how many moves deep can i think ?
what's the material balance etc ?
is my king in the Queening square of that pawn ?
that's the math i use. the rest is spotting anything that can lead to positional advantages, combinations, won endgames etc, being knowledge-based and style preferences.
Your reward for that erudite answer must surely be a big FISH.
@Stevie, great picture of a cat in scuba gear (above). 
yum!
Math and chess are cousins.
They are first cousins.
Whoa! Deja vu!
I guess it's time to wave farewell to this thread. People will continue to argue that positional understanding has nothing to do with "math" because they aren't counting.
Here's a good definition of mathematics as compared to arithmetic:
a·rith·me·tic
(1) the branch of mathematics that deals with addition, subtraction, multiplication, and division,
(2) the use of numbers in calculations
math·e·mat·ics
(1) the study of the relationships among numbers, shapes, and quantities,
(2) it uses signs, symbols, and proofs and includes arithmetic, algebra, calculus, geometry, and trigonometry.
Chess is also the study of the relationships among shapes and quantities. In fact, positional chess is entirely about relationships of shapes and patterns. As chess players, we are constantly evaluating which pattern, which position, is better than the other one. That's mathematics.
But try persuading these people that.
Yeah but the evaluations are more judgmental; evaluations are possible to prove in chess, but would be very hard to actually do. For example, if you say a position is better because of the superior knight, and cite a won game with that knight, another person could reply "but your opponent could have just done this move, solving his problems, but missed it." In practice, I think positional evaluation is almost philosophical in nature.
It's almost like poetry in a way: you interpret what the position of each piece (words) means. Again this kind of poetry (chess planning) is provable in theory, but not so much in practice; and so, you will probably be using certain non-math skills in finding a plan.
We definitely need more dictionary definitions in these threads. I lost my dictionary and don't know how to find one on the 'net.
"these people?" Sheesh!
If I could find that damned dictionary, I'd post the definition of humility. Better yet, I'll go find a publican.
I mean, if we had clear variables, we could define positional chess mathematically -- we could say pawns on e4 and f4 are worth this much, knight on e5 worth this much, but the problem is, it is very arbitrary how we pick these evaluations. For example, it's not good enough for us to say that a knight on e5 is worth "this many tenths of a pawn," because there might be some positions where a knight on e5 does nothing. If we were geniuses we might find a precise numerical way to account for every possible position with a knight on e5 and its value in those respective positions, but we don't. We are much more philosophical about our way of evaluating things.
Philosophy isn't really allowed in calculations like elasticity, is it? But in chess it's something we rely on to make plans as a shortcut. We don't really say "this move is good because we get a knight on e5, +.38, attacks the f6 pawn, +.12, and even though it allows black to play ...b5, -.17, the evaluation comes out to be pretty good for the move." It's more like, "I don't think ...b5 really does that much, whereas my knight on e5 seems to be really useful."
It's true that we are valuing the knight on e5 more than the queenside pawn break ...b5; however, we are justifying it with vague logical ideas, rather than systematic calculations. Although as we have seen this scenario can be expressed by math, the scenario itself doesn't force us to be mathematically strong to reach a good conclusion. Liking one thing more than another could perhaps be called math, but it's the kind of math practically anyone can do, so that's not saying much.
Absolutely not....! Has nothing to do with math. Atleast not as far as us humans playing it anyhow. Chess is a game, that's all. Some people like to relate to chess as some mathmatical thing because of how you record moves. Looks mathmatical on paper but it's not. It's a game....and a good one at that!
at a decent level of abstraction, mathematics is about objects/entities and the interactions between those objects. chess is very similar and much of chess theory attempts to explain/explore the properties of the objects of chess.
i don't know what the latest philosophical status is on the existence of mathematical objects...but it could be argued that even the mathematicians are 'just playing games'.
To me the relevant question is not whether chess can be expressed by math (I agree, it can be), but rather, does it require math skills to be good at it? In some ways, maybe, but not necessarily. I think that judgment, while possible to express in math, can be had as a good quality without that person being good at math at the same time. The point is he just needs to understand relative value; that's a rather soft math if you ask me. A more rigorous math would be finding an equation that expresses a number that nearly precisely represents a relationship, rather than just observing one.
