Man, I love unsolved problems in any field of science or philosophy. This does not mean I don’t enjoy reading the elegant solutions or re-derivations of solutions to problems solved long ago (I’m looking at my grad studies Galois Theory prof and his re-derivation of everything in that subject using category theory.) However, there’s something energizing to seeing that not every problem has been solved and that science isn’t perfected.
In fact, nothing sends a chill up my spine more than when an experiment in Physics could potentially disprove a well accepted theory. Every time that has happened historically, the world changed (and usually for the better.)
But, I’m not a physicist and while I enjoy playing with the mathematics of quantum computation, I am a math major historically, and a mathematics buff through and through. Thus, I’m putting out this request to anyone who sees it. I want to know any unsolved problems you know of (beyond the obvious clay mathematics prizes) that you are aware are unsolved. Whether they are simple conjectures from combinatorics, to open questions from long long ago. If you have them, I want to hear them. If only so I have more fun things to play with whenever I get time.
Plus, it’d be pretty spiff to have one page (this blog entry) on the web as a central resource for mathies who are interested in these problems.