Although both involve a high level of deductive reasoning. How similar are the respective thought processes of chess players and mathematicians? Why would one choose to reason deductively in one context rather than another?

The first question can be answered in several ways, but I won't go into that.

For the second: Chess is fun! IMHO, it could be more addictive than crack but also more frustrating than running flat at poker: e.g., "Chess Tempo" site. What attracts me (unlike so many chessplayers) was the aesthetics of the chess endgame study: not only from the perspective of a "solver", but also from the compositional viewpoint ( IMHO, the endgame study is truly "art" in chess). Mathematics can be "fun" too, but it can be "enormously difficult" (but also challenging) as you probably already know!

Short answer in favor of chess: Competition.

I don't think they're even remotely similar.

Math is like a puzzle. Chess is like a language. I can not think and do perfectly fine at chess simply because it's just so ingrained that thought is not necessary to perform well above average. In math, even once I reached a high level of study - even rudimentary problems would still require thought and effort.

Math: 2+2=4

Chess: Checkmate.

Not similar

not all good chess players are good at math but mathematicians make good chess players

That's a silly answer. You mean mathematicians have strong nerves, are skilled in time management, avoid one move oversights. . .

As a one on one competition, chess in many ways has absolutely nothing to do with math.

Edit: I probably just got levelled?

well not quite, i did cut a few corners with my point though. :P mathematicians seem always to be 1700+ for the sample i have seen, maybe it's because they like boring things

Pretty much agree; e.g., my wife thinks I am often obsessed with "boring" things such as chess. Out of all "games", IMHO, chess and bridge are easily the most interesting.

Math: if x = y and y = z then x = z.

Chess: if 1. f3 e5 then 2. g4 loses.

Similar.

FYP.

I think it's better to state that if someone has some of the requisite skills to be "good" at one of (chess/math), it's likely that he/she will also be "good" at the other, but to be honest, I haven't researched how strong this correlation would be between mathematics and chess, especially at the "higher levels" where it really counts. Another discipline where there is considered to be strong affinity with mathematics is music.

Noam Elkies is a famous mathematician ( he held the record at one time for the youngest full professor at Harvard ) and endgame study composer ( I think he was also editor of EG, a chess periodical as well ), but I don't know much about his musical compositions. Today, being one of the best OTB chess players in the world ( say, top hundred ) usually means a full-time commitment; since it's not much different in mathematics ( to be a "top researcher" ), the people that are heavily interested in both ( yours truly included ) are....not the "cream of the crop"! Of course, chess and mathematics can be highly enjoyable pastimes.

I accomplished more in math than in chess, and I took both semi-seriously at one time.

Competitiveness helps a lot in chess, the old fighting spirit. The eye of the tiger. In math you can sit back and let your thoughts simmer and drink a lot of coffee until the proof comes to you, but chess doesn't afford that luxury.

But not many 1700+ are mathematicians!

In my opinion, people who are able to succeed in one challenging field are frequently able to succeed in other challenging fields assuming they're willing to dedicate themselves to it. But I think this has much more to do with self motivation, discipline, etc than it does with anything like 'intelligence'.

...there's always correspondence.

Heh, correspondence chess has to be the origin of "going postal", cause it makes me want to shoot people. I prefer squandering a winning position and blundering in time pressure in a 2 hour game to ruining an entire evening thinking about 1 silly move.

Chess and math require alot of the same analytical type skills.

I've always felt that a chess combination is a bit like a theorem in which the moves and forced replies are the deductive steps and the final position is the conclusion. The rules are like axioms. In fact, studying opening theory is very similar to studying something like axiomatic geometry. You can't ever prove an absolute truth, but the exploratory/logical/creative thinking required is similar.

Whenever I think about all of the computing power being thrown at the various branches of mathematics and wonder if someday there will be nothing left to prove or discover, I think about chess and how we could devote all of the computing power in the world to solving the game and it still would never happen.

How much of math reduces to pure manipulation of symbols according to certain rules, like in chess, has been an important question. I think a rough analogy is:

opening position = axioms
rules of chess = rules of logic
legally reachable positions = theorems

Fist post in chess forum*

At the risk of sounding stupid (becuase I am certainly no expert on this), isnt there real measurable math in chess? When certain movers are made and then compared against a data base of a million games, cant there be a % win aplied to that specific move in that specific place? Then one can dertermin there esimate of what their oponent will do (just like in poker, "i feel 75% sure he will do this when I do that" kind of logic) . Between the data from the mass sample of games, and your knowledge of an oponent, you can use math like equations (I admit really simple ones like in poker) to chose your opening strategy?

My gut tells me there is alot more direct aplication of math to chess, I just cant find it yet.

Open season to zing me if I said anything really dumb.

Good discusion.

Chess is, I believe, an algebra, technically. I'm not 100% on that, though.

