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RE: Knight tour - graph theory problem related to chess.
Hi. Thanks for Yur comment.
In 2000 7 mathematical problems for XXI century were chosen. Making solution for any of them is paid by Clay Mathematics Institute. However, Russian Gregorij Perelman who solved one in 2003, decided not to take money.
Finding deterministic algorithm running in polynomial time for Hamilton cycle (or proving it does not exist) answers first problem, popular "P vs NP".
Here is more:
https://en.wikipedia.org/wiki/Millennium_Prize_Problems
If You will have more questions I will answer tomorrow.
Thanks for that information about the Millennium Prize problems; it’s just as interesting as the graph.
Thanks. I can write more now, I have cancelled exercises and lectures on studies until 14th April. Do You have any mathematical questions which You want me to write article about?
Yes, as a matter of fact I wrote a chess program a few years ago, haven’t updated it though. And it was always my intention to find some way to use calculus (rate of change) equations to be a part of the chess engine. For many years I believe it could be done as oppose to ten or more iterations (loops). I’ve been lead to believe very early on that calculus could be applied to everything.
Can one apply calculus to a chess program?
Hmm. I think that the future in computer in games is localised in machine learning. I think that it is too hard to measure precisely how arbitrary move will change the strengths. One different postiion of one figure can turn move which is at 1000 situations very good move into a very bad move. I think that chess are too complex to even write such equations, not saying about implementating them. Machine learning computers win in Chess, in Go, in Starcraft 2 easily with human. This is the future I think.
Maybe for checkers it would be possible, but it wouldnt be worth to do it I think.
Thanks for your reply and I agree.
Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute on May 24, 2000. The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap. A correct solution to any of the problems results in a US$1 million prize being awarded by the institute to the discoverer(s).
To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman, who declined the prize money.