The 2008 Euler Conference
July 20 - 23, 2008
Program and Schedule
Although some details are being finalized, the general format of the 2008 Euler Conference is known, and is given here. This page will be filled in as the conference draws closer.
Monday, July 21
All events are in Science 322 unless otherwise indicated
8:30-8:45 Welcome and Introductions
8:45-9:15 Continental Breakfast On Monday and Tuesday and Wednesday, coffee, tea and baked goods are served in the conference room, and are included in your registration fee.
9:15 - 10:15 Rob Bradley
10:15-10:30 morning break
10:30-11:20 Charles Rocca
11:30 Dorm check-in for Monday arrivals
12:00 - 1:00 Lunch in Alumnae Hall, room 116 Monday and Tuesday's lunch are served onsite, and are included in your registration fee.
1:00 - 1:50 Larry D'Antonio
2:00 - 2:50 Hieu Nguyen
3:00 - 3:30 Afternoon break
3:30 - 4:20 Dieter Suisky
4:30 - 5:30(?) Reading Euler from Original Sources Participants at the convention will be invited to join a small group to do a joint reading of one of Euler's untranslated works.
The focus is on understanding what Euler is really saying, and often leads to wide-ranging discussion based on the text. Little to no expertise in the source language is required; in previous years people of all abilities have happily participated in these sessions.
Tuesday, July 22
9:00-9:30 Continental Breakfast On Monday and Tuesday and Wednesday, coffee, tea and baked goods are served in the conference room, and are included in your registration fee.
9:30 - 10:30 Stacy Langton
10:30-10:45 morning break
10:45-11:45 The Euler Lecture: Ed Sandifer
12:00 - 1:00 Lunch in Hagedorn 109 Monday and Tuesday's lunch are served onsite, and are included in your registration fee.
1:15 - 1:50 Ron Calinger
2:00 - 2:50 Dominic Klyve
3:00 - 3:30 Afternoon break
3:30 - 4:20 Jordan Bell
4:30 - 5:30(?) Reading Euler from Original Sources II
6:30 Conference Banquet at Maxxel.s Restaurant
Wednesday, July 23
8:30-9:00 Continental Breakfast On Monday and Tuesday and Wednesday, coffee, tea and baked goods are served in the conference room, and are included in your registration fee.
9:00-9:50 Rudiger Thiele
10:00 - 10:35 Tom Simpson and Dominic Klyve
10:45-11:00 morning break
11:00-11:50 John Glaus
11:50 - 12:00 Closing remarks.
Titles and Abstracts
Jordan Bell - The Euler-Maclaurin summation formula
The Euler-Maclaurin summation formula expresses the sum of a function as an integral and a series involving derivatives of the function. It turns out that this series can diverge but still be used to evaluate the sum. I will explain how we can justify this. In particular I will discuss Stirling's formula for the factorial function. This talk is my attempt to understand and explain David Pengelley's paper "Dances between continuous and discrete: Euler's summation formula" in the MAA Euler series, but I will not assume that you have read this.
Rob Bradley - Euler's Contributions to Probability and Statistics
Todhunter wrote that Euler's "contributions to the Theory of Probability relate to subjects of comparatively small importance, yet they will be found not unworthy of his own great powers and fame." However, Todhunter seems to have overlooked some of Euler's seminal work on statistics and actuarial science. We will attempt to give a more complete assessment of Euler's impact on probability and statistics.
Ron Calinger - Euler's three-volume Letters to a German Princess (1768 - 1772): Origins, Publication, and Synopsis
This paper will trace the beginnings of the letters from the private instruction of the initially fifteen-year-old Margravine Frederike Charlotte, through problems with Frederick II, and the volumes first publication in Russia. It will examine the text as an apologia, a history of science, and the most successsful scientific popularization of the eighteenth and nineteenth centuries. A synopsis of its three sections and major ideas will be given.
Larry D'Antonio - Euler and his Amazing Elastic Curve Identity
In the paper De miris proprietatibus curvae elasticae (.On a remarkable property of elastic curves.) Euler returns to two of his favorite topics, elliptic integrals and elastic curves. He shows that the elliptic integrals which define elastic curves satisfy a most remarkable identity. This paper (E605 in the Eneström catalog) was presented to the St. Petersburg Academy in 1775, but not published until 1786. In some respects this paper represents a summary of all that Euler has discovered about elliptic integrals. Although he was to write several more papers on the subject, this was to be his last significant contribution to the field. In this talk we look at the lovely interplay of products, series, integrals, and geometry that Euler uses in the proof of his identity.