Sort of. Since chess has no luck and has complete information, every move in every position is either drawing, winning or losing. It is only because chess is so complex that we don't know all of this completely. Database statistics can help us guess at what the true value of a move is, but they're very, very imprecise. Normally concrete analysis by top players is what will give us the "truth". So I guess I'm suspicious of using statistics like you would in poker. I'm trying to think of how math is most readily applied to chess and I'm not quite sure.

Computer heuristics break down positions into numbers. "x" points for king safety, "y" for piece mobility, etc and they're good enough to beat most of any human.

Opening win % is not mathematically meaningful for a simple reason. Once a refutation (or refinement of defense or whatever) of some idea is discovered, a line will suddenly be played drastically less. So let's say you have a million games with some move where white was scoring really well like 66%. Then all the sudden it's later discovered that black has some way to force a perpetual or other drawish idea and so the line all but disappears from frequent play. Now you have a million games where white is still scoring 66%, and maybe a few thousand where he's only scoring 52% or whatever so your aggregate will be like 65% still making that line look extremely viable. So basically an opening that's scoring 57% might actually be stronger than one that's scoring 65%.

FYP

There seems to be an unfortunate misunderstanding of what the practice of modern mathematics is as alluded in your post, i.e., many people think that mathematics is simply the "pure manipulation of symbols according to certain rules"; however, what these people fail to understand and appreciate is how those symbols are to be "interpreted" for there are infinitely many ways to "interpret" them. Mathematics is much "richer" than chess and that a more appropriate analogy is how can the "rules of chess" ( board, pieces and movement ) be changed to retain the concepts we would like to have and in a "manageable" way for humans. I'm not merely speaking of something like Chess960, but the board could be enlarged and other "types of pieces" can be included. Then, among "all the variants of chess-like games", what are the right concepts to retain and which "variants" are the most interesting to analyze? Obviously, if we extend the board to 100x100, it isn't "manageable" even though one could have a "chess-like game"; similarly, if we have hundreds of different types of pieces with different characteristics, that would be "unmanageable". Mathematics tries to find those concepts that bear fruit in giving "interesting results", whether they are theorems or more abstractly, other fields of mathematical study. Naturally, for those ideas to be meaningful, they need to be expressed through symbols so that others may be able to comprehend; however, even if they are expressed, they may not necessarily lead to any understanding except for a very small group. Also, a "chess-like game" may not be very interesting practically, if for example, there isn't much "balance" (e.g., if the first player often wins, or one tiny mistake and it's game over!), or little "conflict" ( the opposing "forces" should come into contact without much waiting ), or no "resolution" ( not much point if the game takes more than thousands of moves to finish ) or is extremely difficult/simple to analyze ( e.g., finding candidate moves, and the typical "tree of analysis" isn't significantly larger or smaller than what one typically finds in normal chess). In mathematics, one is sometimes asking for which "reasonable" set of axioms ( which we may or may not know for a long time, if ever! ) can one get these concepts that we would like to have.

I think chess and mathematics are similar in the higher level thinking processes, but they obviously also differ for several reasons. Also, arguably what is fashionable in chess opening theory often has very good reasons; analogously, algebraic geometry is popular because of its applicability to solve problems ( that have been considered important in the last fifty years ) generally.

In chess, at the lowest level, it's something like "if White plays x, then Black can only play one of y1, y2, ... because z1, z2, ... are bad because of ..." with lines in the "tree of analysis"; more abstractly, the logic might be " if White tries to execute the plan of X1, X2, ..., then Black must respond with the plan of Y1, Y2, ...". Opening theory is often like that, too: e.g., some lines are abandoned because either there is a clear plan leading to a known advantage or clear equality or there are "several roads" making it less likely to be "critical". Also, for a chess player OTB/"corres", it's helpful to envision some "target positions" to achieve: e.g., if I can get to one of these "nice positions", there should be some advantage or equality is achieved.

In pure mathematics, at lower levels, it's something like "if these are the axioms, using the rules of logic, these are the theorems". At the higher levels, it's more like "to solve this type of problem, the ideas X1, X2, ... have been shown not to bear fruit; therefore, some new ideas need to be explored, i.e., likely ones that have not been found as of yet" or "the central ideas of theory X turn out to be the concepts Y1, Y2, ...; are there other important ideas?". Usually, these ideas are laid out for us in a "nice way" in textbooks; if not, then that usually means there is some room for discovery. A good question in mathematics is "What are the most important algebraic structures to study and why?". As a simple example: "What are the most important characteristics of binary operations?" [ It turns out that commutativity is not nearly as important as associativity. ] Thus, to explore symmetries, it is clear to consider groups and therefore group theory is highly relevant, but it is not as important to consider only abelian groups. Today, there are probably not many visionary mathematicians trying to create vast frameworks as in the past ( such as Grothendieck ), but there are still many undiscovered fruitful ideas awaiting us.

Well I'm not one of them. I said it has been an important question, and was alluding to this research programme:

http://en.wikipedia.org/wiki/Hilbert's_second_problem

I didn't mean that's the whole of math or anything like it, or to push the analogy too far (see title itt). Awesome post, bigpooch.