(You're talking to one of the people who was part of the project, which is why I took @ocfnash's answer as authoritative: they did not cheat.)

If they're talking to the people who are part of the project I'd hope the answer would contain detail and not expect to be taken as authoritative.

If they're talking to the public I'd hope that they don't face an infinite loop of ever-more stringent requirements for proof they didn't give it the answer in the question.

That's a weird perception of talking to the public.

That wasn't very nice. Are you curious about anything? Happy to help. I'd proactively do it, but I don't want to guess at whats in your mind. My initial guess is you think I think that engaging with the public is an infinite loop. I don't!

I would expect that in their data which they train AlphaProof on they have some concept of a "vague problem" whoch could just look like

{Formal description of the set in question} = ?

And then Alphaproof has to find candidate descriptions of this set and prove a theorem that they are equal to the above.

I doubt they would claim to solve the problem if they provided half of the answer.

> I doubt they would claim to solve the problem if they provided half of the answer.

Stranger things have happened

To be fair, that isn't half the answer it's like 99% of the answer.

They clarified above that it provided the full answer though.

The deepmind team has a history of being misleading. The great StarCraft 2 strategist bot is still in mind.

What’s the story with that bot? Always thought it was cool. Was that all smoke and mirrors?

I think maybe parent comment is referring to it essentially just employing a zerg rush but with the speed and reaction time of an AI? Not 100% sure... Unrelated, iirc the starcraft functionality was an early example of generalizing a pretrained NN, alphaGO, and showing that it could adapt to learn and defeat games across strategic domains, especially after it learned so much strategy from the most difficult, widely played, and most strategically-varied physical game available.

> I doubt they would claim to solve the problem if they provided half of the answer.

This falls under extraordinary claims require extraordinary proof and we have seen nothing of the sort.

its not clear if theorem is actual input formal definition, or formal definition was in different form.

Exactly, a problem and its answer are just different ways of describing the same object. Every step of a proof is a transformation/translation of the same object. It would be disingenuous to say that some heavy lifting isn't done in formalizing a problem but it seems that step is also performed by a machine:

"We established a bridge between these two complementary spheres by fine-tuning a Gemini model to automatically translate natural language problem statements into formal statements, creating a large library of formal problems of varying difficulty."

I'm confused, is the formalization by Gemini or "manually"? Which is it?

Come up with many possible answers, formalize them all, and then try to prove or disprove each of them.

This is probably partially what they did idk why it's downvoted lol