Schedule of Talks for the 2001-2002 Academic Year
Date: Wednesday, October 3, 2001
Speaker: Prof. John McCleary
Department of Mathematics
Vassar College
Title: The Porism of Poncelet: Jacobi , Poncelet, Abel, Steiner
Video Stream: Click here
Abstract: This talk is a part of my investigations of Jacobi's geometrical works. In his paper, Ueber die Anwendung der elliptischen Transcendenten auf ein bekanntes Problem der Elementargeometrie, Jacobi describes a proof of the Porism of Poncelet using his then newly developed elliptic functions to prove a remarkable geometric result. In this talk I will describe how this result drew the attention of Jacobi, and how it fits the theory of elliptic functions into an older tradition of analysis.
Date: Wednesday, November 7, 2001
Speaker: John Glaus
Unaffiliated Scholar
Rumford, Maine
Title: Euler: Mathematician and Diligent Bureaucrat -- The Great Balancing Act
Video Stream: Click here
Abstract: Euler was the quintessential mathematician, but he also proved his worth to the Russian and Prussian imperial courts as an evenhanded, competent and tightfisted official.

The intention of this paper is to show the human armor Euler developed to circumvent the complications caused by outrageous administrators and belligerent autocrats. The information contained in this talk has been taken from newly translated letters written between 1748 and 1763 to Kiril Razumovsky and Grigory Teplov while Euler was in Berlin.

Date: Wednesday, December 5, 2001
Speaker: Prof. Paul C. Pasles
Department of Mathematical Sciences
Villanova University
Title: The Lost Squares of Dr. Franklin
Abstract: In colonial times, America was hardly the hotbed of frenzied mathematical activity it would later become. One Philadelphian, however, was an avid builder of magic squares, those numerical novelties that entertained early mathematicians from China to India to Islam. Until recently, only two of Benjamin Franklin's squares were well known to mathematicians. Since Franklin had little formal schooling, it might be assumed that he stumbled upon his discoveries. However, it turns out that a few more examples survived, and these show a more varied set of tricks. Today, see the lost squares of Dr. Franklin in this colloquium.

I will also describe Franklin's procedure for constructing "magic circles" reminiscent of the traditional Chinese and Japanese varieties.

This talk will be accessible to mathematicians and historians, from undergraduate to faculty.

Date: Wednesday, February 6, 2002
Speaker: William Dunham
Koehler Professor of Mathematics
Muhlenberg College
Title: Volterra and the Limits of Pathology
Video Stream: Click here
Abstract: This talk describes the rise of "pathological functions" in nineteenth century analysis, citing examples from Dirichlet (1829), Riemann (1854), and Weierstrass (1872). Their work seemed to suggest that functions could be arbitrarily bizarre. Such a suggestion was countered by the young Vito Volterra in 1881. In an elegant and relatively simple proof, Volterra established the non-existence of a function continuous on the rationals and discontinuous on the irrationals. We examine his argument, which is not only of historical interest but also of pedagogical value in the analysis classroom.
Title: Newton's (Original) Method -- or -- Though this be Method, yet there is madness in't
(a special lecture, suitable for undergraduates, given earlier the same day by Professor Dunham)
Video Stream: Click here
Abstract: This talk sketches the life and career of Isaac Newton - including his nasty skirmishes with Leibniz over the creation of the calculus - before considering in greater detail the method he advocated for approximating solutions to equations. We examine his lone example of this approximation technique and compare it to what is now called "Newton's Method." The presentations features roughly equal doses of history, biography, and mathematics and is accessible to anyone acquainted with calculus.
Date: Wednesday, March 6, 2002
Speaker: Prof. Antonella Cupillari
School of Science
Penn State Erie, The Behrend College
Title: Maria Gaetana Agnesi: Myths and Mathematics
Abstract: Most mathematicians are familiar with the "witch of Agnesi." To the mistranslation of the name of this curve, Agnesi (1718-1799) might owe some of her fame. But what is the truth about the woman who authored the Instituzion Matematiche, the first calculus book in Italian? Some answers can be found in the Elogio Storico di Donna Maria Gaetana Agnesi, a biography written only five months after her death by a family friend and well-known historian of the time, Canon Antonio Francesco Frisi. This biography mentions explicitly only one mathematical problem about conics, taken from Agnesi's extensive correspondence, and not related to the "witch." The solution is given, but her work, which can be found in the original letter, is not included.
Date: Wednesday, April 3, 2002
Speaker: Prof. Steven Gimbel
Department of Philosophy
Gettysburg College
Title: Poincaré, the Language of Mathematics, and the Intuitionist/Formalist Debate
Abstract: Jules Henri Poincaré was simultaneously claimed as a forefather for both sides of the intuitionist/formalist debate. He explicitly opposed the analytic axiomatic approach to mathematics which was beginning to blossom at the end of the 19th century, but the conventional approach to geometry that emerges from his writings on the conceptual foundations of mathematics are generally cited as a great influence on the acceptance of the axiomatic approach. This discussion considers the work that Poincaré does in order to separate his view from that of Immanuel Kant, arguments that are mistakenly taken to be directed against empiricism. In pointing out what he sees as Kant's conceptual misunderstandings, Poincaré is led to view geometry as a branch of group theory and oppose considering the general treatment of manifolds by Bernhard Riemann to be geometry at all. The rationale for this restrictive definition of geometry leads to the conclusion that Poincaré is to be labeled as neither a proto-intuitionist nor a proto-formalist, but rather posits a deep mathematical linguistic faculty in the human mind of the sort Noam Chomsky would champion over half a century later.
Date: Thursday, May 2, 2002
Speaker: Prof. Walter Meyer
Department of Mathematics and Computer Science
Adelphi University

Prof. Joseph Malkevitch
Department of Mathematics
York College (CUNY)

Prof. Jack Winn
Department of Mathematics
SUNY at Farmingdale
Title: Theory and Applications in the teaching of Linear Algebra: Evolution During 1948-1999
Abstract: Although some mathematics courses are relatively timeless, some have been newly created in recent decades or had their contents substantially changed (at times because new mathematics or new applications were discovered). Studying the evolution of curriculum can be intellectually interesting and may offer lessons so that future efforts at curriculum change can be more effective.

As a particular example, the history of the teaching of linear algebra has been eventful in the last half-century. We will present an outline of some of the developments, with special attention to the applied versus pure issue. Many questions are still unresolved and we hope for useful input from the audience.