The fact that AlphaZero was trained without using any pre-existing human chess games (or games played by other chess engines) seems of less importance than the fact that it taught human beings new techniques - something about how to put pressure on individual pawns, I heard. Any method to produce new techniques that humans can learn and use is interesting, regardless of whether a human or computer did it, and regardless of how much existing knowledge was or wasn't fed in.
In math, rather than arguing over what conjectures are too big or small to include on the list or the plausibility of computers proving conjectures without prior input, it seems better to formulate problems that, if solved by computers, would constitute computers helping human mathematicians in some way, for example by teaching us new techniques.
One could carefully select conjectures that the greatest number of mathematicians would like to cite a proof of but the least number of mathematicians want to prove or one could literally try to get someone to bet on a challenge like "10 new entries are added to Tricki describing tricks of a similar nature to the existing entries developed by AI mathematicians" or "AI programs a virtual reality system that allows humans to prove the geometrization conjecture visually." Why not?
The fact that AlphaZero was trained without using any pre-existing human chess games (or games played by other chess engines) seems of less importance than the fact that it taught human beings new techniques - something about how to put pressure on individual pawns, I heard. Any method to produce new techniques that humans can learn and use is interesting, regardless of whether a human or computer did it, and regardless of how much existing knowledge was or wasn't fed in.
In math, rather than arguing over what conjectures are too big or small to include on the list or the plausibility of computers proving conjectures without prior input, it seems better to formulate problems that, if solved by computers, would constitute computers helping human mathematicians in some way, for example by teaching us new techniques.
One could carefully select conjectures that the greatest number of mathematicians would like to cite a proof of but the least number of mathematicians want to prove or one could literally try to get someone to bet on a challenge like "10 new entries are added to Tricki describing tricks of a similar nature to the existing entries developed by AI mathematicians" or "AI programs a virtual reality system that allows humans to prove the geometrization conjecture visually." Why not?