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Formalizing Fermat's Last Theorem

anthropic.com

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Re: Formalizing Fermat's Last Theorem

#161
post #22

On a tangential note, I highly recommend this book by Simon Singh. https://en.wikipedia.org/wiki/Fermat's_Last_Theorem_(book)

100% It is a very insightful book

i read it from a library. this all just makes me feel cozy and nostalgic and uplifted and sad all at once

Re: Formalizing Fermat's Last Theorem

#163

Earlier quoted context omitted.

It sounds plausible they spent more, given the output tokens (6 billion of them) would cost $300k at API prices and presumably there will have been many more input tokens than output tokens.

Unlikely, api pricing includes a healthy profit margin (as near as we can tell from the outside) which they wouldn’t charge themselves.

> healthy profit margin (as near as we can tell from the outside)

Ugh we still don't know if this is true and it's nearly impossible to calculate without a full understanding of the real CAPEX cycle. Stop spreading these rumors until we know for sure.

Re: Formalizing Fermat's Last Theorem

#164

This is quite useless actually. The whole point of formalizing FLT was to clean up modern number theory into reusable abstractions that prove it. If its 13 million LoC, it might involve so much spaghetti that its unusable other than the result

physics is like sex: sure, it may give some practical results, but that's not why we do it

Re: Formalizing Fermat's Last Theorem

#165

Earlier quoted context omitted.

So much doom and gloom on this site. Makes it almost not worth reading.

Please tell me how AI is going to make regular people's lives better. You optimisitic types keep saying "just wait, its going to cure diseases" without any outlook on how thats going to happen. You're actually just repeating marketing jargon from AI companies who want people to think they're going to possibly live longer if you let them build more datacenters, so they can make another 30%. Its all about money, thats…

some say it will cure all diseases and lead to utopia. some, like you, say it will be "100% strictly negative".

i don't really understand either take. nothing else in the world is so perfectly black or white. there will be good, there will be bad.

i think i especially dislike the "100% strictly negative" take, considering the good things that ai has already done or accelerated.

Re: Formalizing Fermat's Last Theorem

#166

Earlier quoted context omitted.

While pretty much everyone is certain Fermat was mistaken in believing he had a valid proof for the theorem, this is an expanded (compared to proof presentations) version of one proof - not the shortest presentation of the shortest valid proof.

Given the likely length of the shortest possible proof, I feel like Fermat is 100% vindicated - the proof won’t fit in the margin. My strong hunch is that it was a joke - he knew how difficult the problem was and claiming he had a solution was I think a huge motivating factor for many mathematicians trying to prove it. The greatest nerd snipe troll in history.

Most likely an error. Some time after he wrote that margin note, he wrote a document proving a special case of the FLT (i.e. it's true for n satisfying some property). Why would he do that if he had already proved it?

Re: Formalizing Fermat's Last Theorem

#167

This is quite useless actually. The whole point of formalizing FLT was to clean up modern number theory into reusable abstractions that prove it. If its 13 million LoC, it might involve so much spaghetti that its unusable other than the result

physics is like sex: sure, it may give some practical results, but that's not why we do it

I mean at this point there's no doubt that LLM cans be RL maxxed and give you _some working output_ but the next frontier is whether they can create good abstractions, a.k.a use the correct level of expressivity so as to not inline everything yet not play code golf.

Re: Formalizing Fermat's Last Theorem

#168

Earlier quoted context omitted.

I hope you keep these horrible thoughts to yourself if you ever walk through a paediatric hospital

Thinking that aging is a natural part of the human experience is a horrible thought? Please explain...

Childhood deaths and fatal diseases are also natural parts but that doesn't make them desirable to everyday humans. But with new advances, people might have the ability to CHOOSE in future.

Re: Formalizing Fermat's Last Theorem

#169

Earlier quoted context omitted.

So much doom and gloom on this site. Makes it almost not worth reading.

maybe that's because the doom and gloom is the transparently correct outcome?

Why? Even communists weren't this doomed and were actively rooting for it to solve the economic calculation problem which ai might take us to. People are just pessimistic in general ig
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