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Formalizing Fermat's Last Theorem

anthropic.com

171–180 of 527 posts

Re: Formalizing Fermat's Last Theorem

#171

Earlier quoted context omitted.

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

Right let's give those AI companies a break, it's not like swarms of autonomous agents are committing felonies

You talk as though they are making it to intentionally commit felony or not taking measures to reduce harm etc.

Re: Formalizing Fermat's Last Theorem

#172

Earlier quoted context omitted.

I think you're missing the point of the comment you responded to, lol.

Regardless the profit margin as a talking point seems to be bad as AI as a tech might never be reversed whether anthropic failed or succeeded. Indeed it's imperative we subsidize AI companies and tech to make them explore more solutions to scientific problems which has a downstream effect on human flourishing.

Or we could invest in a ton of other non AI related research we're underinvesting in.

Re: Formalizing Fermat's Last Theorem

#174

Earlier quoted context omitted.

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?

I think that point actually agrees with GP's take (joking/lying about having had a proof too big to fit in the margin): He would do that because if he thought the problem was extremely difficult but didn't actually have a proof when writing the note he would still want to go on and try to pick away at the problem.

Re: Formalizing Fermat's Last Theorem

#175

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.

Maybe, we'd have to go back and ask him to be sure. I mostly just didn't want to leave an as of yet certainly unproven vindication about this hanging in a thread about finally having a formalized proof of the star topic :D

Re: Formalizing Fermat's Last Theorem

#176

Earlier quoted context omitted.

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

my messages are so gloomy because i am heartbroken, that given a technological miracle again, we could snatch tragedy from the jaws of our emancipation. will you not see that people could be truly empowered and yet will instead be oppressed?

So oppressed that they are one of the main reasons for positive gdp growth in the USA, tax revenues, mathematical/scientific innovations etc. They're doing all this but still can't imagine a positive vision for the world but be a doomer. What a sad state the world is in, the humans are more prosperous, healthier than ever but looks like the seven deadly sins might never go away.

Re: Formalizing Fermat's Last Theorem

#177

Earlier quoted context omitted.

It's wild to think that aging is something that needs to be cured, and isn't a part of the natural human experience. I'm so tired of people trying to play the role of God, as well as people that cheer these sorts of things on.

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

What does a pediatric hospital have to do with aging...?

Re: Formalizing Fermat's Last Theorem

#179

> it wrote 13 million lines of Lean Is this basically like opening up a black box and seeing 13 million gears all rotating seemingly randomly and still having no idea how the machine actually works?

That is already the case for most neural networks and LLMs.
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