# Nearest Points and the Chebyshev Set Problem

#### Dr. Jon Vanderwerff

The question as to whether a Chebyshev set in a Hilbert space must be convex has been described by some authors as perhaps the most important problem in abstract approximation theory. This talk will attempt to explain the Chebyshev problem and use it to illustrate that unanswered questions in abstract mathematics are not just esoteric puzzles that fascinate specialists, but that they can be geometrically intuitive and related to relevant topics---and this particular problem just might even involve mathematical concepts connected to research interests of Tom Thompson and Ken Wiggins.

A link to slides from a talk that describe the Chebyshev set problem and provide some additional background information and references is as follows:

Jon completed a mathematics degree from Walla Walla College in 1985 and in doing so he was fortunate to have taken classes from some of the best mathematics professors anywhere! In his doctoral program he studied the geometry of Banach spaces, although that topic has very little to do with what most people would consider geometry or space.

Currently, Jon is a professor of mathematics at La Sierra University and has found that a career teaching mathematics is not only fun and rewarding, but along the way he has met fascinating people and visited interesting places that he otherwise would not have imagined doing.