John Glaus - (Nearly) Ten years before the Mast(er). 1999-2008
Reminiscences of a decade of Euleriana: Some of the lore, some of the magic. Some of he people who introduced me to Leonhard Euler; the people that Leonhard Euler introduced to me; a tale of the exploits in the realm of Euleriana and of the adventures before, during and now.
Dominic Klyve - On the Formation of Gravity and the Voice: some lesser-known works of Euler.
It is well known that Euler did not restrict his scholarly attention merely to problems of mechanics and mathematics. He ranged widely over the landscape of all knowledge of the time, occasionally dabbling in metaphysics and theories of phonetics. We shall consider two such papers, one published anonymously, and one published posthumously, in which Euler moves beyond his "comfort zone." In the end, he shows himself to be both surprisingly prescient, and quite fallible.
Stacy Langton - Euler's analysis of the skew elastic
Euler's E471, "De motu turbinatorio chordarum musicarum" (presented in November, 1774), is a sequel to the papers E410 and E481, which I spoke about at last summer's meeting in San Jose. In those papers, Euler worked out the basic principles of elasticity applied to an elastic filament whose shape or motion were contained entirely in one plane. Now Euler wishes to generalize those results to a filament in three-dimensional space.
Euler had based his previous work on Jacob Bernoulli's "constitutive" principle that the bending moment is proportional to the curvature of the filament. Now Euler must figure out how to generalize that principle to a filament in space. After an unsatisfactory first attempt, Euler realizes that the key to the solution is to generalize the concept of curvature to a space curve. In the course of doing this, he determines the osculating plane and the binormal.
Hieu Nguyen - Paradoxical Euler or Integration by Differentiation: A Synopsis of E236
This talk will present a synopsis of Leonard Euler's E236 paper, Exposition de quelques paradoxes dans le calcul intégral (Explanation of certain paradoxes in integral calculus), based on a recent English translation by Andrew Fabian. Two interesting paradoxes are treated by this 1758 paper. The first involves a novel method of solving a special family of differential equations by differentiating them again (as opposed to the traditional method of integration). The second paradox explains how the traditional method of integration does not always lead to the most general solution for the same family of differential equations (even when the constant of integration is taken into account). Several geometrical problems relating to these paradoxes will be discussed, including some interesting generalizations.
Chuck Rocca - "Philosophy to a German Princess"
Euler's "Letters to a German Princess" are well known for giving a thorough exposition of the science of their time in a popular or vernacular format. However, in addition to science they also covered, to some degree, all the issues in what is today labeled modern philosophy. In this talk we examine briefly what philosophy is discussed and referenced by Euler in the letters, and take an in depth look at how he covers one or two particular topics.
The Euler Lecture: Ed Sandifer - What makes "classic" mathematics?
In the title essay of his collection of essays Why read the classics? Italo Calvino gives us fourteen definitions of the word "classic" as applied to literature. We look at some of those definitions and whether they apply to works of mathematics as well as to works of literature, and we ask which of Euler's works meet Calvino's standards.
Tom Simpson and Dominic Klyve - The Mathematics of Faith: Science and Religion in the thought of Leonhard Euler
In 1747, Euler wrote his "Rettung der gottlichen Offenbahrung...", defending the validity of divine revelation as a valid source of knowledge. His work includes his attempts to reconcile his belief in predestination and his belief in free will, with interesting connections to the writings of John Calvin, and Swiss Reform Theology. In this talk, we shall attempt to elucidate more precisely some of Euler's religious views, and draw connections between this work and his contemporaneous work in mathematics and mechanics.
Dieter Suisky - Euler and Lagrange
It will be demonstrated that (i) Euler and Lagrange successfully paved the way for the replacement of geometric with analytic methods. The change was simultaneously performed in mechanics and mathematics. (ii) A fruitful and satisfactory result is conditioned by the requirement to attain the rigor in demonstrations known from the sciences of the Ancients, i.e. from static and geometry, respectively. (iii) Euler did not confine this substitution of methods to the physical part of Newton.s mechanics, but included a reconsideration of the foundation of calculus whereby the theory underwent a considerable modification . Euler invented (iv) the concept of infinitely small body in the treatise Mechanica sive motus scientia analytice exposita [E015] and, moreover, (v) postulated a hierarchy of quantities being of infinitesimal, finite and infinite magnitude which is centered upon finite quantities [E212].
Rüdiger Thiele - Magnitudes, variables, and functions