Schedule of Talks for the 2014-2015 Academic Year
Date: Wednesday, October 8, 2014
Speaker: Prof. Harold Edwards
Courant Institute of Matheamtical Sciences
New York University
Email: edwards AT cims DOT nyu DOT edu
Title: An Introduction to Abel's Theorem
Abstract: Modern treatments of Abel's theorem involve line integrals on Riemann surfaces and therefore depend heavily on the use of complex variables. But the theory of complex variables was in its infancy in Abel's time, and Riemann surfaces were yet to be invented. The talk will explain Abel's point of view, which was motivated by Euler's (easy to understand) work on elliptic curves, and makes perfect sense without any mention of complex variables.
Date: Wednesday, November 5, 2014
Speaker: Prof. William Dunham
Department of Mathematics
Muhlenberg College
Email: wdunham AT muhlenberg DOT edu
Title: When Euler Met L'Hospital
Abstract: Leonhard Euler (1707-1783) was, of course, a mathematical giant whose contributions ranged far and wide. In this talk we look to analysis and consider his treatment of l'Hospital's rule as found in Chapter 15 of his Institutiones calculi differentialis from 1755.

Euler started the chapter with a general discussion of indeterminate forms and then took up specific examples. He began with a few problems that could be done either with or without l'Hospital's rule, then moved to a curious example requiring logarithmic differentiation, and ended with a spectacular solution to the "Basel problem" - i.e., he showed that 1 + 1/4 + 1/9 + 1/16 + ... = π2/6 by applying l'Hospital's rule not once nor twice, but thrice.

It's Euler at his symbol manipulating best.

Date: Wednesday, December 3, 2014
Speaker: Dr. Jonathan Sondow
New York City
Email: jsondow AT alumni DOT princeton DOT edu
Title: Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis
Abstract: We provide an historical account of equivalent conditions for the Riemann Hypothesis arising from the work of Ramanujan and, later, Guy Robin on generalized highly composite numbers. The first part of the talk is on the mathematical background of our subject. The second part is on its history, which includes several surprises.
Date: Wednesday, March 4, 2015
Speaker: Michael J. Barany
Program in History of Science
Princeton Univesity
Email: mbarany AT princeton DOT edu
Title: Intermediate Values: Augustin-Louis Cauchy and the Dusty, Contentious, Reactionary Origins of Modern Mathematics
Abstract: Historians of mathematics have long recognized the early nineteenth century as a turning point in the history of analysis, one that set the stage for far-reaching transformations in mathematical theories and institutions. Augustin-Louis Cauchy's work in his early years as professor at the École Royale Polytechnique contributed directly to some of the period's striking changes, and was symptomatic of many others. But what kind of transformation did Cauchy represent? Viewed in hindsight, Cauchy often looks like a rigorous visionary who contributed needed principles in the interest of a pure mathematical discipline. Placed amidst the contentious politics, social turmoil, and technological upheaval of his time, Cauchy and his mathematics look rather more complex, ambivalent, and historiographically provocative. I will argue that this latter view of Cauchy helps explain crucial aspects of modern mathematics and the nature of its theories and institutions that the Cauchy of hindsight obscures.
Date: Wednesday, April 1, 2015
Speaker: Prof. Maria Zack
Department of Mathematical, Information and Computer Sciences
Point Loma Nazarene University
Email: mzack AT pointloma DOT edu
Title: What can the Lisbon Earthquake Tell Us about the Connections between Mathematics, Urban Planning and Engineering in Eighteenth Century Portugal?
Abstract: In 1755 the commercial district of Lisbon was destroyed by an earthquake and a subsequent fire and tsunami. This catastrophe along with an interesting constellation of political circumstances provided an opportunity for Lisbon to be completely rebuilt from first principles, there was no attempt to preserve old street patterns or buildings. Because port wine provided a centuries old connection between Lisbon and London, those who redesigned Lisbon were aware of the post-fire rebuilding that has transpired in London a century earlier. This talk looks at some of the advances in the mathematics of materials in the seventeenth and eighteenth centuries and considers specific attributes of Lisbon's reconstruction in light of those advances.
Date: Wednesday, May 6, 2015
Speaker: Prof. Rob Bradley
Department of Mathematics and Computer Science
Adelphi University
Email: bradley AT adelphi DOT edu
Title: L'Hôpital's Synthesis of Calculus and Geometry
Abstract: 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 present some examples of this synthesis, drawn from my forthcoming translation of l'Hôpital's Analyse des infiniment petits, a joint project with Sal Petrilli and Ed Sandifer.