The Chess Mind

Author: Dennis Monokroussos.
This is a blog for chess fans by a chess fan who is more than a chess fan - other topics do creep in from time to time, per my interest.
All material here is copyrighted, and may not be reproduced without my prior permission.
Is Chess A Theorem?

That's the question GM Genna Sosonko raises in the newest New In Chess Yearbook (#90). What does he mean, and what is his conclusion?

He doesn't offer a definition, but from his examples one gets a clear enough picture of what he has in mind. Theorem-chess, we might say, is a way of approaching the problems in a game as a series of formulae to solve: by playing this or that opening (for Black) and exchanging pieces x, y and z, even at the cost of a pawn, I achieve such-and-such an ending (e.g. with opposite-colored bishops), force the White pawns on the right squares, and draw in my sleep. It's an approach I sometimes call "recipe chess", and it's one I've used at certain times, and have seen in some of Kramnik's and Anand's draws with Black (examples: Kramnik's 6th game vs. Topalov in their match and Anand's draw with Gelfand in the second cycle of Mexico City).

There's something very seductive about this approach. Much of theory - in junk openings especially, but in serious openings too - attempts to structure series of moves into wholes - recipes (or formulas, or "theorems") - allowing Black to achieve a technically drawn or White a technically won position. And given many of Sosonko's examples (very good ones, at that) you might think he's advocating it as well. At the end of the day, though, he's not - or at least not without very heavy reservations. Here are the final paragraphs of his essay (p. 26):

I am not without sin in this respect. [DM: Playing lines where Black is worse and has to suffer a bit trying to hold one of these formula draws.] For a very long time I considered the position after 1.d4 d5 2.Nf3 Nf6 3.c4 c5 to be almost equal and I analysed it time and again, trying to keep slightly inferior endgames upright. In my results I alternated a string of draws with the occasional defeat.

I quit playing the line when I read a comment by the great Aaron Nimzowitsch. In a complex position he was trying to find the best move, calculating several lines over and over again until he said to himself: 'Quit! A chess game is a struggle, not a theorem'.

This looks like a repudiation of especially the modern theoretical approach, but Sosonko takes a step back in his final comment.

Although the ever-present computer has made certain corrections to this definition, I strongly believe these words should not be forgotten, even in our days.

I believe this strikes the right balance. Qua chess players, we should know as much as possible, but we must know that there are things we don't (and maybe can't) know, too. Chess is a struggle!

Posted by Dennis Monokroussos on Monday March 9, 2009 at 10:21pm
Daniel:
An interesting though that he mentions computers because isn't this the main human advantage computers still don't have? I mean to be able to think in these theorems terms where appropriate.
3.9.2009 10:29pm
NateC (mail):
Don't tablebases prove that chess is a theorem or at least that chess games that are simplified into endgames with few enough pieces become theorems?

If every game can be eventually simplified into a set of theorems it would make sense that chess begins as a set of theorems that we just haven't defined yet. I realize that this seems sterile and definitely not romantic.

Dennis' thoughts on opening repertoires sometimes being structured into recipes reminded me of this link that I had recently read. Reading Wolfram's thoughts in the context of this blog entry makes me wonder if we took a large sample of chess literature and represented that data as mathematical formulae if we could use that knowledge to solve certain chess positions. Say for instance IQP positions with a certain set of pieces is always won or lost for a certain side. I assume ideas like this frighten and sadden correspondence players, but bears little significance to OTB chess as most humans would be incapable of memorizing all of the synthesized data.
3.10.2009 1:33pm
KWRegan (mail) (www):
A particular case is what I know as the "[GM Boris] Alterman Gambit" in the Dragon with 9.0-0-0 (12...Nxc3!?), called the "[GM Kai] Bjerring Variation" in this recent ChessBase item. I think a knowledgable player with a computer and a few disposable weeks (and an engine with persistent hash or easily-reloadable analysis trees) could pretty much prove it a draw. Parts of the tree would have to be knowledgable assessment rather than exhaustive analysis, but that can be handled by storing user evaluations a-la Crafty or Shredder (or Rybka?)---and is indeed no different from proof-case shortcuts that are standardly fine when proving mathematical theorems.

Mind you, GM Nigel Short in PlayChess chat once referred to the Sveshnikov Sicilian as a "drawing line". Yes, Capa &Co. prematurely worried that chess was being "played out", but the difference is that now we may have the technology to effectively play it out. Another coal-mine canary IMHO is this by Kasparov quoted today by Susan Polgar here: “About 50 years ago, the average age of a chess player was about 35 years. Nowadays, 14- year- olds are becoming Grandmasters. This is due to ( the advent of) computers and sophisticated softwares,” he said. [emphasis mine]. A quote at the end about people today wanting to know not "a good move" but "the move" [the engine's move?] is also relevant.

I stand by my position that by mid-century, chess at top levels will have to become something like this---which I don't think is so easily "theorematizable"!
3.10.2009 5:59pm