide rule is a simple example of one such method.)It was established as a mathematical discipline in 1899 by Maurice d'Ocagne (1862-1938), an accomplished French engineer who synthesized earlier work on this subject. His 1899 volume "Traite de Nomographie" is a systematic development of the construction and use of what came to be called nomograms (variously called charts, alignment diagrams, intersection diagrams, or abaques) for use in computations in diverse engineering disciplines. While the use of nomograms to aid in calculation became widespread in Europe in the following years, the mathematics associated with their construction received attention as well. This resulted in articles in mathematical journals and a mention of the field by Hilbert in connection with problem 13 of his list of 23 problems of 1900. Nomograms have been described by one writer as the "fractals of their day" due to their relation to mathematical law and visual appeal.
This talk attempts to survey how nomography was introduced into the United States in the years following the publication of d'Ocagne's book, looking at its debut in the various communities of mechanical, civil, and electrical engineers, scientists, and mathematicians, with special focus on the latter. During the period from 1900 to 1950 mathematicians such as Frank Morley,E. H. Moore, T. H. Gronwall, O. D. Kellogg, Lester Ford and Edward Kasner concerned themselves with popularizing, extending, and using the ideas of nomography. The subject was taught in colleges and technical institutes, often out of textbooks written by the instructors. It appealed to all types of mathematical people:pure researchers, college professors and high school teachers, and had its enthusiasts among algebraists, geometers and analysts. Nomograms became particularly popular as a graphical method for solving polynomial equations of degree five or less, and found a place in the changing nature of college algebra during this time. We also will mention some mathematical obstacles which occurred as they came into wider use in scientific, engineering and industrial settings.
March18, 2010 Eisso Atzema, University of Maine:
As is well known, there was little concern in Apollonius' Conics
about the actual "mechanical" construction of the conic sections. In
fact, it is not entirely clear whether there ever was an interest in
Classical Antiquity in any tool that would draw a given conic
section in the same way one can draw a circle with the help of a
compass. There certainly was an interest in such a tool among Muslim
mathematicians. In Renaissance Europe, a number of mathematicians
suggested various mechanical ways to construct the conic sections as
well-although no actual drawing devices seem to have been built.
February 18, 2010
Steven
H. Weintraub, Lehigh University:
On Legendre's Work on the Law of Quadratic Reciprocity
As is well-known, Legendre was the
first to state the Law of Quadratic Reciprocity in the form that we
now know it (though an equivalent result had earlier been
conjectured by Euler), and he was able to prove it in some but not
all cases, with the first complete proof being given by Gauss. In
this talk we trace the evolution of Legendre's work on quadratic
reciprocity in his four great works on number theory, from 1785, 1797, 1808, and 1830.
January 21, 2010 Eugene
(Bud) Bowman, Pennsylvania State University, Harrisburg:
Ghosts of Departed Errors: A Look at Bishop Berkeley's The
Analyst and the Scientific Community's Initial
Response to It
In 1734 Bishop Berkeley criticized the logical foundations of the Calculus in The Analyst and set off a small 'pamphlet war'. James Jurin and John Walton replied immediately and angrily. Berkeley then responded to each of them. Shortly after this exchange Jurin and Benjamin Robins engaged in a lengthy and eventually acrimonious public debate on the same topic. Somewhat later Benjamin Robins, Collin Maclaurin, Thomas Simpson and others wrote treatises on "The Method of Fluxions" which were at least in part intended as responses to The Analyst. view of Calculus in its earliest stages. I will attempt to peer through that window.
December 10, 2009 John W. Dawson, Penn State, York:
The Development of the Notion of Compactness in Topology and
Logic
During the early decades of the twentieth century the notion of a
compact topological space arose as a generalization of results
obtained in studies of the topology of the real line (in particular,
the Heine-Borel theorem). Somewhat later, what is now called the
Compactness Theorem for first-order logic was proved by Godel as a
lemma in his proof that every first-order axiom system is
semantically complete. But for years thereafter connections between
the two notions of compactness lay unrecognized and applications of
compactness in logical contexts were not pursued. This talk will
survey how the Compactness Theorem eventually came to be regarded as
a fundamental tool in model theory and algebra, and will explore why
recognition of it's usefulness was so long delayed.
November 19, 2009 Shelly
Costa:
Throwing the Book at Mathematical Talent
In this talk I contrast the careers of late
seventeenth-/mid-eighteenth-century mathematical authors Guillaume
de I' Hôpital
(1661-1704), Emilie du Châtelet
(1706-1749), and Maria Gaetana Agnesi (1718-1799). My basic aim is
to assess the impact of social factors such as class, gender, and
economic status on contemporary perceptions of mathematical talent
and originality. I will recount my recent attempts to do so through
a material approach--that is, through a close inspection of
the physical features of relevant primary sources.
October 15, 2009 Frank Swetz:
Glimpses of Chinese Mathematics
The history of mathematics in traditional China is often clouded
by myth and uncertainty. For the Chinese Empire, mathematics was not
a priority. Mathematicians were not highly honored nor recognized
for their work. They worked in isolation. Social and political
upheavals within the Kingdom were frequent, resulting in the
destruction of books and libraries. In such a climate of turmoil,
efforts at preservation focused on Confucian and philosophical
classics. Scientific works, including those about mathematics were
frequently destroyed and lost. Later mathematicians were forced to
rediscover techniques and concepts established by their
predecessors. Thus, in examining the state and content of
traditional mathematics in China, one must rely on "glimpses. " This
talk will survey some of the accomplishments of traditional Chinese
mathematics and discuss the interaction of societal pressures on the
development of mathematical thinking.
