An Open Problem Approach to Mathematics

Jour Fixe talk by Patrick Speissegger June 07, 2017

Patrick Speissegger is a professor at the department of mathematics & statistics, McMaster University, Canada, and a Senior Fellow of the Zukunftskolleg.

What motivates researchers in pure mathematics?  Sometimes it happens through a bottom-up approach: you enjoy building on existing theories by generalizing their concepts and ideas.  Other times, it happens more through a bottom-down approach: you consider some open problem (called a "conjecture" in mathematics) and try to figure out how to improve existing theories or outright invent new ones, so that an answer to the open problem (or often some variant of it) can be given.  For the most part of his stay here at the Zukunftskolleg (and a few years before that...), Patrick has been working with the second approach, motivated by the second part of Hilbert's 16th problem, which was conjectured in 1900.  He will give an overview of some of the lively history of this problem and along the way explain his own related work.