Chess will never be solved, here's why

Like "true", "rigorously" is a boolean concept, not one with a continuous scale. It pervades all of the mathematical sciences, distinguishing them from all of the natural sciences.

Either a proposition is proven or it is not. When there is a dispute, it is about whether a step is invalid, which invalidates the entire proof until it is fixed.

No person with relevant expertise claims chess has been solved: there is no more than an impractical sketch of what a proof would require.

@12368

"mathematical sciences, distinguishing them from all of the natural sciences"
++ Science is science. Mathematics is useful for other sciences.
Much of mathematics has been developed for other sciences.
The Egyptians developed the Pythagorean Theorem to re-establish borders after Nile flooding.
Thales developed his theorem to measure the height of the pyramids.
Gauss developed mathematical theories for astronomy.
Gauss developed modulo rings to calculate the date of Easter.
Newton developed calculus he needed for his mechanics.

Well ... perhaps. But that's not technically "solving" chess.

Solving chess would be a hypothetical 32-man tablebase, where every possible position has been tabulated, and the draw/DTM (or DTZ) has been assigned.

From my understanding, even with some ultra-compressed form of storage, like digital DNA (which scientists are already doing), the amount of space needed to store such a tablebase would be immense.

Others can correct me if I'm wrong, but I've read that the storage space needed to have chess fully solved would be exponentially more than we currently use for all the data on Earth ... It's a tremendous hurdle.

@12370

"Solving chess would be a hypothetical 32-man tablebase" ++ That would be strongly solving like has been done for Connect Four. There is also weakly solving as has been done for Checkers and Nine Men's Morris, and there is ultra-weakly solving, as has been done for Hex.

"the amount of space needed to store such a tablebase would be immense"
With 1 bit draw/nodraw per position, the 26-men tablebase would be the largest: 1.08 × 10^37 positions, thus 1.08 × 10^37 bit per Table 3. Synthetic DNA could be possible.

The Egyptians developed the Pythagorean Theorem to re-establish borders after Nile flooding.Thales developed his theorem to measure the height of the pyramids.Gauss developed mathematical theories for astronomy.Gauss developed modulo rings to calculate the date of Easter.Newton developed calculus he needed for his mechanics.

...and albert manipulated it to make abuncha guesses abt deep space ten.

"the amount of space needed to store such a tablebase would be immense"

just like how this one man (J.D.) told me when i was 12 that the new 10-Mb hard drive abt to come out was incredibly immense and nothing would ever be able to compare to it for yrs & yrs to come. LOL !

I can tell you the very unambiguous distinction, what you get from it is beyond my control. You are right that mathematics is created for the needs of science in some cases. This is about what people do, not about mathematics or science as domains of knowledge.

Mathematics is about abstract truth, never having any dependence on the physical world or any science. This truth is determined by deduction from axioms to theorems (merely a word for a an important proposition).

Science applies mathematics for the purpose of modelling reality. The model has to be chosen so that the abstract truth is consistent with the empirical truth about what the model is being used to represent.

It is fair to say that much of science can't do without mathematics, so it is dependent on it. But it is also true that none of mathematics has any dependence on any science (science consisting of knowledge about how the real world behaves). This includes any mathematics created solely for the needs of a science. Once created it has an independent existence as a purely abstract branch of mathematics. Interestingly, while before the 20th century, most mathematics used in science predated its use, sometimes by centuries, more recently, much new mathematics has arisen within theoretical physics.

[A fact about human behaviour is that theoretical physicists tend to be very loose with rigour in their use of mathematics. They are happy with arguments that refer loosely to physical principles or to use reasoning that is known not to be valid but found to work in practice. Usually, this gets fixed later by mathematicians, but not always.

An example of this in renormalisation, which started as a fudge introduced because the mathematics of quantum field theory led to calculations like infinity minus infinity, which does not give a unique answer. Later a new mathematical theory was built that made the reasoning rigorous].

Anyhow, a key point is that within mathematics, all the reasoning is deduction, leading to abstract truths, while in science, all the reasoning is induction, leading to confidence in a model of reality, or about more specific scientific proposition.

The best you can ever have in science is a theory that is consistent with abundant observations - you can never prove it is true for observations to come, especially those that are in some way significantly different to those you have made. As a result, all reasoning is about the strength of belief, empirical data reinforcing or weakening it.

Lol

That would not be strongly solving either FIDE competition rules chess or ICCF chess. Not with any current or proposed format of tablebase.

I have been pointing that out to you for years now. When will you take it in?

Under competition rules we don't currently have a strong solution of even any ply count 0 KRvK position that is not already mate or stalemate.

A strong solution of any position must provide a strategy for reaching the correct result from any position that may occur in a continuation from that position.

No tablebase currently available will give you such a strategy from the last position shown here under competition rules.

The only correct strategy for Black is to play 32...Ka1 followed by KxR if the white king moves anywhere except b3 or the white rook plays to b1, which draws, but all tablebases will give a strategy starting 32...Kc1 instead, which loses. The initial position in the example is therefore just one instance of a position not strongly solved by tablebases under competition rules. (All ply count 0 positions in this endgame that are not mate or stalemate are a tiny fraction of further instances in this endgame.)

Try it https://syzygy-tables.info/?fen=8/8/8/8/8/K7/1R6/1k6_b_-_-_62_32.

Can you suggest an algorithm for constructing a tablebase that strongly solves just the initial position in that example under competition rules and might plausibly be contained using synthetic DNA? What percentage of a tablebase that strongly solves the chess starting position with your algorithm would you estimate that would constitute?

Its not a hurdle. It would be foolishness.
But regarding the 'storage space needed' -
if you're talking game tree analysis - you'd need more volume than the earth itself.
Numbers trillions of times 10^100th power.

It's either solve chess or cure cancer...

'rigor' is a term to be avoided though. Like 'game theoretic value'
'rigor' has rigor mortis. As it were.

Quite correct. It should be "rigour".

MAR i think im misreading or smth because syzygy quite easily deals with Ka1

Which also has 'rigour mortis'.

Yes, I think you're missing something.

If you click on my link, Syzygy recommends only Kc1 (Syzygy only guarantees a weak solution if you consistently take one of the top moves with minimal DTZ from the first appearance of the endgame - though it can also work from later positions).

Of Ka1, Syzygy says it's losing with DTZ 5. It's not. It draws.

Click on the two fingers and try it against the computer with the strategy I suggested.

But is the topic under discussion whether you like it or not.

(And "rigor mortis" is actually correct - it's from the Latin.)

Is only one term to refer to a much larger topic.
I didn't say I disliked it.
I think it can be improved on.
Many things can be.

But I think the thread topic is clearly about a rigorous solution and is large enough already.