October 8, 2009 Danny Otero,
Xavier University:
Determining the Determinant
Nearly every undergraduate student of mathematics learns how to
solve linear systems with the help of determinants, so it may come
as a surprise that the history of the development of the determinant
is not better known than it is. In fact, there may be a good reason
for this: befitting the complexity of the idea, its history is also
quite complicated. The story of its genesis and evolution involves
the interplay of a number of different problems, perspectives and
approaches, and contributions were made by dozens of people over
centuries. We plan to survey a key period of this history, for the
time of Leibniz at the end of the 17th century, up to the watershed
day of November 30, 1812, when Binet and Cauchy both presented
papers on the determinant at the same meeting in Paris.
Over 30 colleges and universities offered cryptology courses during World War II. There was great diversity in who delivered the classes. Mathematicians were represented, as were the departments of astronomy, biology, classics, English, geology, Greek, philosophy, and psychology. Even a dean managed to make himself useful...Some classes were secret, run for the benefit of the military, while others were open to all. The lecture surveys these courses, along with biosketches of the professors and, in some cases, describes original research contributions they made to the field of cryptology.
April 16, 2009 John Bukowski, Juniata
College:
Christiaan Huygens and the Hanging Chain
In the mid-seventeenth century, it was generally thought that the shape of a hanging chain was a parabola. In a series of letters with Marin Mersenne, the 17-year-old Christiaan Huygens showed that the hanging chain did not in fact take the form of a parabola. We will investigate some of Huygens's geometrical arguments in detail, and we will discuss some of the general history of the problem.
March 19, 2009 Marina Vulis, Independent Scholar:
Russian Mathematics Textbooks
In 1703, Leonty Magnitsky, a mathematics teacher at a Moscow
school, published the book "Arithmetika, i.e. the Science of
Numbers". This was the first Russian mathematics textbook written by
a Russian author.This presentation will discuss the contents
of "Arifmetika" and the story of its publication.
February 19, 2009 Paul Wolfson, West Chester
University:
After Galois, What?
Many accounts of the nineteenth century theory of equations
emphasize the contributions of Abel and Galois and the resulting
shift towards algebra. Nevertheless, some followed other lines
of research. Mathematicians had originally introduced a resolvent
equation as a step towards solving a given equation by radicals.
After Galois' theory became known, mathematicians still studied
resolvent equations, but now with new aims. This talk is the
outgrowth of my attempt understand the background to one of the late
manuscripts of Arthur Cayley that were previously discussed by Dr.
Weintraub.
January 15, 2009 Yibao Xu, Borough of
Manhattan Community College, City University of New York:
Mathematicians and Mathematics in China during the Cultural
Revolution
The Cultural Revolution (1966-1976) was the most destructive
political movement in modern China. During that tumultuous ten-year
period millions died as a direct consequence of political struggles
and tens of millions were dislocated. Higher education was abandoned
for the first five years. Leading experts in virtually all academic
areas were deprived their rights of conducting research of their own
interest. The promise of mathematical research during the first
fifteen years of the newly created Communist China came to a halt,
and then faded away. After briefly describing the status of
mathematical research in Communist China before 1966, the speaker
will provide a setting for the Cultural Revolution by showing a
10-minute documentary film. He will then take two leading Chinese
mathematicians, Wu Wenjun, better known in the West as Wen- tsun Wu,
and Gong Sheng, as examples, to discuss how the Cultural Revolution
affected mathematicians’ personal lives and research. In order to
show how politics and Marxist ideology determined mathematical
research in mainland China during this period, the talk will also
discuss Chinese translations of Karl Marx’s Mathematical Manuscripts
and the nation-wide discussion of the Manuscripts.
December 11, 2008 Thomas L.
Bartlow, Villanova University:
Edward V. Huntington and Engineering Education
Edward V. Huntington is best known as a prototypical American postulate theorist (Michael Scanlon, Who were the American Postulate Theorists?, The Journal of Symbolic Logic 56:3 (Sep 1991), 981--1002) and as the mathematician behind the method of apportioning Representatives among the states (Thomas L. Bartlow, Mathematics and Politics: Edward V. Huntington and the Apportionment of the United States Congress, Proceedings of the Canadian Society for History and Philosophy of Mathematics 19 (2006), 29--54). However, much of his teaching was in the Lawrence Scientific School at Harvard and, in 1907, he became chairman of the Committee on the Teaching of Mathematics to Students of Engineering, a joint committee of the AMS and the AAAS. This led him to become involved in the Society for the Promotion of Engineering Education and to write several papers on mathematics and mechanics in the training of engineers.
November 20, 2008 George M. Rosenstein,
Emeritus Professor of Mathematics, Franklin & Marshall College:
How Did Gibbs Discover the Gibbs Phenomena? A Speculation
Although it is very easy with computers to demonstrate the Gibb's
Phenomena to today's students of Fourier Series, it was not a simple
matter in 1899. I will trace the interesting history leading up to
Gibb's announcement, and then speculate on his discovery.
October 16, 2008 Steven Weintraub,
Lehigh University :
Cayley Documents in Lehigh's Possession
The Lehigh University Library has acquired a set of letters and an
unpublished manuscript by Arthur Cayley. I will report on this
collection and its background, both mathematical and historical.
September 18, 2008 Patricia Kenschaft, Montclair State University:
Minority Mathematicians
A summary of some of the known facts about minority participation
in the mathematical community, including some biographies, some
statistical information, and a report of a survey of black
mathematicians of New Jersey twenty years ago.
