If anyone is serious about proving things about chess I would suggest they start by proving things about simpler chess variants.
The variant of chess "wild 5" where your pawns start on the 7th rank and pieces on the 8th (so pawns promote in one move) has far fewer choices than in chess. It's a simpler game. It has a significant advantage for white, much larger than in normal chess. Humans came somewhat near to proving it's a win for white just by learning the (relatively few) openings out to 20 or so moves. At each step there's usually only a couple moves that aren't terrible. For the first six moves there is a single way of playing which is considered best for both sides.
Yet even in this much simpler game which humans are near cracking, I think a pure math type approach would have a very hard time getting anywhere.
If you can't do anything there, you could always try an even simpler game. There is a game called pawns where you start with only your pawns. If you promote you win instantly. Math ought to be able to solve that one. If you crack that, move on to little chess (normal chess but only with pawns and kings). Little chess should no doubt be a draw (you can waste moves with your king unlike in pawns where it's less clear) but proving that would be a good accomplishment I think.
The variant of chess "wild 5" where your pawns start on the 7th rank and pieces on the 8th (so pawns promote in one move) has far fewer choices than in chess. It's a simpler game. It has a significant advantage for white, much larger than in normal chess. Humans came somewhat near to proving it's a win for white just by learning the (relatively few) openings out to 20 or so moves. At each step there's usually only a couple moves that aren't terrible. For the first six moves there is a single way of playing which is considered best for both sides.
Yet even in this much simpler game which humans are near cracking, I think a pure math type approach would have a very hard time getting anywhere.
If you can't do anything there, you could always try an even simpler game. There is a game called pawns where you start with only your pawns. If you promote you win instantly. Math ought to be able to solve that one. If you crack that, move on to little chess (normal chess but only with pawns and kings). Little chess should no doubt be a draw (you can waste moves with your king unlike in pawns where it's less clear) but proving that would be a good accomplishment I think.