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Formalizing Fermat's Last Theorem

anthropic.com

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Re: Formalizing Fermat's Last Theorem

#6
An aside on Lean and it's massive library of results: As someone who's put non trivial effort into slowly learning geometric algebra, lie theory and other slightly advanced math topics, I have to say my brain cannot read Lean. It feels so unprocessable.

I've tried the various intros to Lean multiple times (even before Lean 4 came out) and something about the way Lean proofs are written does not align with how I think about proofs. My very brief attempts at Isabelle / RCoq feel more natural.

I think it's a pity that the future of proofs is Lean. I'd love for someone to come up with a more digestable proof language!

Re: Formalizing Fermat's Last Theorem

#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.

Re: Formalizing Fermat's Last Theorem

#9
We'll increasingly observe announcements of this kind as AI tooling scales. As impressive as agentic coding is, it pales in comparison to the value proposition of medical, mathematical, and physics research.

I optimistically expect to witness the advent of a global 'panacea' in my lifetime thanks to AI's efforts. Cost effective large scale genetic engineering, a cure for every disease, potentially even a cure for aging.

The future is both beautiful and terrifying.

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