Tao is saying that there is very little insight from something like an LLM counterexample (e.g. Jacobian conjecture counterexample he investigated further on his blog) - you don't learn much about the subject and _why_ a conjecture was true or false from an LLM giving a counterexample. That's why he wrote the blog post - to analyse what the counterexample says about the subject.

Tao does not disbelieve the counterexample (it's seemingly easy enough for him to verify it is a counterexample).

Parent is saying something very different - they're saying they literally don't have any faith that this is a proof. Given its size, it could just be a bunch of completely useless statements that do pass the type checker.

He also made a video on the same topic for Big Think: https://news.ycombinator.com/item?id=49551848

I'd like to note that we should remember a formalized Lean proof does have value in that it enters the pantheon of true things other Lean proofs can rely on. Agreed that for the humans, descriptions and being able to 'grok' the proof / assess it for new tools and concepts is extremely helpful.

Is this human-written? Axiom Math is a company building AI theorem provers, one would think this would also be heavily AI-generated.

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Wasn’t the proof of Fermatt’s Last Theorem proof similar in complexity?

Worthless is a pretty good description IMO in the context of what Lean is trying to achieve: "enable correct, maintainable, and formally verified code". Tens of millions of lines of LLM vomit may be many things, but it often turns out to not be correct and certainly not maintainable. Formally verified remains as a thin fig leaf covering the uncomfortable truth that formal methods only provide assurances under assumptions (your toolchain, libraries, compiler, OS, and hardware are "correct" and don't expose some exploitable flaw).

It doesn't mean that it cannot improve over time, maybe the proof can be "minified" to a state where human reviewers are able to comprehend it; but as it stands there isn't really much insight or confidence to be gained from the artifact itself.

There's a branch of mathematics called "pointless topology" [1].

[1] https://en.wikipedia.org/wiki/Pointless_topology

You can have your opinions about modern math, its usefulness in the world as it is, whether or not knowing if hairy balls can divide by three is actually going to be beneficial for anything but just obscure knowledge's sake. You may even say it's useless.

Needless to say, a useless result that absolutely no mathematician will ever read, confirm, understand, agree with or even consider to solve their "useless" problems is an impressive waste of resources.