Chess will never be solved, here's why

a mathematical solution for chess is impossible

now tell me again why that is ?

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.

Firstly there's been a misunderstanding about what a mathematical approach consists of. There's no doubt that any Game Theoretical approach is heuristical and not good heuristics either from the pov of solving. However, there's a diff. between Games Theory and Combinatorial Games Theory. It means that combinatorial games can be analysed completely using mathematical theory. Elroch's argument is that chess is a game of perfect information and therefore can be fully analysed.

There's a problem with that. My son tells me that it's impossible at the moment at least and will almost certainly always remain impossible. Chess will never be depicted mathematically, he says. Although he's a data scientist, he approached that via being a really first class mathematical analyst. So a mathematically based solution to chess seems to be impossible.

I also think that chess is not a game of perfect info, since the info on the board is the equivalent of it being in an unbreakable code. That's the entire point. Break the unbreakable code and you've solved chess mathematically. It's too complex. It may be that in the future, Real A.I. may FIND a way to solve chess mathematically. I always assumed that would be possible. I asked my son and he says "nope".

Read the above post. You are certainly not qualified to disagree with him and neither is anyone else here.

Mathematical simply refers to deductive here. For example, a brute force solution counts as mathematical, just not a pretty example.

And please note that it is not "my opinion" that chess is a game of perfect information. It simply is. Ask a game theorist. It is absurd that at this stage in the discussion you don't know that :

1. there is a precise mathematical definition of a game of perfect information
2. chess satisfies it, as do all combinatorial games
3. the branch of game theory that applies to chess is combinatorial game theory
4. you need to avoid using standard terminology for something different, or in a vague way based on not knowing the definition

I can't see why you say "any Game Theoretical approach is heuristical". The solution of checkers was a game theoretical approach and was not. Counterexamples disprove conjectures.

I dunno I think a guy taking proofs right now is more qualified then a guy who has taken that class 10+ years ago

MEGA, I think you've done about the same amount of university maths as me, which mean that you can't speak from authority, even if you tried.

Let me explain it in a way you may understand.

The issue is he has like ten maths professors supposedly a few with phds

You have 1 lol

@Optimissed, I don't think you are well placed to enter a maths competition against MEGACH3SE. I would buy a ticket for that.

[Humility discourages me from another similar statement].

"There's no doubt that any Game Theoretical approach is heuristical"

but... by definition it isnt.

You are saying that it is axiomatic that chess can be mathematically solved, aren't you? Not only that but that's it's a CORE AXIOM OF MATHEMATICAL PROOF.

Do you know what axioms are? Because it seems as though you don't know what they are.

"An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα, meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'."

An axiom is an assumption which is taken as self-evident. It is not self-evident that chess may be solved mathematically so therefore it is not axiomatic. End of conversation. I don't care whether you understand why, which would mean you have ability, or you don't understand. I understand it.

It's not axiomatic, it's a theorem of the relevant branch of game theory.

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

I could certainly write such a program. It's not difficult if you don't add other constraints. It's not worth the effort since all of us know it requires impractical resources to get to the answer.

Except for the part where we are trying to solve chess...a process that has strictly defined solutions, all of which require "ideal", i.e. not imperfect, efforts.

It's a ridiculous statement in this context. Maybe if you are trying to tell your kids that they are human beings and it's okay not to be perfect, it works...

"You are saying that it is axiomatic that chess can be mathematically solved, aren't you? Not only that but that's it's a CORE AXIOM OF MATHEMATICAL PROOF."

never said that

I thought he was talking to me. But we surely agree on this issue.

basically optimissed's argument that chess cannot be solved mathematically is that he casts doubt on the very nature of such a proof, however the way he casts doubt makes no distinction between chess and any other math proof that could exist. I was pointing that out, and optimissed thought that I meant that the proof itself was just an axiom, even though we agree it is in fact derived directly from axioms.

tbh tho this thread hasnt required any more than the mathematics I learnt in middle school (tbf i was a couple years ahead and did competitions that focused heavily on game theory topics but still)

there's no calculus required here. no vectors, fields, or groups.

Lol...this applies to Tygxc, and to you. Not to anyone sticking with the defined parameters of solving games.

Anyone that "knows" chess is a forced draw (your stated position) is the undisputed king of "your complete insistence that you're right raises questions regarding the assumptions you must have made for you to be so sure".

Glad you found out what your son does for a living...kudos.

You are easily impressed. Curved monitors have been around for 10 years now. You can buy them at Costco.

Tygxc is in no way "entitled" to makes claims about solving chess using his faulty methods. What he is entitled to is his personal opinion. Every time he states "chess can be solved by 10^17 blah blah blah..." in response to people, he is knowingly lying at this point, in much the same way that when you claim to have paranormal powers, you are willfully saying something you know to be false no matter how much you wish to believe it.

Humility discourages me

thatsa first lol ! just teezing L♥