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bsderyesterday at 3:50 AM2 repliesview on HN

> checking an existing fully fleshed out proof is simple

The controversy around Mochizuki and the "abc Conjecture" proof is a contrary example.


Replies

pfdietzyesterday at 3:38 PM

His partisans are trying to formalize his proof. I expect they're not going to be able to do it, because the proof is flawed.

This is one of the great things about formalization: it would have avoided this entire debacle.

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akoboldfryingyesterday at 6:45 AM

How does this involve computer checking of a formal proof?

Last time I checked, it was a disagreement over whether an informal proof is sound, which is exactly the problem with informal proofs.

ETA: There might be a misunderstanding about what "formal proof" means. Even a very detailed, precise English-language description of a proof is generally not a formal proof. The bar is essentially: "It could be checked by a machine that follows simple rules." If different interpretations of a "proof" are possible, the "proof" is by definition informal. Informal proofs are valuable because they are strong evidence that there's a corresponding formal proof "underneath" that would establish the theorem's truth, and because they are (usually) much easier to understand.