I have to choose a research-like project to follow the next year. Because I'm a chess enthusiast, I was thinking of trying to tackle an (open) problem related to chess, and relevant to mathematics.
Can you suggest some material on the "mathematical side of chess" and related problems?
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Writing a chess engine that plays only moderately well, is a considerable programming challenge. Imo, very few people have the discipline, ability and patience to actually organize and execute something like that from scratch, programming-wise.
There are some open sources which you can see and read, like that of GNU chess, Borland's Turbo chess and several others which have ended up public, yet it still is fairly difficult to even manage to improve some already existing engine.
I'd gladly consider it a fairly hot subject for a Ph.D. thesis.
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I studied rook polynomials. This problem asks how many rooks can be placed on a board in non-taking positions and has applications in scheduling.
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The following link in chess.stackexchange https://chess.stackexchange.com/questions/27259/has-anyone-attempted-to-characterize-chess-mathematically is a quick sketch I made of some math areas for chess. Something might catch your interest - please ask me if you want to know more.
In the most recent issue of the Spanish magazine Problemas, there’s an article (in English) attempting to resuscitate the genre of mathematical chess problems for the prestigious FIDE Album. Perhaps a bit dry, it has been well-received by the chess problem community. See issue 40 at the bottom of http://sepa64.blogspot.com/p/revista-problemas-nueva-epoca.html?m=1.
Chess is really so plastic a form, that it’s perhaps best to ask what kind of mathematics interests you, and I can maybe give more focused examples of what folk have been doing in this space.
The Knights tour is a famous chess/math problem.