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Formalizing Fermat's Last Theorem

anthropic.com

191–200 of 524 posts

Re: Formalizing Fermat's Last Theorem

#191
post #7

> Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems. Pretty insane. I suppose it lends further credence to the idea that anything that can be shown to be correct can be done by a model.

especially compared to existing 129 pages proof by human

A human can cite previous published results. I am sure a lot of this development was formalising the prerequisites.

Re: Formalizing Fermat's Last Theorem

#192
post #163

Earlier quoted context omitted.

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.

SemiAnalysis estimates their profit margin to be 70%. To be losing money on inference implies that their costs are almost 4X higher than SemiAnalysis has calculated. That's not credible.

Re: Formalizing Fermat's Last Theorem

#194
post #172

Earlier quoted context omitted.

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.

Like? I feel breakthroughs that can be found via AI might help us more in the long term where even previously non AI fields can be helped by AI. So you have specific non AI research in mind that we're underinvesting in? Because the USA is already spending crazy anyway for healthcare and I don't feel like funding is the issue but better incentives, reforms etc

Re: Formalizing Fermat's Last Theorem

#195
I wonder if any piece of the lean code is in a shape which means it could be contributed to one of the Lean libraries.

My experience is that it takes a lot of human input to make Fable write code nice enough for a formalisation library others can work on. But since this is certainly a lot of prerequisites formalised as well, it would be nice if not all of the effort was wasted on one capstone proof!

Re: Formalizing Fermat's Last Theorem

#196
"The effort succeeded when we switched to using Prove2Me, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University."

So in the end, it required tooling crafted by humans.

Re: Formalizing Fermat's Last Theorem

#197

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.

Most people want more life. For most people it's also the most terrifying part of "the natural human experience". If you're happy to die, why be bothered by others' trying to live longer? You won't be around. And assuming people can finance it themselves, is it really a problem for society?

Because living longer is a huge drain on resources that could be better spent on other things. End of life care is expensive and rarely results in a "good" life for the the life being extended.

Re: Formalizing Fermat's Last Theorem

#198

"The effort succeeded when we switched to using Prove2Me, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University." So in the end, it required tooling crafted by humans.

For now. That, too, will change in the future.

Re: Formalizing Fermat's Last Theorem

#199

"The effort succeeded when we switched to using Prove2Me, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University." So in the end, it required tooling crafted by humans.

By this standard, no computer has ever accomplished anything, because humans built the computer. AI bubble about to burst any second now.

Re: Formalizing Fermat's Last Theorem

#200

"The effort succeeded when we switched to using Prove2Me, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University." So in the end, it required tooling crafted by humans.

For now. That, too, will change in the future.

Same thing was said about cryptocurrency for like 15 years: "_in the future_ it will replace all fiat currency".
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