Comment by TheOtherHobbes
1 day ago
Math that isn't communicated is valueless - by definition.
Applies to STEM generally, because the foundation of STEM is peer review and independent testing and confirmation.
Even if the practice never quite lives up to the theory (true) that's no excuse to hand-wave away the requirement as if it doesn't matter.
Proofs that can't be confirmed are valueless because no one learns anything from them. The value of a proof isn't just in proving something but in inventing new techniques and insights that can be reused for other applications.
Brute force searches are fundamentally less valuable, because the creative foundation of math is discovering leaps of logic that solve problems with insightful shortcuts that can be generalised and reused for other applications.
> Math that isn't communicated is valueless - by definition.
That is quite a bold claim.
Math can always be used as a tool just to achieve results. This can include even novel math. Due to the maturity of the field it is just becoming more and more unlikely that somebody will come up with something novel without realizing the significance.
One example: Quicksort was almost not published because Tony Hoare initially considered the idea behind the algorithm trivial. In the end, all he wanted to do was to sort some numbers.
Maybe there is a polynomial time SAT solver running somewhere just because some overworked engineer implemented it for a completely different problem. And he was just annoyed that all existing libraries were so slow and he doesn't realize that he is sitting on a proof that P=NP. Who knows.