To Tom
on his Retirement [from Villanova University]
by
Doug Norton May 13, 2008
The hist’ry of things mathematical
At times can make folks quite fanatical;
But someone we know,
Our own Tom Bartlow,
Instead made a move not so radical:
Along with his bud Zitarelli,
He runs a series that’s quite swell. He,
With grace and aplomb,
Hosts talks at PASHoM
[The
Philadelphia Area Seminar on the History of Mathematics],
And also puts food in your belly
[As usual,
I will provide a light supper, at a cost of $6, or $7, or $8 …].
So now that his teaching he’s leaving,
You Math Hist’ry folks: please, no grieving!
With all that free
time,
He’s still in his
prime:
Math Hist’ry we’ll all keep receiving.
So as you go off in the sunset,
We all know you are not quite done yet:
You’ll make with
Michele
More stories to tell;
We know you’re not through having fun yet!
April 10, 2008 Babak Ashrafi, Executive
Director of the Philadelphia Area Center for History of Science
(PACHS):
Using the Ether to Save Quantum Mechanics
As Max Born fled Germany in 1933, he
started a research project in which he used concepts and methods
from ether theory to reformulate classical electrodynamics in order
to produce a quantum electrodynamics. In this talk, I will describe
the circumstances that led Born to leap backwards in order to try
and leap forwards, what he and his collaborators achieved, and what
this episode tells us about the history of the development of
quantum mechanics.
March 13, 2008
Amy K. Ackerberg-Hastings, University of Maryland University
College:
The Acknowledged National Standard": Charles Davies, A. S. Barnes,
and Textbooks as Teaching Tools
Book historians have added a number of dimensions to our
understanding of texts in the history of science and mathematics,
including how readers and publishers participate alongside authors
in the transmission of knowledge, how patterns of use indicate
intellectual reception, and how textbooks communicate scientific
ideas to popular audiences. However, promotion has been at least as
important a factor as pedagogical and intellectual superiority in
determining which objects have become widely established instruments
for teaching mathematics and science. This talk explores the
evolution of the textbook into a commercialized teaching tool by
concentrating on how the partnership of Charles Davies (1798-1876)
and Alfred Smith Barnes (1817-1888) shaped mathematics instruction
in the United States. Davies parlayed his reputation as a professor
at the United States Military Academy at West Point into a
successful career of defining himself primarily as a producer of
textbooks. Barnes, his publisher, organized the books into graded
series and utilized aggressive marketing techniques. Together, the
men sought to enlarge their audience of American students and laid
claim to national status as the standard for the nascent mathematics
textbook industry. This talk is based upon the first chapter of
Material to Learn: Tools of American Mathematics Teaching, 1800-2000,
a forthcoming book prepared jointly with Peggy Aldrich Kidwell and
David Lindsay Roberts, and will include a few highlights from the
entire volume.
February 21, 2008 Paul Pasles, Villanova University:
Benjamin Franklin's Numbers
Quantitative literacy is a necessity for good citizenship, so it
is appropriate that the "first American" was numerate in the
extreme. That's not to say that Ben Franklin ever proved a novel
theorem, but he was willing to apply basic mathematics to situations
where only qualitative arguments had been admitted previously. This
talk will explore the various mathematical aspects of Franklin’s
life.
January 17, 2008 Alan Gluchoff, Villanova University:
Philip Schwartz, Probable Error, and the Variability of the
Ballistic Trajectory
At the close of World War I those who studied ballistics began to
turn their attention to the "second order effects" - how such
factors as wind, density of air, and small changes in initial
velocity affected the range of a projectile.Related to these
questionsis the matter of the dispersion of a series of shots
fired under as nearly identical conditions as possible, and how one
measures this dispersion. In the United States efforts were made to
introduce standard tools of elementary probability: mean, standard
deviation (actually "probable error") , and normal distribution of
errors, into this milieu, with mixed results.The talk
highlights the attempt of Philip Schwartz, a young artillery officer
with some mathematical background and an associate of Oswald Veblen,
to analyze these concepts as they were used in dealing with the data
of artillery firing.Emphasis is given on how difficult men
found it to understand, defend, and apply these concepts by
viewing a controversy played out in the pages of the Coast Artillery
Journal during the years 1924-1930. No knowledge other than
that of elementary probability and the normal distribution is
required.
December 13, 2007 POSTPONED
November 15, 2007 Maryam Vulis:
Life and Work of Luca Pacioli
We will examine Luca Pacioli’s contributions to mathematics.
The Italian mathematician
Luca Pacioli discussed mathematics with Leonardo Da Vinci, wrote
books on arithmetic, and worked
on chess problems. His long-lost manuscript on chess was recently
discovered in Italy. Pacioli’s
system of double-entry bookkeeping has a group structure and can be
viewed as error-detecting code.
We will also discuss some of the controversy surrounding his work
and publications.
October 18, 2007 Edward Hogan, East Stroudsburg University:
Benjamin Peirce as Head of the Coast Survey
Under Alexander Dallas Bache the United States Coast Survey grew into an important, perhaps the most important, institution for American science. With little graduate work available in the United States, it served as an essential training ground as well as a source of employment for American scientists. When Peirce took over the Coast Survey after Bache’s death, he had no administrative experience. Yet he was able to garner even better congressional support for the Survey than had the politically savvy Bache. Peirce continued to support a broad spectrum of scientific activity. He was also successful in expanding the Survey my making a geodetic link between the existing surveys on the east and west coasts.This was not only a political triumph, but a scientific one.It was the longest arc of a parallel ever surveyed by one country. The extended scope of the Survey led to it being renamed the United States Coast and Geodetic Survey. During his tenure as superintendent of the Coast Survey, Peirce maintained his professorship at Harvard and his residence in Cambridge.He also wrote his Linear Associate Algebra, his most important mathematical work, during this period.
