alt Hacker NewsClassification of Finite Simple Groups Formalized in Lean
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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.
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.
Groups were my gateway drug into abstract algebra. A friend clued me into symmetry being everywhere and Groups are how symmetry is formalized, and it’s been a crazy journey understanding all that. The frontier models can tie those abstract concepts to plain English examples and answer questions decently well, it’s never been a better time to pick up the field solo and see what it has to offer us
Somehow the classification of finite simple groups makes me feel uneasy as a mathematician, but I suppose this helps quell that feeling.
Note they found one gap (and filled it) in the previously accepted 1,000+ page proof. So that's pretty cool.
Filling in well-known gaps like this is the kind of thing the AI companies should be doing, not trying to scoop research in progress.
LLM formalization is not as useful as human formalization, but nice to know that the Classification is correct
Page has some kind of redirect bug that steals the back button, may want to open it in a new tab to avoid that.
I'm surprised they only found one gap. I would have expected multiple (fixable) gaps would have been uncovered, especially since the result was spread over many papers by many different people.
Looking at the visualizations made me wonder if the embeddings themselves can be used to suggest, if not derive, mathematical results. I realize it depends on the quality of the embeddings.
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based if true
Makes me sad that the homotopical foundation people never got their shit together and now formalization is so mature but it's still done in set theoretic foundations.