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Past MAA Distinguished Lectures

Karl Rubin, UC Irvine

Abstract: Which natural numbers occur as the area of a right triangle with three rational sides?  This is a very old question and is still unsolved, although partial answers are known (for example, five is the smallest such natural number).  In this talk we will discuss this problem and recent progress that has come about through its connections with other important open questions in number theory.

MAA Distinguished Lecture: Karl Rubin

Biography: Karl Rubin is the Thorp Professor of Mathematics at the University of California, Irvine.  His research deals with elliptic curves and other aspects of number theory.  Rubin attended Washington DC public schools, was a Putnam Fellow as an undergraduate at Princeton, and received his Ph.D. from Harvard.  He was a professor at Ohio State, Columbia, and Stanford before moving to UC Irvine in 2004.  Rubin received the Cole Prize in Number Theory from the American Mathematical Society, a National Science Foundation Presidential Young Investigator award, a Humboldt Research Award, and Guggenheim and Sloan fellowships.

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Margaret H. Wright, Courant Institute of Mathematical Sciences, New York University

Abstract: Mathematicians believe, correctly, that they are uniquely qualified to answer complicated questions in science and engineering. But it very often happens that such problems are unsolvable or intractable in their original form. Is it acceptable to say politely "I'm sorry; this problem is impossible" and then return to answering questions that can be answered? Or should we do more? How can we do more? This talk, intended for a general audience, will describe, with examples from the speaker's experiences in optimization, how mathematicians can become local heroes after they say they're sorry.

MAA Distinguished Lecture: Margaret Wright

Biography: Margaret H. Wright is Silver Professor of Computer Science and Mathematics and chair of the Computer Science Department in the Courant Institute of Mathematical Sciences, New York University. She received her B.S., M.S., and Ph.D. from Stanford University. Her research interests include optimization, scientific computing, and real-world applications. Prior to joining NYU, she worked at Bell Laboratories (AT&T/Lucent Technologies) and Stanford University. She was elected to the National Academy of Engineering (1997), the American Academy of Arts and Sciences (2001), and the National Academy of Sciences (2005). During 1995-1996 she served as president of the Society for Industrial and Applied Mathematics (SIAM).

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Ravi Vakil, Stanford University

Abstract: Doodling has many mathematical aspects: patterns, shapes, numbers, and more.  Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles.  Vakil will begin by doodling, and there is no telling where it could take him.

MAA Distinguished Lecture: Ravi Vakil

Biography: Ravi Vakil is Professor of Mathematics at Stanford University.  He was born in Toronto, Canada, and studied at the University of Toronto, where he was a four-time winner of the Putnam competition (``Putnam Fellow'').  He received his Ph.D. from Harvard in 1997, and taught at Princeton and MIT before moving to Stanford in 2001.  He is an algebraic geometer, and his work involves many other parts of mathematics, including topology, string theory, applied mathematics, combinatorics, number theory, and more.  His awards include the Alfred P. Sloan Research Fellowship, the National Science Foundation CAREER Award, the American Mathematical Society Centennial Fellowship, the Dean's Award for Distinguished Teaching, and the Presidential Early Career Award for Scientists and Engineers.  He works extensively with talented younger mathematicians at all levels, from high school (through math circles, camps, and olympiads), through recent Ph.D.'s.  Vakil runs a problem-solving seminar each  fall for Stanford undergraduates, involving up to 150 students, as well as a masterclass for experts.  He is also the faculty advisor to the Stanford Math  Circle. You can read more at Prof. Vakil's Home Page.

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David Bressoud, Macalester College

Abstract: What is the role of proof in mathematics? Most of the time, the search for proof is less about establishing truth than it is about exploring  unknown territory. In finding a route from what is known to the result one believes is out there, the mathematician often encounters unexpected insights into seemingly unrelated problems. I will illustrate this point with an example of recent research into a generalization of the permutation matrix known as the "alternating sign matrix." This is a story that began with Charles Dodgson (aka Lewis Carroll), matured at the Institute for Defense Analysis, drew in researchers from combinatorics, analysis, and algebra, and ultimately was solved with insights from statistical mechanics. This talk is intended for a general audience and should be accessible to anyone interested in a window into the true nature of research in mathematics.

MAA Distinguished Lecture: David Bressoud

Biography: David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple University and then teaching at Penn State for 17 years, eight of them as full professor. He chaired the Department of Mathematics and Computer Science at Macalester from 1995 until 2001. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Université Louis Pasteur (Strasbourg, France), and the State College Area High School.

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Rüdiger Thiele, University of Leipzig
August 8, 2007

Nowadays, the idea of function pervades mathematics, and math students readily recognize the notation f(x) as representing a function. But it took centuries for mathematicians to go from the use of algebraic expressions for describing certain curves to the general notion of formulas (or functions) as stand-alone objects of considerable mathematical interest in themselves. Leonhard Euler (1707-1783) played a fundamental role in making the function one of the central objects of mathematics.

On Aug. 8, an audience of Euler enthusiasts at the MAA's Carriage House Conference Center heard mathematician and historian Rüdiger Thiele of the University of Leipzig speak about Euler's work on functions. Thiele's lecture, titled "How Euler Changed Analysis," focused on Euler's efforts to broaden and apply the notion of a function in a variety of mathematical contexts.

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