September 20 David Zitarelli and Tom Bartlow
preliminary report on Who Was Miss
Mullikin?
March 15, 2007 Dave Richeson, Dickenson College:
Euler's Polyhedron Formula: a Prehistory of Topology
A
polyhedron with V vertices, E edges, and F faces satisfies the
relation V-E+F=2.
This relationship was first noticed by Euler in 1750 (although a
related formula was known to Descartes in 1630). Euler's proof
turned out to be flawed. From 1750 to 1850 mathematicians tried to
come to grips with this formula. Legendre, Cauchy, Staudt, and
others presented new proofs and generalizations. Meanwhile,
Lhuilier, Hessel, and Poinsot unveiled exotic "counterexamples". In
this talk we present the history of this beloved formula up to the
middle of the nineteenth century, while it was still a theorem about
polyhedra and before it was recognized as a topological theorem.
February 15, 2007
Lawrence
D’Antonio, Ramapo College of New Jersey:
Euler’s Contributions to Diophantine Analysis
In 2007 we celebrate the 300th anniversary of Euler’s birth. Many aspects of Euler’s vast output will be examined during this year. In this talk we will focus on Euler’s research in the field of Diophantine problems. Such problems were a long-term interest of Euler and are still of interest today.We will consider particular highlights from Euler’s work on Diophantine equations, such as Euler’s landmark text Vollständige Anleitung zur Algebra, his work on Fermat’s Last Theorem and the Euler conjecture. This conjecture is related to Fermat’s Last Theorem. Euler had proven the special case that the sum of two cubes is never a cube. He then conjectured that the sum of three fourth-powers is never a fourth-power, the sum of four fifth-powers never a fifth power and so on. Many of the problems considered by Euler fall under the heading of what are now called Euler sums. These are Diophantine equations equating sums of like powers. For example, in a paper from 1754 we see Euler discussing the problem of when the sum of three cubics will equal a cubic. We will examine the subsequent history of research on Euler sums.
January 18, 2007 Jeff Suzuki,Brooklyn College:
The Fundamental Theorem of Algebra, or Why Did Gauss Title
His Dissertation A "New" Proof?
Gauss is usually credited with being the first to prove the fundamental theorem of algebra, but his dissertation is actually titled a "new" proof of the fundamental theorem.We will examine a few pre-Gaussian proofs, and make an argument that Lagrange, not Gauss, was the first to make a truly rigorous proof of the Fundamental Theorem.
December 14, 2006 Paul Wolfson, West Chester University:
Topology Visits Algebraic Invariant Theory
During the 1930’s and 40’s, several mathematicians—notably Stiefel, Whitney, Pontrjagin, and Chern—developed the basic ideas of characteristic classes. These cohomology classes of a bundle over a manifold measure how far that bundle is from being a product. The existence of non-zero classes proved the impossibility of certain embeddings of manifolds. While these results were being found, other results connected the characteristic classes to the curvature of the base manifold. Then, André Weil systematized that connection via classical invariant theory. His unification led to new developments in topology and geometry.
November 26, 2006 Adrian Rice, Randolph-Macon College:
The Life and Legacy of Augustus De Morgan (1806-1871)
De Morgan's Laws are familiar to any mathematician who has taken
an undergraduate course in set theory.
Yet it is ironic that the man afterwhom they were named is
remembered almost exclusively for a set of rules he did not invent
in a subject he would never have known.
But the mathematical legacy of Augustus De Morgan spreads far
wider than his limited fame of today would suggest.
In the last few decades historical research has shed light on
forgotten aspects of De Morgan's work to give us a more complete
picture of the range and diversity of his mathematical activities.
To mark the 200th anniversary of De Morgan's birth, this talk
will examine the influence of these contributions and thus
re-evaluate the impact of his work on the mathematical landscape of
both his time and ours.
October 12, 2006 Ed Sandifer, Western Connecticut State University:
Some Number Theory that Gauss Learned from Euler
**
September 21, 2006 Alexander Soifer, Princeton
University, Department of Mathematics,
Rutgers University, Center
for Discrete Mathematics (DIMACS), University of
Colorado:
Bartel-Shur-Van der Waerden’s Theorem
In 1926 Bartel L. van der Waerden
proved – and in 1927 published – a magnificent theorem:
For any k, l, there is
N = N(k,l) such
that the set of whole rational numbers 1, 2, ..., N,
partitioned into k classes, contains an arithmetic
progression of length l in one of the classes. This result,
which I call (in honor of the authors of the conjecture and the
author of the first proof) Baudet-Schur-Van der Waerden Theorem,
belongs to a few revolutionary, classic results which form “Ramsey
Theory before Ramsey”, and it has awakened my interest in the
life of Van der Waerden. I found the literature about his life
surprisingly contradictory. On the one hand, in the writings of
Günther Frei, Yvonne Dold-Samplonius, W. Peremans, and most recently
Rüdiger Thiele, I found the highest praise of Van der Waerden as a
man of utmost integrity, a hero of the opposition to the Third
Reich. On the other hand, Queen Wilhelmina of the
As a trained problem-solver, I commenced the
search for the real Van der Waerden. Now, 12+ years and many
hundreds of documents later, I can grant my predecessors one thing:
it is hard to understand B. L. van der Waerden. And while a complete
insight is impossible, my research has produced, I believe for the
first time, a comprehensive portrait of Van der Waerden the man. I
would have liked to share with you much of my findings, but it would
take a few days, and thus overstep Tom Bartlow’s hospitality. I will
therefore try to do my best with the time I am given. We will visit
Van der Waerden during his early years, although my main interest
will be the two turbulent decades of his life: 1931-1951.
