Schedule of Talks for the 2002-2003 Academic Year
Date: Wednesday, October 2, 2002
Speaker: Prof. Ronald Calinger
Department of History
Catholic University of America
Title: Leonhard Euler in Berlin to 1746: "I Think I Am the Happiest Man in the World"
Abstract: This paper will examine the life, work, and influence of Euler during his first five years in Berlin from 1741 to 1746. During his quarter century there, he completed or wrote more than 380 memoirs and books, of which 275 were published by 1766. Their combined originality, depth, and range make Euler's achievement unparalleled in the history of the mathematical sciences. This paper begins with the initial Frederician plans for a royal academy of the sciences and belles arts in Berlin, the arrival of Euler, and his role in founding the academy. Next, it investigates the most signal scientific contributions of Euler to 1746, namely his landmark books on the calculus of variations and infinitary analysis, his state project in ballistics, and his research in number theory, mapping, and an influential pulse theory in optics. It closes with his connections with the Paris and St. Petersburg Academies of Science.
Date: Wednesday, November 6, 2002
Speaker: Prof. Homer White
Department of Mathematics
Cornell University/Georgetown College
Title: More veterum Geometrarum: A Back-roads Tour of Leonhard Euler's Classical Euclidean Geometry.
Abstract: As a geometer, Leonhard Euler is probably best-known for his work on planar graphs and for the discovery of the Euler Line. However, his lesser-known contributions to classical Euclidean geometry provide excellent illustrations of Euler's commitment to a visual understanding of mathematics, his ability to recover important themes from historical sources, and his substantial influence on later mathematians, even in fields that were not his central focus of interest. We will survey a few of Euler's delightful "minor" results, place them in historical context, and consider their possible uses in undergraduate teaching and research.
Date: Wednesday, December 4, 2002
Speaker: Prof. Jeff Suzuki
Department of Mathematics
Bard College
Title: Optimization Before Newton
Abstract: Today optimization is one of the traditional uses of the derivative, though the problem of finding the maximum or minimum value of a quantity is far older than calculus. We'll take a look at how various optimization problems were solved by mathematicians from Euclid to Archimedes to al-Khayyami to Hudde, and examine the role these problems played in the mathematics of the time, including their place in the birth of calculus.
Date: Wednesday, February 5, 2003
Speaker: Joan L. Richards
Department of History
Brown University
Title: Mathematics in her dotage: Radicals, rationals and reaction in England after the French Revolution
Abstract: In 1811, Charles Babbage famously contrasted the deism of continental mathematics with the dotage of Cambridge University. In this paper I want to move past Babbage's perhaps self-serving claim about the dotage of his university, by exploring the state of mathematics in Cambridge and in France in the years after the French revolution.
Date: Wednesday, March 5, 2003
Speaker: Prof. Adrian Rice
Department of Mathematics
Randolph-Macon College
Title: Inexplicable? The status of complex numbers in Britain, 1750-1850
Abstract: The period from the mid-18th to the mid-19th century is generally regarded as the time when complex numbers were finally accepted as legitimate algebraic objects by the mathematical community. It is also widely considered to have been the work of Gauss that was primarily responsible for bringing these numbers into the mathematical mainstream. However, the story of the acceptance of complex numbers was a little different in the British Isles.

This paper surveys the peculiarly British position towards complex and imaginary numbers in the period up to around 1850, a subject which still awaits a definitive history. Following a brief summary of the early history of complex numbers, it highlights the largely forgotten but influential research of two British mathematicians, John Warren and John Thomas Graves. It then traces the influence of their work on the changing British mathematical attitudes during this time, concluding with a look at how the notion of "inexplicable quantities" subsequently came to be extended.

Date: Wednesday, April 2, 2003
Speaker: Prof. Lawrence D'Antonio
School of Theoretical and Applied Sciences
Ramapo College
Title: Title: Charles de Freycinet and the Fundamental Theorem of Calculus
Abstract: The Fundamental Theorem of Calculus (FTC) plays a familiar role in the modern calculus syllabus. The history behind the FTC is important and interesting. How did it come to play this role? Who gave the theorem its name? How has the presentation of the theorem in calculus texts changed historically?

The history of the FTC parallels the development of the theory of integration. This history follows a clearly defined path from the geometric proofs of Newton and Leibniz, to the first rigorous proof as presented by Cauchy, to the extension of the integral to discontinuous functions by Riemann, and finally, to the version of the FTC in Lebesgue's theory.

Who first called the FTC fundamental? The earliest source using the phrase "Fundamental Theorem" for the FTC is the 1860 calculus text of Charles de Freycinet, who, interestingly enough, later became the premier of France. Freycinet, a student of Sturm at the Ecole Polytechnique,is himself a minor figure in the history of mathematics, but is representative of a long line of French analysts who worked on the FTC (e.g., Lagrange, Cauchy, Sturm, Serret, Hermite, and Darboux).

An assortment of calculus texts are examined for the way in which they present the FTC. Texts such as those by Euler, Lacroix, DeMorgan, Raabe, Moigno, Church, Todhunter, Serret, Granville, and Osgood are considered. In the end, some sense, hopefully, has been conveyed of the evolution of a cornerstone of the calculus.

Date: Wednesday, May 7, 2003
Speaker: Prof. Edward Sandifer
Department of Mathematics
Western Connecticut State University
Title: Euler's Fourteen Problems
Abstract: In 1757, Euler presented 14 unsolved "Quaestiones Mathematicae" and 18 "Quaestiones Physicae" to the St. Petersburg Academy. The problems seem to be intended both to guide the research of the Academy and to provide problems for the Academy's prize. The parallels with the Hilbert Problems are inescapable. The problems provide a glimpse of what Euler thought were the important problems of his day, and also into what he thought was the nature and purpose of mathematics itself.