Too difficult for computers

Being interested only in the objective truth of a chess position is fine, and this probably parallels your preference for objective truth in the real world, i.e. the scientific perspective. If you're into philosophy, we can consider how most complex things have both a subjective aspect (e.g. artistic) and an objective one (e.g. physical sciences). Thus a painting has both subjective/artistic properties (in the minds of viewers) and objective/physical properties (its paints and wood). Likewise a chess composition, where its objective "truth" – win in X moves or draw – is uncovered by analysis or tools like tablebases.

The issue of soundness/unique play, though closely related to the artistic, actually belongs to the objective side. This is why, even though it's normal for problemists to have different (subjective) views on the value of a composition, they practically never disagree on whether it's sound. Soundness is on a higher objective level compared with the more fundamental "win/draw" lower level. Using paintings as an analogy, soundness is the colour/chemical properties while win/draw is the particle-physics properties.

It's fine to focus on the objective side of things, as scientists do, but this can be carried too far when subjective things are devalued or viewed as just illusions (e.g. emotions are nothing more than chemical processes in the brain). That's a type of reductionism common in the modern world.

@Elroch: We've come closer on nothing but the minimax analysis. Indeed you need not provide all the white options only all the black ones which is let's say just 1483664754 variations. That's quite a bit more than 1. "Forced mate" and "forced win" are total non-concepts that replace proof with a result. It is loosely used to suggest that a proof can be delivered in a few lines - taking into account the knowledge level of a decent chess player". The truth is that unless a win or a mate is a forced mate it is not a win or mate at all. A truth seeker will never use the term "forced anything". It does have a deeper meaning though. It's another way of saying "we are playing fighting chess". Fighting chess is the description of the relationship between the 2 parties in a chess game with regard to a goal and their presumed relationship in solving certain composition types like studies and directmates. It is not universal as it is replaced by different strategies and goals for helpmates and selfmates. The fighting condition is not self-evident in goals and strategies of composition land. What we know as minimax evaluations formalizes the decisions in fighting strategy and thus all "forced" outcomes.

Btw, "winning strategy" is either meaningless in proofs or it is also the same as "forced win" and "fighting win". The way the term "strategy" is used in chess game analyses is 90% based on the knowledge level of players and seeks to avoid delivering actual proof lines. But I suppose you know that.

Indeed, you know nothing about "solving". Though chess compositions have a solution they are not made "to be solved". They are made to present a panoramic view of ideas in the composer's mind. The solving approach is an elegant way to demonstrate them plus a challenge for the mind. Did you know that most readers of composition magazines do not seriously attempt to solve the challenges? They much rather browse through the solutions and comments to enjoy the views. And the last thing any composer will want the solvers to get away with is some accidental solution. His task of course to prevent that. He only wants to see it "solved" in the exact way he created it because that is his piece of art. And that includes for instance "the thematic white failures" which are lost in the pruned minimax analysis. And it includes discarding the lines not showing any part of his artistic creation. They only muddy the scenery. Therefore in solving competitions the focus is on thematic content. Providing 1 thematic solution line gets you a point while 6 others may get you naught. There is some arbitrariness in the judging of solutions and points and referees have backroom discussions about it with solvers (occasionally). Just to show that solving is not about mathematical proof. 

Your sort of solving is imaginary. - not only because it is uninteresting but also because it is undoable for any but the simplest puzzles - unless of course you are cheating with non-existent forced win lines and computer or poster generated counterplay. You missed out on the design perspective as much as the math requirements.

Note: I will not go into your example as it is atypical for endgame studies like most of drdos7 posts; that's just his interest. Due to the narrow algorithmic solution there is not much choice to go by unlike most endgame studies.

I have great respect for mathematics and very little for mathematicians. Usually when they leave their universities - even when they are still pursuing professional careers - they start replacing their expertise with authority as happens in so many other fields. I know from another subject that is certainly true in chess. I did not complete my math education though I was considered one of the most talented students in the country - by test. Never lost my talent and caught up some of my backlog by studying formal systems later.

Instead of arguing expertise I choose to dismantle one of the corner stones of your approach. The "win" stipulation for studies can be restated as "forced win" or "forced mate", absolutely identical concepts. Which gives us the recursive definition "a winning position with white on move is one where either (a) white can checkmate black on his next move, or (b) white can play a move which still gives him a winning position after any black countermove. That should do. What does this tell you about the traditional abortion points in solution lines? Let's see your answer: "give a line providing a forced mate". That's awkward isn't it? That is simply restating the same action that was part of the 'win' definition and has been applied on every move so far. So your process is empty besides that what we did all along. One difference. Without any justification you dropped the requirement to assess all the black defenses which were part of the preceding solution procedure. Suddenly there is a whole new meaning to the term "forced mate". That's called inconsistency. The truth is here that nothing can change in the tail-ends handling until you include external knowledge sources which teleport you to Mecca in no time.

Now, if you are a true mathematician you will appreciate the power of this argument. If not, well, be happy with your diploma's.

Second note: I am not concerned with duals here; that's another subject.

I am not responsible for your multiple failures to understand things clearly stated by me.

But I am sufficiently bored of this not to be going to waste any more time on someone who first states "'Forced mate' and 'forced win' are total non-concepts", then says they mean the same thing (don't you mean the same nothing?) then tries to argue that they aren't relevant to problem solving!

You could sum this up with something like "I am way too smart and literate to admit that i was saying nonsense".

I was not the one who said that "forced mate" is a non-concept. I was the one who pointed out it is a fundamental concept.

I was also the one who pointed out that the example in the OP was an explicit counterexample to the claim of the confused @Arisktotle, who dealt with it by saying "I will not go into your example as it is atypical", which makes me wonder what the heck he was doing in a discussion about it.

Offensive comments sometimes need a factual response.

But I agree with the general sentiment.

Excellent article! 👏

:D

Try putting the FEN for a classic puzzle into the Stockfish 15 analysis tool.

7k/4K1pp/7N/8/8/8/8/B7 w - - 0 1

How is it that the strongest chess computer in the world can't solve it? My belief is that it relies on unreliable heuristics about remaining material.

Thanks to @GhostNight for drawing this puzzle to my attention.

Is it not showing the mate in 3?

Here it is on my computer:

It is not showing up the position. Maybe I can try to post it here?

Here is the starting position if it comes out? White to move.

The Stockfish analysis shows a mate in three in that position with 1.Bf6 gxf6 2.Kf8 f5 3.Nf7#

Great, but did you try to figure it out on your own first. That is the point of this chess problem. You don't learn/gain anything if the AI does the thinking for you. Oh btw I did! It was one heck have a hard problem for me.

It was easy for me, I thought Elroch was insinuating that the chess.com Stockfish had trouble with this mate in 3 problem in post #55

Love to have a game with you! You can teach me a thing or two!

The cloud engine of chess dot come is a crippo, and this is not news.

Just feed it to a local stockfish installation, and 1.Bf6 will come into fractions of a second.

Even the cloud SF 14-NNUE from "the other site" finds the solution instantly.

I know that 3 move mate! Actually learned that one in my elementary school chess club. What's funny about it is on this site, after white plays 2. Kf8, black could actually deliberately let his time run out and obtain a draw since it would declare the king and knight insufficient mating material even though it's mate next move. That's why the FIDE flagging rule should be used.