(edit, 4:29 pm: the New York Times has picked up the checkers story. Jonathan Schaeffer, who led the research, says:
“It’s a computational proof,” Dr. Schaeffer said. “It’s certainly not a formal mathematical proof.”
By this, it seems that he means that it doesn't "count" as a formal proof because basically what they did was go through all the possibilities that could occur in a game of checkers, without really having any insight into the game. I would still call it a formal proof, as it does establish beyond a doubt that there is a winning strategy for checkers (assuming that no errors slipped in) but I can understand Schaeffer's feeling that what he has done is not mathematics. I fear this sentence might give the wrong impression to laypeople, though.)
Math is like music, statistics is like literature: basically, math and music are both self-contained worlds, while practitioners of statistics and literature both benefit from having life experience. Thus the best mathematicians and musicians are younger than the best statisticians and novelists. (In the comments to this post, I claim that this differs among different branches of mathematics; the conventional wisdom says this is true but I know of no hard evidence.)
7 comments:
Well, there's also the qualm that there might have been a glitch at some point and the computer might have made a mistake. The same goes for the proof of the four-color theorem.
John,
that's true, of course, but more traditional proofs can have errors in them as well.
NOOOOOOOOOOOOOOOOOOO! This is even worse than that horrible day when I first solved tic-tac-toe... :(
;)
Aaron,
perhaps we as a culture will just have to design more and more difficult games in order to counteract this?
From what I remember, tic-tac-toe variants on larger boards are actually quite difficult, although I don't have that much experience with them. (It's not entirely clear how one measures the "difficulty" of a game, though. I've heard various measures and none of them seem *entirely* satisfactory.)
I think that he said that it was not a mathematical proof because he didn't check all the possibilities. He just checked the likely ones.
Yeah... five-in-a-row tic-tac-toe on large boards can be pretty difficult. I know because I used to play it a lot in middle school. :)
Speaking of games I played in middle school, have you ever played the one where a turn consists of connecting two dots on a grid? If you make a square, you get one point and also another turn. Gameplay is maddening, because once there's no way to move without making a square, the outcome is pretty much predetermined... but it's impossible (at least for your average middle-schooler) to predict or control beforehand what the outcome will be!
Aaron, most people call it "the dots and boxes game", and it's far from predetermined at the beginning. To the contrary, it can be pushed either way by a skilled player. Elwyn Berlekamp even wrote a book about it.
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