Schedule of Talks for the 2005-2006 Academic Year

Date: Wednesday, September 28, 2005 Speaker: Prof. James Lightner Department of Matheamtics & Computer Science McDaniel College jlightne@mcdaniel.edu Title: Remembering Howard Eves Abstract: Meet Howard Eves, geometer, algebraist, analyst, and one of the foremost American historians of mathematics of the twentieth century. You'll see him via pictures, hear him via several tapes and videoclips, and learn more about his remarkable life and contributions to mathematics, often in his own words, taken from some of his prodigious publications. Some personal reflections on the man will also round out the presentation.

Date: Wednesday, November 2, 2005 Speaker: Prof. David Richeson Department of Mathematics & Computer Science Dickinson College richesod@dickinson.edu Title: Euler's polyhedral formula Abstract: A polyhedron with F faces, E edges, and V vertices satisfies the relation F-E+V=2. This relationship was first noticed by Euler in 1750 (and a modified version 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. Meahwhile, Lhuilier, Hessel, and Poinsot unveiled exotic "counterexamples." In this talk we present the history of this beloved formula up to 1850, while it was still a theorem about polyhedra and before it became a topological theorem.

Date: Wednesday, December 7, 2005 Speaker: Prof. Amy Ackerberg-Hastings Department of History University of Maryland University College aackerbe@erols.com Title: John Playfair: The Mathematics of Correspondence Abstract: I am currently preparing the letters of John Playfair (1748-1819) for publication in the History of Earth Sciences Series of Scholars' Facsimiles & Reprints. While Playfair is best-known among historians of science for his efforts to gain acceptance for James Hutton's geology in Enlightenment and Romantic Scotland, several of his contributions are of interest to mathematicians as well, including: his influential 1795 edition of Euclid's Elements of Geometry, his papers on negative numbers and on porisms, his formal and informal teaching activities as professor of mathematics at Edinburgh University, his enthusiasm for French mathematics, and his interest in mathematical instruments. The talk will describe some of the evidence for these activities that can be found in the surviving letters to and from Playfair and will report on the process of locating, transcribing, and editing historical correspondence.

Date: Wednesday, February 1, 2006 Speaker: Prof. Sandro Caparrini Department of History of Mathematics The Dibner Institute caparrini@libero.it Title: The discovery of the vector properties of moments and angular velocity Abstract: As a consequence of the new understanding of the general dynamics of rigid bodies induced by the researches of Euler and d'Alembert, between 1759 and 1826 several mathematicians discovered the vectorial properties of moments of vector quantities and angular velocity. Among those who investigated these matters are some of the leading mathematicians of the period: Euler, Lagrange, Laplace, Poinsot, Poisson and Cauchy. The detailed development of their results gave rise to the establishment of vector mechanics at the middle of nineteenth century. The study of the different threads that make up this story yields new insights into the relationship between mechanics and geometry.

Date: Wednesday, March 1, 2006 Speaker: Prof. Alexander Jones School of Historical Studies - Institute for Advanced Study Department of Classics - University of Toronto alexander.jones@utoronto.ca Title: Locus theorems in ancient Greek geometry Abstract: During the third century B.C. Greek mathematicians (including Euclid and Apollonius) took a particular interest in locus theorems and their applications in problem solving. A Greek locus theorem demonstrated that a geometrical object (typically a point) having a defined relation to given objects lies on a geometrical object (typically a line or surface) that can be constructed from the givens. A classification was devised of locus theorems, and construction problems in general, according to whether they could be solved using only the postulates in Euclid's Elements, i.e. straight lines and circles, or required conic sections or special curves. An interesting question is whether anyone in antiquity broke from this rigid conception of loci by defining a curve or surface as a locus.

Date: Wednesday, April 5, 2006 Speaker: Prof. Brian Hopkins Department of Mathematics and Physics St. Peter's College bhopkins@spc.edu Title: Königsberg: What Euler did and did not do Abstract: Euler's 1735 work on the bridges of Königsberg is recognized as the beginning of graph theory and is referenced in almost every discrete mathematics textbook. Several show a picture of four dots and seven lines and outline Euler's proof of the impossibility of what we now call an Euler cycle. But the illustrations in Euler's paper show rivers and bridges; the "dot & line" representation of graphs seems not to have arisen until the 1890's. In this talk, we work through how Euler actually addressed the problem, in addition to considering correspondence leading up to the article and later work associated with cycles on graphs.

Date: Wednesday, May 3, 2006 Speaker: Prof. Harry Coonce Department of Mathematics North Dakota State University harry.coonce@ndsu.nodak.edu Title: Tales from the Genealogy Project Abstract: In or around 1995 we asked a question regarding who advised my advisor. In this talk we will discuss how this query led to the Mathematics Genealogy Project. We will present a look at the history of the project, including how it was started and how it has developed over the last decade. We will also relate some of the amusing - and not so amusing - incidents along the way.