May 18, 2006 Shelley Costa, Swarthmore College:
Making a Name for Oneself in Professional Mathematics:
Women’s Lives and “Women’s Work” in the 19th Century
The concept of the professional mathematician came
relatively
late to European history.(This truism is expressed in history
of
mathematics code as “Fermat was a lawyer)After the ingenious
dabblers
had had their due, an array of institutions, titles, degrees, prizes
and
professorships secured mathematics as a professional endeavor.
Among its
other consequences, the rise of professional mathematics created a
new set
of formal barriers to women.I will summarize the experiences
of three who
succeeded in the new atmosphere:Sophie Germain, Sofia
Kovalevskaia, and
Alicia Boole Stott.These 19th-century mathematicians came
from different
countries, were of three distinct generations and hailed from
contrasting
economic backgrounds.I am uniting them here not merely to pay
homage to
exceptional talent, luck, and resources, but to highlight
commonalities in
their experiences as women.I wish to pose an important and
difficult
question:What do these women’s experiences tell us about the
construction
of mathematical knowledge?
April 20, 2006 Peter Freyd
Saunders Mac Lane **
March 16, 2006 David Zitarelli,Temple University:
J. B. Reynolds and the Research Mission at Lehigh University
Joseph B. Reynolds (1881-1975) was a student and professor at
Lehigh University from 1903 to 1948.We examine his major
accomplishments in terms of Lehigh's change to a research mission in
the 1920s.Reynolds's exploits include contributions to
engineering as well as pure and applied mathematics.He is
also viewed as an amateur historian, departmental administrator at
Lehigh, and founder of our local EPADEL section.
February 16, 2006 Bill Ewald, University of
Pennsylvania :
Informal Presentation on the State of Hilbert's Papers
and Progress on a Forthcoming Volume of Hilbert's Papers and
Notebooks on Logic in the 1920s **
January 19, 2006 Chris Rorres, University of
Pennsylvania:
If Archimedes Had a Computer: Continuing his Work on Floating Bodies
According to legend, Archimedes ran naked through the streets of
ancient Syracuse shouting "Eureka!" after discovering his famous Law
of Buoyancy, the basic law that determines how things float. He
illustrated this law in his work "On Floating Bodies" by computing
various floating positions of a solid paraboloid. With the geometric
tools of his day Archimedes could only consider those cases when the
flat base of the paraboloid is not cut by the water. However, as I
show using modern computing power, the most interesting things
happen when the base is cut by the water. For example, an iceberg
that is slowly melting can suddenly overturn, or an obelisk
originally sitting on solid ground can come crashing down when the
soil under it liquefies during an earthquake. Such drastic phenomena
are now studied in Catastrophe Theory, a field that Archimedes could
have begun if he had had the computational tools to investigate all
the possible cases of his floating paraboloids.
[article
website] [Rorres
website]
December 8, 2005 Alan Gluchoff, Villanova
University:
The Contributions of Four 'Mathematical People' to the Mathematical
Ballistics of the World War I Era in America
By 1917 the American
mathematical community was quitediverse and stratified,
comprising, among others, word class researchers, university and
college instructors, some applied mathematicians, and students with
Masters and Bachelors degrees who found various uses for their
talents. This work focus on four such "mathematical people," Gilbert
Ames Bliss, Forest Ray Moulton, Roger Sherman Hoar, and Philip
Schwartz, to the "New Ballistics" of the World War I era. Their
efforts included a revision of the approach to calculating
trajectories by the introduction of numerical integration, a tying
of the new methods to the newly emerging research area of functional
analysis, an organization of this mass of material into a coherent,
presentable form with some physical motivation of required formulae,
and a critical and experimental look at the resulting work. These
efforts were characterized by an unusual emphasis on mathematical
rigor which is in some ways analogous to the movement in
sophistication from calculus to advanced calculus, but also included
instructional activities geared to making the new methods accessible
to its users.
November 17, 2005
Reinhard Siegmund-Schultze, Agder University College, Norway:
Richard von Mises - a Non-Conformist Between Mathematics,
Engineering, Philosophy and Politics
The main focus of the talk is von Mises’s “outsider-position” or
“non-conformism” in scientific, philosophical, and - to a lesser
degree - political respects and the implications for the reception
of his theory of probability, the one achievement he is still most
known for today. Not unexpectedly, a considerable part of von Mises’
“non-conformism” was related to his “betweenness” with respect to
mathematics and its applications, which can be related to his
education as an engineer and mathematician and to his practical
work.
Von Mises gave in 1919 a definition for the then rather new
discipline “theory of probability” and tried to relate and connect
it to existing “pure mathematics” on the one hand and to
applications in statistics and physics on the other. This attempt
was, indeed, very influential, if perhaps even more in a “critical”
than in a constructive meaning, “critical” including both von
Mises’s criticism of existing notions and applications of
probability and ensuing criticism of von Mises’s proposals by others
such as A.N.Kolmogorov and A.Ya.Khinchin.
