<i>Euler's hypothesis was disproved in 1987 by a Harvard graduate student named Noam Elkies.</i><p>And partially as a result, Noam ended up one of the youngest ever tenured professors at Harvard (at the age of 26).<p>I met Noam when hanging out with guys from the Harvard Glee Club, which Noam accompanies on piano.
Reading Noam's CV (<a href="http://www.math.harvard.edu/~elkies/math_cv.html" rel="nofollow">http://www.math.harvard.edu/~elkies/math_cv.html</a>) was one of the most humbling experiences I've ever had.
I'm amazed that more of these are not posted to Hacker News. The solution of math problems seems to forecast innovation:<p>ie: <a href="http://en.wikipedia.org/wiki/Road_coloring_conjecture" rel="nofollow">http://en.wikipedia.org/wiki/Road_coloring_conjecture</a><p>was just recently solved.
Mathematica is a great tool for math hackers. The only problem is that these kinds of problems are addictive, and take time away from what I "should" be doing.<p>But often I learn something by allowing myself to play "just a little..."