Chess will never be solved, here's why

any combinatorial game

it can be (transpositional) but its more like a big giant permutation.

don't need to be constrained to inhabit a world of mathematical purism, which is an ideal world, only loosely related to reality

PERFECT ! (just 4u dodo due)

Repeating the ridiculous does not make it any more correct. But otherwise, kudos for actually asking some basic questions and engaging after only 620+ pages.

That's more like it. Axioms are fundamental building blocks, necessary for deductions to be made. The idea that it's axiomatic, which means that we may assume it to be the case since it's obvious, that chess may be solved mathematically, is quite ridiculous. It also assumes that which we're trying to establish, as to whether chess can be represented mathematically by means of sets of equations. It assumes it to be the case, which is of course is the problem with the game theory stuff.

<<THEOREM: There is a methodical way to find optimal strategies for any combinatorial game. The procedure can be implemented as a program.>>

Says who? If you can't prove it then it's an axiom and we've just rejected axioms which put the cart before the horse. Can you prove that chess can be exactly represented as a set of equations?? My son says it's almost certainly impossible. He should know.

As you can see, Dio still inhabits a fairyland in which the meanings of words are forever obscured from him. Some say he's thick but it's where he lives. Really!!!

"Can you prove that chess can be exactly represented as a set of equations??"

"My son says it's almost certainly impossible"

I can almost guarantee a misunderstanding between you and your son. your son probably believes that you are referring to some positional algorithm of a solution, which is almost impossible.

the mathematical representation of chess literally exists within the code used in chess.com.

a game to be represented mathematically is not necessarily a solution of the game directly from a mathematical framework, but just an explanation of the rules of the game as a mathematical object.

"Says who? If you can't prove it then it's an axiom"

the definition literally dictates that it has been proven already, unless there is some miscommunication relating to you.

Dio, I am so much more intelligent than you that you would not have the faintest idea when, how or why I'm right. Everything is so completely beyond you.

You are talking about apples and oranges. Programming a solution that solves chess and reducing chess in its entirety to mathematical equations are not equivalent in any way. The latter might be required for your premise of a pure algorithmic solution to chess, not but for solving chess via a combination of brute force and pruning. Your son is correct, your approach is actually harder to complete as things sit. Now if brute force produces enough quantifiable truisms over the centuries, maybe the algorithmic approach will become more plausible. As is the case for a number of games, though, brute force and proper pruning (*not* 27 orders of magnitude of vague casting off of positions) may solve the game, at which point backing into a pure logic and rules-based solution of chess that fits your bill might be possible. But certainly not within our lifetimes with any foreseeable technology we are working on currently.

This argument is, of course, completely empty (as most of yours tend to be). There's not a single word after "Dio" that is not pure opinion and conjecture on your part. Not one iota of data. Not one ounce of supporting detail. This is your method of analysis and exposition in general...bereft and empty.

well he outsmarts u all day. and thats a fact !

esp when u bumble out s/t 1900's dum like this:

certainly not within our lifetimes with any foreseeable technology we are working on

its ok to be behind...we u/s lol !

He outsmarts everyone according to criteria he sets himself and his own judgements. Whether these have any real value is questionable.

Especaly when they pretend they know more about a subject than a math nerd

<<optimissed attacks the core axioms of mathematical proof with this claim. to say that chess cant be solved mathematically is to also claim that the universally accepted checkers proof is false.>>
Looks like you DID say it though, doesn't it.

What a pity but it's irrelevant. I'll tell you why.

Sleepybyes for you!

Anyway, I asked Elroch to prove that it's correct, according to a theorem of combinatorial games theory, that chess can be solved mathematically.

He just told us that it wasn't an axiom, by the way, MEGA. I thought we were making some progress. However, you were more correct than Elroch, seemingly, because if he can't prove that it can be solved mathematically (and that proof has to be a syllogistic proof, which is what he always demands of others) then it's a axiom.

Having an axiom that chess can be solved mathematically is exactly equivalent to an axiom that states that mankind will reach other galaxies in their space exploration. Now, I'm not saying it's impossible but I strongly doubt it. The axiom is based on "mankind can travel, therefore mankind can travel to other galaxies" and is exactly equivalent to "simple combinatorial games can be solved mathematically: therefore chess can." I would require a proof, please, or you've lost the argument.

You would lose the argument since you would not have responded in kind. You required deductive proofs from tygxc but you cannot give them to defend your own far less reasonable claims.

Dio, you made a decent argument a few posts back. I wasn't going to respond to you but I read it and I liked your thinking. I didn't think it "won" any points however but it's nice to see you can raise your game (said he, patronisingly). But I mean it. Thankyou for agreeing that my son is correct. The trouble is that you seem to have interpreted the mathematical thing as NOT depicting chess exactly by means of sets of equations; but as representing it by means of mathematical heuristics, which is EXACTLY what Elroch is criticising in others. I actually think he's changed his pitch on that and tacitly accepted an argument I made some time back. Anyway thankyou for that. I'll let you call me dumb if you like.

@Optimissed, this theorem even has its own wikipedia page.

If you want a formal proof, here is one (it's half a page long after the definitions have been made):

Zermelo's Theorem

The original paper was published in 1913 (in German), and apparently it was the first published paper on game theory. It needed an addition published in 1927 to be a truly rigorous proof for basic chess (where there are a finite number of possible positions, but games can be indefinitely long).

Interestingly, this is the same Zermelo who has his name attached to the Zermelo-Fraenkel axiomatisation of set theory that is perhaps the most popular foundation for mathematics.

[Remark: It strikes me that Zermelo's theorem can be easily generalised to a game where there is a general finite ordered set of outcomes].