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> though a counterexample to a conjecture, does not advance mathematical theory in any way. [I realize it's sarcasm but in case it's not clear to everyone, I'l

> though a counterexample to a conjecture, does not advance mathematical theory in any way. [I realize it's sarcasm but in case it's not clear to everyone, I'll speak my mind about it] I think it's a pretty serious advancement. Confirming a conjecture is just as important as invalidating it with a counter example. It doesn't matter if that counter example fits on one line.

vostok 10y ago
Maybe my mind is warped, but I actually agree with that. The conjecture isn't the point. There are plenty of interesting counterexamples, but a direct search does nothing to advance mathematics.
- ipsin 10y ago
  It advances mathematics by saving the time of people who might otherwise try to prove a false conjecture?