Literature: Siegmund-Schultze, R.: A non-conformist longing for
unity in the fractures of modernity: towards a scientific biography
of Richard von Mises (1883-1953); Science in Context 17 (2004),
333-370.
September 15, 2005
Ed
Sandifer, Western Connecticut State University:
A Series of Extraordinary Events:How Some Lesser Euler Fits
Together
Leonhard Euler (1707-1783) published more than 800 books and
articles, many of which are among the most important mathematics
ever discovered. Over 80 of his papers are about series, and two of
his books deal primarily with series.Some of his results
appear in "blockbuster" papers that make a huge contribution in just
a single paper.Examples include the Basel Problem paper in
which he evaluates zeta(2), Philip Naudé's problem in which he
solves many problems of partition numbers, his paper on the
Sum-Product formula for the zeta function and his paper on the
foundations of continued fractions.There are other ideas,
though, where the results are spread out over several papers, like
the Euler-Mascheroni constant and Euler-Maclaurin series, were
developed over several papers and several years.We will
follow some of these lesser threads and trace a few of these longer
stories, and connect them to the mathematical and scientific life in
the 18th century.
April 21, 2005 David L. Roberts,
Prince George's Community College:
Mathematicians
in the Schools: The 'New Math' as an Arena of Professional Struggle,
1950-1970
What is sometimes casually described as the "mathematics community"
in the United States already by the late 19th century was displaying
divisions, which became more distinct and variegated through the
course of the 20th century. The aim of this talk is to use the arena
of mathematics education during the 1950s and 1960s, which
encompassed most of the so-called "new math" educational reforms, to
illuminate fine distinctions between and within professional groups
involved with mathematics, notably the American Mathematics Society,
the Mathematical Association of America, and the National Council of
Teachers of Mathematics. Simple dichotomies such as researchers
versus teachers, pure mathematicians versus applied mathematicians,
mathematicians versus mathematics educators, or progressive versus
traditional educators offer only limited utility in understanding
the complex jurisdictional struggle that in fact occurred.By
close analysis of the career trajectories of several representative
figures from the period, a more nuanced categorization will be
proposed, yielding a better understanding of the outcome of the
reforms.Special attention will be given to individuals
associated with two of the most prominent curriculum reform
projects: the University of Illinois Committee on School Mathematics
(UICSM), and the School Mathematics Study Group (SMSG), originally
headquartered at Yale and later at Stanford.
March 24, 2005 Nathan L. Ensmenger, University of
Pennsylvania:
Chess Players, Music Lovers, and Mathematicians: Towards a
Psychological Profile of the Ideal Computer Scientist
In the early 1950s, the
academic discipline that we know today as
computer science existed only as a loose association of
institutions,
individuals, and techniques. Although computers were widely
used in
this period as instruments of scientific production, their status as
legitimate objects of scientific scrutiny had not yet been
established.Computer programming in particular was considered
by
many to be a "black art", a private arcane matter. General programming
principles were largely nonexistent" and the success of a program
depended primarily on the programmer's private techniques and
inventions. Those scientists and mathematicians who left
"respectable" disciplines for the uncharted waters of computer
science
faced ridicule, self-doubt, and professional uncertainty.
As the commercial computer industry expanded at the end of
the decade,
however, corporate interest in the science of computing increased
significantly.Faced with a serious shortage of experienced,
capable
software developers, corporate employers turned to the universities
as
a source of qualified programmers.Academic researchers,
unsure of
what skills and knowledge were associated with computing expertise,
began to develop a detailed psychological profile of the "ideal"
computer scientist.Their profile included not only an
aptitude for
chess, music, and mathematics, but also specific personality
characteristics ("uninterested in people," "highly detail oriented,"
etc.).Many of these early empirical studies turned out to be
of
questionable validity and were of almost no use to potential
employers; nevertheless, many of the characteristics identified in
these early personality profiles survived in the cultural lore of
the
industry and are still believed to be indicators of computer science
ability.
My paper explores the development of computer science as an
academic
discipline from the perspective of the corporate employers who
encouraged it as a means of producing capable programming personnel.
I explore the uneasy symbiotic relationship that existed between
academic researchers and their more industrial-oriented colleagues.
I
focus on the use of psychological profiles and aptitudes as a means
of
identifying "scientific" and mathematical abilities and expertise.
February 17, 2005 Paul Halpern, University of the Sciences in Philadelphia:
The Rise and Decline of the Goettingen Mathematical Institute
(1929-1945)
In 1929, a new Mathematical Institute opened just outside the old
city
walls of Goettingen, with Richard Courant assuming its
prestigious
directorship. This modern facility offered the
venerable department a
spacious library, comfortable offices, housing
facilities for visitors, and
prominent exhibit space for its valuable collection of
mathematical models
and instruments. Only four years later, however, the
ascendancy of the
Nazi party forced the faculty to emigrate to the United
States. Their
hastily chosen replacements needed to steer an
impossible course between
the department's hallowed tradition and the odious
dictates of the regime.
December 16, 2004 George Rosenstein, Franklin
and Marshall College:
Calculators for a New Century
One of the unusual features
of the 1904 edition of Granville's
calculus, a book I have described as the first 20th
century calculus
text, is a final chapter called "Integraph. Table of
Integrals". In
this chapter, Granville describes the theory and
operation of a
machine that draws integral curves by tracing a given
curve. Later
editions describe not only the Integraph, but also
polar planimeters.
By the 1941 edition, this material had disappeared. I
will examine
the operation of the relatively simple Integraph and
speculate on the
reasons for its inclusion in the text.
