Checking every possible case with a computer doesn't give any great insight into mathematics, but proof by exhaustion is as valid a method as any other.
this post was submitted on 05 Aug 2022
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the title says "a large number of cases" which isn't necessarily every possible case.
linking the original story or paper would have been good so we could check these things
That's the key indeed. Testing "a large number of cases" is not a proof per se, but can be proven to be sufficient, which is what happened with the four color theorem
No.