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ivancho | 2 years ago

Their "proof" that there are only 12 solutions to 8 Mutually Non-Attacking Queens on Chessboard is just "That there are only these 12 can be proved by brute force." :/

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geor9e|2 years ago

You have proof in sarcasm quotes, but it counts https://en.wikipedia.org/wiki/Proof_by_exhaustion

In my university math departments putnam problem competition (they'd just be on the wall, prize was a $40 giant pizza each week) they would accept the most elegant solution, so if nobody else submitted something better I'd get a pizza for just running a few lines of python.

ivancho|2 years ago

I'm not gatekeeping proofs here, and I'm glad you got math pizza :) If proofwiki had exhaustively printed all possible arrangements, or the decision tree of constructing them, or if they had even included the code that would do the checking (like, say, https://www.richard-towers.com/2023/03/11/typescripting-the-...), then I would agree it counts. But without even a rough ballpark estimate of possible arrangements to check, asserting "brute force" does not make a proof. If I incorporate understanding of the problem, I can see that at most we need to check 8!, which is reasonable. But if the constraints were not so simple, then we might be dealing with 64-choose-8 cases instead, which is heading into not-reasonable.

They can add the same sentence under every finite fact in their wiki, but then it won't be a proof wiki, it would be a list of numeric facts they checked by brute force and we can either trust them, or check ourselves.

jusuhi|2 years ago

The task proving some statement and the task of finding the shortest, or a "reasonably short" proof, are very different endeavours.

The first is about certainty that a statement is valid ("true"). The other is about simplifying the understanding of _why_ it is valid. Most of the time, you don't care much about the latter.

zamadatix|2 years ago

It would be nice to have an reproducible example of how the result was achieved though. Otherwise it's a compendium of results, not proofs.

ivancho|2 years ago

What is your certainty that that statement is true? What if it was a calculation which takes decades on a supercomputer?