Philadelphia Area Seminar on the History of Mathematics (PASHoM)

This is a seminar for faculty from colleges and universities in the Philadelphia area who share an interest in the history of mathematics, open to the public and also available via Zoom to allow remote participants. The seminar meets monthly during the academic year, usually at 6:00 p.m. on a Thursday evening at Villanova University for a light meal (donation $10.00), followed by a presentation by the seminar speaker usually one hour long starting at 6:30pm which is then is followed by open discussion for up to about 30 minutes.

This group was established in January 2001 for persons in the greater Philadelphia area to:

and it currently directed by Alan Gluchoff.

To add your name to our emailing list,  send information to Zoom links are sent via email from Alan in response to requests.


Click here for general directions to Villanova University.
The Mendel Science Center is at the west end of campus next to the train station [Google maps] on the other side of St Augustine Center adjacent to the M1 parking garage. Room 103 is at the far end of the building on the first floor.

Villanova University is located on route 30, Lancaster Avenue, just east of I-476. Set your GPS to
                800 Lancaster Ave, Villanova, PA 19085

If you drive to the meeting, you may park on the Ithan Avenue I-1 parking garage at the intersection of Lancaster and Ithan Avenues free for 1 hour and then for a low hourly fee after that.

To enter Villanova by the main gate on Ithan Avenue and park in the multilevel M-2 parking garage adjacent to St. Augustine Center, you must fill out an electronic form requested from Alan by email. The Mendel Science Center is on the other side of the St. Augustine Center.

Public transportation: Take SEPTA's Paoli - Thorndale train to the Villanova station. If outbound from center city go down through the tunnel to the inbound side. From the inbound platform a few steps lead to a parking lot behind Mendel. Proceed to the archway entrance on the right to go up to the first floor and then down the hallway away from the city to Room 103 on the left just before the stairwell.

Remote Zoom Participants

During the Zoom session, please keep your Zoom participation muted unless you wish to make a comment or ask a question of the speaker, since background sounds in any participant window will switch the Zoom session recognition of the person speaking away from the seminar speaker and show the errant window instead of the seminar speaker. During the shared screen talk, you may select Speaker or Gallery View from the Zoom View menu: select Speaker view to see the speaker together with the presentation, with the vertical screen division moveable from left to right to maximize either one.

PASHoM events

Some recent talks to give a flavor of the group [see archives for additional links to talk materials]:

2023 Fall

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. 

Archived Past Events are here.