November 18, 2004 Paul Pasles, Villanova
University:
The Most Magically Magical Dr. Franklin
In a parallel universe, the Philadelphia Area
Seminar on the History of Mathematics
celebrated its semiquincentennial in 2001. There, our alternate
selves reflected on the
founding members, local scholars who managed to do a little
mathematics in the isolated
colonial backwater called Philadelphia. Most prominent of these
early mathematicians was
Benjamin Franklin, master of the magic square.
Until recently it appeared that only two of Franklin's magic
squares were still extant. In
fact these were really two instances of the same example, extended
to different orders.
Now, however, it is clear that more than a half-dozen squares
survive. How do these
compare with their predecessors? How exactly did Franklin effect his
numerical oddities?
What is the state of the art today? We consider these questions as
well as some other
mathematics of the day.
October 28, 2004 David Alan Grier, George
Washington University:
When Computers were Human
Before we had electronic devices to do
scientific computation, lengthy
calculations were done by large groups of human
computers. These individuals
were usually intelligent persons who were unable to
pursue a career in science
because of their social or economic standing. They are
best characterized as
"blue collar mathematicians." Several of the human
computers, notably the
staff at the U. S. Nautical Almanac, the workers at
George Snedecor's
Statistical Laboratory and the members of the WPA
Mathematical Tables Project,
made many small contributions to the development of
numerical analysis. The
Mathematical Tables Project, which was probably the
largest computing group of
modern time with over 450 computers at its prime,
became the basis for the
Institute for Numerical Analysis at UCLA and the
Applied Mathematics
Laboratory at the National Bureau of Standards. This
talk is based on a new book, which
is being published by Princeton University Press
September 23, 2004 Tom Archibald,Dibner Institute and Acadia University:
Aspects of the Reception of Fredholm's Work on Integral
Equations
In 1899, Ivar Fredholm (1866-1927) devised a method for solving a
type of
functional equation where the unknown function appears
under the integral
sign, a problem going back to Abel and which had
already received some
study at the hands of Vito Volterra and Picard's
student J. Le Roux. This
rather special-sounding problem had profound
resonances. For one thing, it
could be combined with methods of Carl Neumann and
Henri Poincaré to prove
the existence of solutions to many boundary-value
problems, and indeed to
find these solutions using Picard's successive
approximation method. Still
more far-reaching were the insights it provided to
David Hilbert and his
student Erhard Schmidt, who reinterpreted Fredholm's
methods into the point
of departure for what we now term operator theory on
Hilbert spaces. In
this paper, I examine the first of these threads,
mostly concentrating on
French and Italian work of the period from 1902 to
1910. This represents
joint work with Rossana Tazzioli (Catania).
June 25, 2004 Ioan James:
The Mind of the Mathematician
An introduction to the literature on the
psychology of mathematicians, and other scientists. For example,
highly intelligent people with mild forms of autism
often love mathematics and tend to excel at it. This leads into a
discussion of the nature of mathematical creativity and what has
been learned about it since Poincare gave his famous lecture on the
subject just a century ago.
May 13, 2004 Alexander Soifer, Professor of
Mathematics, Art & Film History, University of Colorado at Colorado
Springs, visiting at Princeton University:
Three Lives: Issai Schur, Bartel van der Waerden, Pierre
Joseph Henry Baudet
A talk on the history of the classic van der
Waerden-proved theorem onmonochromatic arithmetic
progressions in finitely-coloredintegers.
April 15, 2004 Vicki Hill
presents a film on
The Life and Work of Constantin Caratheodory
March 18, 2004 Peggy Kidwell, Smithsonian
Institution:
Geometric Models for the Twentieth Century American Classroom:
Richard P. Baker and his Contemporaries
Relatively few mathematical instruments have been designed, made and sold by a single mathematician. However, in the early decades of the twentieth century, the English-born mathematician Richard P. Baker not only taught mathematics in the Midwestern United States, but designed and made several hundred types of mathematical models. He sold copies of many of these to colleges and high schools throughout the country. Baker’s models reflect traditions in American teaching, the concerns of contemporary mathematicians and scientists, and his own wide-ranging interests.
February 19, 2004 V. Frederick Rickey, United
States Military Academy:
Mathematics at West Point in the Early
Twentieth Century (a very preliminary report)
The United States Military Academy celebrated
its centennial in 1902 but was it a vibrant intellectual center or a
school with a hundred years of tradition unimpeded
by progress? Since the study of mathematics occupied a
substantial portion of the education of every graduate, this
motivates us to look at all aspects of the department of
mathematics: Who were the faculty? What was their education and
experience? What was the curriculum? Which textbooks were used? How
were the classes conducted? How did the department interact with the
national mathematical community? How did world events impact the
department?
The Brachistochrone Problem and its Sequels
To a large extent Hilbert's list of
problems (Paris, 1900)
steered the course of mathematics in the 20th century. However,
posing problems is an old mathematical tradition and there are many
famous problems from the 17th century, among them the most
influential Brachistochrone Problem (Johann Bernoulli, 1696). As a
consequence of this problem mathematical physics (in its true
meaning) got its start by developing essential variational methods
that resulted in a new branch of mathematics. Moreover, the concept
of an analytic function was formulated
(Bernoulli, 1697) and extended (Euler, since 1727). This
lecture gives a comprehensive overview on these cornerstones of
mathematics.
December 11, 2003
David Zitarelli, Temple University:
The Bicentennial of American Mathematics Journals
The first journal devoted entirely to mathematics in the United States was founded 200 years ago, in 1804. This talk will present an overview of the contents of the Mathematical Correspondent and discuss its relative importance in the history of mathematics in the U.S. It will also provide biographical snippets of the founder, George Baron, and some of the major contributors.
