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?