For instance, I would say it requires more mathematical skill to be able to write equations for evaluation systems in an engine than it would be to actually be good at evaluating positions accurately yourself, as a human.
The point is, the human doesn't have to express what he thinks as a complicated function; he merely follows this function 
. I think it's pretty easy to value the taste of chocolate ice cream higher than that of vanilla (you prefer one without any effort at all), but much harder to determine what neuron placement and concentrations of neruons (among other things, of course) in our brain makes a person like or dislike a certain type of ice cream more than others.
Back in the 40's and 50's chess was considered a game for geeks and high I.Q. people with mathmatical skills. Nothing could be further from the truth ! It was just a game that was played by those that didn't get into football or any other comtact sport,,,that's all. Don;t wast your time putting some matmatical crap into chess. It's just a game where if you play it often,,you'll get better and better.
"Elubas wrote:
To me the relevant question is not whether chess can be expressed by math (I agree, it can be), but rather, does it require math skills to be good at it?"
I fail to see the relevance of such a silly question. It's spurious. Any idiot who puts forth some effort can do math . Any idiot can play chess if they're willing to put forth some effort.
Quite frankly, I'm surprised that you find that question relevant, Elubas. It's quite contradictory to your established view-point as regards talent, i.q., and the other ubiquitous, spurious questions that are bandied about hearabouts.
... I posted a funny image, in which a character made a comment relevant to math, but then I deleted it because it had a bit of profanity. Sorry, chess fans. :(
I'm not really sure what your point is here, bigpoison. For example, what are you implying with your "any idiot can do math or chess?" In fact, I probably agree with whatever point you are making, I just want to know what that point is. For instance, I wouldn't disagree that math skills could be learned.
Otherwise, it just seems like you are unnecessarily insulting me for what I am talking about. I'm just throwing out ideas here; this forum posting isn't a matter of life or death. In any case I'm not sure from your post what specific problems you have; I know you have problems with them, but I don't know what they actually are.
By the way, I'm not sure how a question, not a statement, that isn't intended to fool people can be consistent with the definition of spurious.
Oh, I wouldn't call it a problem. The point is simple: some goof rated 2000 USCF might not have any idea what a tangent is, but he can learn if he does the work.
I'm certainly not saying that anybody who works hard enough can achieve the pinnacle in any given skill; but any normal person can gain proficiency in nearly any non-physical human endeavor.
To say, "oh this dude's good at math; he'll be good at at chess," is no more relevant than saying, "oh, that dude can identify every tree in the woods; he'll be good at chess."
It's not a genuine question; rather, a statement that aims to nudge people into making associations that are based simply on what the questioner is leading his audience to believe. Thus spurious.
I certainly never intended to insult you. You're a charming young lad whose posts I read regularly.
Well, bigpoison, I happen to agree with everything you are saying. Even though one can find similarities between two things, they are still different things. My quoted post was simply saying that just because something can be represented by math doesn't mean that it's all about math.
After all, in my post I did imply that, despite that sentence, I don't think math skills are necessary to be a great player.
You could akin mathematics to anything,even taking a dump..Analysis and chess are related.Analysis and mathematicians are related..But analysis is not the excluse of mathematics,nor chess alike.Mathematicians use analysis daily therefore putting them in good stead for playing chess(A strong analytical mind).There is no congruity between mathmeticians and chess.There is no congruity between humans and mathematics.You have to learn both.Analysis is the common factor.
As the OP's question is only" Chess and mathematics" then the simple answer is yes as everything has mathematics in it.But i think that is a little shallow as we all know mathematics is in everything.Not sure if Tantale meant that!
However if the question had been "playing chess and mathematics" that to me has a little more depth.
You could akin mathematics to anything,even taking a dump
Why do they call it "take a dump" when actually you "leave a dump."
how many moves deep can i think ?
what's the material balance etc ?
is my king in the Queening square of that pawn ?
that's the math i use. the rest is spotting anything that can lead to positional advantages, combinations, won endgames etc, being knowledge-based and style preferences.