It is possible that it may be solved recursively.Uri Blass wrote:I cannot prove that there is no short mathematical proof to the solution of chess but I believe that there is no short mathematical proof that human can understand.playjunior wrote:Uri, a "mathematical proof" has nothing to do with "number of possibilities". Out of all mathematical proofs I have seen, very few are considering distinct cases.
There may be a proof that does not consider every possibility and only has size of 10^20 but I do not believe that there is a proof that human can understand.
Note that the claim that every map needs only 4 colors was proved with the help of computer so I believe that a proof with the help of computer for the solution of chess may be possible in the future.
If you prove that 1.e4 has a certain outcome, then you have to prove the other 19 possible first moves have a certain outcome.
Perhaps that is too tough, and it is 20 plies deep where you can prove it. Now we have what looks like an insurmoutable mountain of things to prove, but maybe they are really much easier and maybe a million computers working in tandem can solve it.