What is ... Hilbert's 16th problem?

This page hosts information on Eyal Ron's talk "What is ... Hilbert's 16th problem?" at the "What is ...?" seminar. The talk will take place on Friday, April 16, 4pm at FU Arnimallee 6, SR 031.


Ever think that the Millennium problems were the first of their kind to be posed? Not at all! In 1900, David Hilbert, the godfather of math at that time, posed a list of no less than 23 unsolved problems in various math disciplines. These problems received remarkably large attention from the math community and a solution of one bestowed the solver with huge appreciation–and, much more importantly–a modest field medal.

As of today, ten of the problems have been completely solved. Another seven were "solved", where the quotation marks denote that the solution is either not fully accepted, or, worse, nobody is really sure what Hilbert meant when posing the problem. The remaining six problems still lay in the dark, waiting for a brave mathematician to one day come and save(=solve) them. An example? the 16th problem: the problem of the topology of algebraic curves and surfaces.

There are two equivalent phrasings of the 16th problem. The incomprehensible one–at least for me–and the one that concerns phase plane analysis and dynamical systems tools. What are these? what's the problem? and how can you solve it and earn an easy ticket to a good post-doc position and a comfortable tenure? all of these, and a myriad of other questions, will be answered during this seminar talk!

Bonus: It seems that bounty-problems generate much more media interest than regular ones. Therefore, I will personally offer a 100-Euro prize to anybody that solves this problem during the seminar talk!*

*In return the solver would be obliged to include my name as a co-author in the resulting paper. Fair is fair, right?


The video for Eyal's talk can be found at http://vimeo.com/12571548.


Topic revision: r2 - 07 Oct 2010, MimiTsuruga
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