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Classification of Finite Simple Groups Formalized in Lean

https://cfsg.axiommath.ai/
28•pfdietz•56m ago

Comments

pfdietz•56m ago
The formalization is 43.1M lines of Lean.
bwestergard•30m ago
Is that going to be mathematically useful?
sebzim4500•7m ago
It's nice to know that they didn't miss anything. The natural language proof is 10,000 pages and they have missed groups in the past.
curt15•3m ago
More so if Lean uncovers logical errors. There are already human 2nd and 3rd generation proofs to streamline the original arguments.
sebzim4500•52m ago
This seems like a very good use of auto-formalization, because in the past mathematicians have incorrectly believed that they were finished with the classification only discover a missing class/sporadic group.

The original proof was a collaboration of ~100 mathematicians, if Tao is correct then we should expect to see more such collaborations in the future like we do in e.g. physics.

mlmonkey•47m ago
Out of curiosity: is it possible to take a frontier model and just let it loose on all math textbooks out there, converting each and every proof/theorem/lemma/etc. into Lean? A frontier model should be able to do that, right? And it's a one-time task: do it once and it's there for eternity, available as a library to be used in other proofs.

Maybe my understanding of Lean is wrong; I'm thinking of it as a programming language but for Math.

tyromaniac•35m ago
Write a few proofs with it and then come back to this
bananaflag•30m ago
Yes, but thing is, for a lot of basic stuff there are myriad ways in which it is formulated, so humans have to decide which of them goes in the library. Of course you can include two or five or ten equivalent formulations (like textbooks sometimes do) but still, not everything under the sun.

Probably this will be done in some form in the coming months.

jonath_laurent•30m ago
Axiom MTS here. What you describe is pretty close to how we formalised this proof, which is scattered across more than 500 articles and books: a swarm of agents was tasked with going through all these sources.

One challenge is assembling everything into a coherent whole, since the same informal concept can be formalised in slightly different but incompatible ways.

pixl97•46m ago
Page has some kind of redirect bug that steals the back button, may want to open it in a new tab to avoid that.
vatsachak•33m ago
LLM formalization is not as useful as human formalization, but nice to know that the Classification is correct
v3ai•15m ago
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