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An interesting perspective on programs-as-proof is I-forget-his-name-but... the mathematician who made really bold claims, if only you'd study under his tutelage for a number of years to understand this whole new terminology he invented.

With programs-as-proof it really wouldn't matter. It's either "computer says yes" or "compu'er says noooo".

EDIT: Whoop, sibling post mentioned, it's Mochizuki.



This doesn't seem a very generous description of Mochizuki's work. You don't "need" to study under him for a number of years and there's no evidence he's being obscurantist. The proof is long and has a lot of novel techniques he's invented, and he works primarily in Japanese. You can reasonably side with e.g. Scholze's interpretation without thinking Mochizuki is disingenuous or some kind of scammer.

He's considerably less esoteric than e.g. Grothendieck was even during his more "public" years.


I have nothing invested in whether or not any given mathematician is right or wrong. I just picked a random example of a controversial proof -- the point was more that proof-as-computation could settle and any all disputes.

It might not lend more understanding to people not invested in "field X" (or even people who are invested in field X!), but it would be proof.

Proof in the current world of math is quite intangible.


I think the demand for "tangible" proof (if by that you mean, fully mechanically-verifiable proofs and a style unlike anything common in mathematics papers today) is a bit silly and seems to be driven by some ideologies well outside of mathematics, rather than mathematicians themselves.

A proof is whatever convinces sufficient mathematicians that the theorem is consequent! Classical logical systems are a very good way to do that so they get used a lot. But they're not the only way, and involving a computer program makes most proofs less convincing rather than more.


> It's either "computer says yes" or "compu'er says noooo".

Sadly not sometimes it is just:

computer says


Or "computer says x but you don't trust the hardware/software".

Or "computer says x but you don't agree the mathematical concept was correctly formalized into the proof engine language".




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