Abstracts for Keynote Speakers
Mathematics on the Northern Plains
2005


DO MATHEMATICIANS REALLY MEAN WHAT THEY SAY?  QUESTIONS FROM THE PHILOSOPHY OF MATHEMATICS
Jason Douma

Mathematicians are more than willing to throw around phrases like "there exists" and "we know that...is true" in their formal writing and informal conversations.  But what do the notions of "existence" and "truth"-or even "knowledge"- mean in the context of mathematics?  Surely, a finite cyclic group does not "exists" in the same sense as the chair in my office.  A true mathematical statement such as "all continuous functions are integrable" seems qualitatively different than a true empirical statement such as "I have a brother named greg."  This talk will explore possible responses to the philosophical questions raised by attempts to find meaning in mathematics.

CROSSING THE BORDERS BETWEEN THE MATHEMATICAL COUNTRIES.
Isaac Kornfeld

In this talk I will discuss some of my favorite mathematical problems. Most of them can be called "problems with unexpected solutions". They are formulated in terms of certain areas of mathematics (say, in algebra or in calculus), but the ideas for their solutions come from "across the border", that is, from different mathematical subjects. For example, one can look for a geometric solution of an algebraic problem, or probabilistic approach to a geometric problem.

Problems of this kind illustrate the aesthetical side of mathematics and help people to understand that mathematics should be valued not only for its utility, but also for the remarkable beauty and elegance of the mathematical way of thinking.

All problems discussed in this talk will be accessible to freshmen and sophomores interested in mathematics.