November 20, 2003, John McCleary, Vassar College:
Heinz Hopf and the Early Development of Algebraic Topology
**
October 23, 2003, Amy K Ackerberg-Hastings, Anne Arundel Community College:
Francis Nichols: Philadelphian, Bookseller, Mathematical
Critic **
Francis Nichols is a little-known figure whose most significant accomplishment may have been commissioning Thomas and George Palmer to print the first American edition of John Playfair's Elements of Geometry in 1806. Over the next fifteen years, Nichols sold numerous copies of this book to the students at Yale via Jeremiah Day, the professor of mathematics and natural philosophy there. Letters by Nichols in the Day Correspondence discuss the necessary transactions, Day's efforts to complete a series of mathematical textbooks, and the textbook series translated by Harvard professor John Farrar. The paper will explore Nichols's comments on these works as a case study of the reception of mathematics textbooks in early republican America.
September 18, 2003, Fritz Hartmann, Villanova University:
Apollonius’ Ellipse and Evolute Revisited
**
The ancient work of Apollonius studying the
normals to an ellipse from any point in the plane is reviewed from a
modern point of view.
[website]
May 22, 2003 Amy Shell-Gellasch, United States Military Academy -
West Point, New York:
Descriptive Geometry in the New Nation: West Point 1817-1870
**
April 24, 2003 Thomas L. Bartlow, Villanova University:
Mathematics and Politics: The Apportionment Debate of
1920-1940
**
March 20, 2003 Frederick A. Homann, S.J., St. Joseph's University:
Combinatorial Theory in Boscovich's Mathematics
**
February 26, 2003 John Dawson, Pennsylvania State University, York:
Twenty Years of Gödel Studies in Retrospect
**
January 23, 2003 Eleanor Robson, All Souls College:
Mesopotamian Mathematics: Tablets at the University of
Pennsyslvania Museum **
November 21, 2002 Paul Halpern, University of the Sciences in
Philadelphia:
History of Dimensionality
**
October 24, 2002 Robert Jantzen, Villanova University:
The Princeton Mathematics Community of the 1930's: An Oral
History Project
A paper only oral history project on the Princeton University math department and Institute for Advanced Study which shared a building on campus during this decade was converted to a web document at Princeton University and given context with mny history of math articles.
September 19, 2002 William Dunham, Muhlenberg College:
Volterra and Pathological Functions from 19th Century Analysis
**
April 25, 2002
Research-in-progress by Four Temple Graduate
Students **
March 21, 2002 Alan Gluchoff, Villanova University:
Thomas Gronwall
**
February 24, 2002 George Rosenstein, Franklin and Marshal College:
The Man and His Book **
January 22, 2002 Joel Goldstein:
A Bridge over Troubled Waters: Evidences of Christianity
Courses at Dissenting Academies and the Emergence of Rational
Dissent, 1729-1798
November 30, 2001 Rob Bradley, Adelphi University:
The Euler d'Alembert Correspondence and Complex Logarithms
**
October 25, 2001 Tom Foley, St. Joseph's University:
The Golden Ratio in Physics -- Revisited
**
September 20, 2001 Alan Gluchoff, Villanova University:
Close-to-Convexity: An Episode in Function Theory, 1915-1952
**
April 26, 2001 Paul Wolfson, West Chester University:
How Relativity Changed Invariant Theory
**
March 15, 2001 Brief work-in-progress reports by members
February 15, 2001 Fr. Homann, S.J., St. Joseph's University:
Mathematical History of Surveying
**
This is an early description from the summer of 2004 explaining how PASHoM started:
For many years friends interested in history
of mathematics from colleges and universities in and around
Philadelphia would greet one another at national meetings with the
question, "Why do we have to travel hundreds of miles to talk about
our common interest in history of mathematics? Why don't we get
together at home?" In the fall of 2000 David Zitarelli of Temple
University and Paul Wolfson of West Chester University took the
initiative, independently inviting people to colloquia at their
institutions. At West Chester spoke on in November and in December
at Temple Jim Stasheff talked about his experiences as a graduate
student at Princeton in the 1950's.
These two efforts prompted Tom Bartlow of Villanova University to
invite all interested persons to an organizational meeting at
Villanova University in January 2001. There it was agreed to
establish the Philadelphia Area Seminar on the History of
Mathematics to share our common interest in mathematics, to
encourage one another in our research efforts, and to offer a forum
for reporting on work in progress. Rudiger Thiele, who happed to be
in town at the time, attended, offered us encouragement, and spoke
informally about his investigation of Hilbert's twenty-fourth
problem. He continues to claim status as the only foreign associate
of PASHoM. Since then the seminar has met monthly, with
interruptions in December and for summer. There are no officers or
formal structure but David Zitarelli and Tom Bartlow have
voluntarily assumed responsibility for necessary arrangements.
We have been fortunate that several well known historians of
mathematics have had other business in Philadelphia and have spoken
to us while in town and that others have been willing to travel at
their own expense to share their research with us.
The seminar will resume in the fall with a talk by Frederick W.
Hartman of Villanova University on "Apollonius’ Ellipse and Evolute
Revisited" on September 18, 2003 and a talk by Amy Ackerberg-Hastings on
October 23, 2003.
Meetings are at Villanova University, usually on the third Thursday
of the month.
Tom Bartlow retired leadership in Summer 2012. Alan Gluchoff took over Fall 2012.