What's the relation between chess and math?

You are reviving my romance with Math ♥️  I haven't opened a Math book in the last 25 years. I stop aftert Numerical Analysis.

l don"t get it!!!!!!!!!! l don"t get why people think chess and math is kind of the same!!!!!!!!

There might be some relation

Yah

yes.

Pattern recognition is the recognition of patterns.

I think people may differ on what they consider to be a pattern. Is proof-by-induction a pattern?

The reason for prodigies in chess, music, and math is the same as that of a 1-year-old being able to learn any language on earth in less than a year without teaching.

There is something inherent in human logic, the ability to see and understand certain patterns. Chess, before all theory of openings and theoretical endgames, is all about combining the pieces into formations favorable to the checkmate, which is in itself something simple to understand.

So, just as there is no need for further explanation of what a square is and what a circle is (from the empirical point of view), it is also not necessary for a 4 or 5 year old to understand what music is or such as playing chess or mathematics (the language present in both arts: chess and music).

Unlike a sport that would require a more evolved biological structure, chess can already be applied as soon as humans can recognize geometric patterns!

I once heard someone note that chess, math, and music were all fields that do not require much in the way of outside-the-field knowledge.

Regarding the 3 fields

GM Kamsky, Taimanov excel in Chess, Music

GM Nunn and Lasker Chess, Math

Anybody knows any GM excelling in Chess, Music and Math?

What I understand is 'recognize geometric patterns' is possible and 'natural', but not evolved at maximum in each person. IQ tests, for example, can test that sptatial and recognition of some patterns, symetry, continuity, etc.. And as we all know, not everyone will get good scores on these tests.

What I'm  thinking now is: What if IQ test for GMs? It is not certain that every GM has a high IQ, but what if an IQ test is done to test only logical-spatial intelligence, would a GM always score higher than average? (although I do not want to say that who does not play chess does not have a good score, anyway, I think you understand where I want to go ...)

WC Smyslov is Opera singer too.

I seem to be pretty good at music, maths, and chess.

By that, I mean above average for the first two and relatively good for the latter for the amount of time I've been playing.

Hahaha.....computer player will never understand chess

As an electrical engineer I often build analogies when learning things to help create models in my mind-  a very basic example of this when learning circuit theory dealing with voltage and current is the plumbing analogy-  current is the diameter of the pipe and voltage is the pressure(or height of the water),  a capacitor is equivalent to a water storage tank, etc...   Basic elements that you can model in your mind that build a working picture.  I also grouped equations in my mind- most physics and engineering formulas are one of just a few equations with simply the formulas changed Force = mass * velocity is the same basic equation as power = current * voltage. 

These are simple examples, but you can use visualization techniques to help understand much more complex subjects like maxwell modeling of electromagnetic fields, fourier transforms, etc.... 

I think one of the greatest challenges I have had learning chess (and why I still stuck very badly at it)  is there is no universal equation and I have yet to create a model or system in my mind that really provides me with intuition about chess.  There are so many elements, think about all the different values that can be used to evaluate a game:

Tactical-  "white has no hanging pieces, blacks bishop is attacked twice and defended once"

Strategic -  higher level view of game flow than tactical

Pawn Structure - this can be it's own unique element in the game

Space- who controls more space has more liberty to arrange their pieces in the best possible way

Tempo-  taking time from your opponent with checks and discovered attacks for example

Each of these "layers" can be viewed as unique elements yet they are all related and all interact with each other.

I have tried to model chess in my mind using topology, viewing pieces as fields of potential or logic gates or gravity wells, but I very quickly learned that chess is it's own unique animal and there is no model to use except for chess.  This leaves me uncomfortable when playing as it makes me doubt any intuition I have about the game- I dont trust things I cant fully model in my mind or wrap my head around.  Maybe this is why chess is fun - you cant just stick it in a karnaugh map and minimize it (well you could if you had a quantum computer with enough qubits perhaps).

AndBell: I’m a mechanical engineer and i fully follow and understand your points about how you can use math (such as the 2nd order differential equation solutions you mentioned - and many more) to explain physics like interactions between objects and electrical phenomena, etc.. But i would suggest that all of that, in the analogy between understanding the world and understanding chess, is more accurately equated to ‘knowing how the pieces move’. There is no unifying ‘theory of everything’ in science that allows you to predict things like what colour of socks your boss will wear next tuesday, or whether your cat might go out tomorrow and not come back for 3 days instead of the usual day or two. You can certainly use mathematic expressions to explain how chess pieces move, and the outcomes of combinations, and well.. enough to program komodo, for example. So we can use math to explain chess in the ways you describe about how we can use it to explain reality. But on both sides of the analogy, there are and perhaps always will be unknowns. I’d say we are closer to ‘solving chess’ than we are to any analogous solution to reality - that’s why people have religion :-)

I think we are in agreement then -  the section of my post where I mention the various "layers" of chess - tactical, strategic, space, pawn structure and tempo (or time), I was implying that there are too many variables to break chess down into simple models or rules.  Much of learning to play is more analagous to intuition and pattern recognition (similar in a way to machine vision which relies much more on statistical processing than concrete rule sets or finite algorithms).

   Stockfish for example uses a combination of brute force + an opening book + some heuristics data to evaluate positions - a rook on the seventh rank evaluates a little stronger than your rook on home square for example or the closer your pieces are to the enemy king that might add a couple centipawns to the evaluation even though in a purely mathenatical brute-force approach it might not be the most mathematically efficient solution.  This is what makes AlphaZero vs Stockfish so compelling. 

I feel chess is unique though as many games have been "solved"  -checkers, tic-tac-toe, poker (hand odds at least, bluffing is a whole other element).  Some games like chess, go, and shogi are still are beyond the limits of our computing power. 

I completely forget where I was going with this... but yes trying to learn chess like you would study a book on math or physics is not the best approach.  Human chess seems to be much more centered around recognizing certain patterns and themes than some hard algorithmic approach, which is part of why I hate it and love it at the same time.  It makes me feel dumb in the right kind of way

Sure. If a statement being true for k implies the statement is true k + 1, and you know the statement is true for n = 1, then you know the statement is true for n = 2, and then you know the statement is true for n = 3, and then you know the statement is true for n = 4, etc. etc. To get from there to the statement being true for all n necessarily requires you to pick up on the pattern. Else you'd be here for an eternity saying "and that means the statement is true for n = 1549751800314279".

Does it have much in common with learning to spot the removal-of-the-guard technique?

Induction specifically? No. Pattern recognition in general (which is math)? Yes. Because the thing you are spotting is a pattern.