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AI solves International Math Olympiad problems at silver medal level

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Re: AI solves International Math Olympiad problems at silver medal level

#281
post #8

Earlier quoted context omitted.

I haven't read TFA as I'm at work, but I would be very interested to know what the system was doing in those three days. Were there failed branches it explored? Was it just fumbling its way around until it guessed correctly? What did the feedback loop look like?

> just fumbling its way around until it guessed correctly As opposed to 0.999999% of the human population who can't do it even if their life depends on it?

I guess you mean 99.9999%?

Re: AI solves International Math Olympiad problems at silver medal level

#282

Machines have been better than humans at chess for decades. Yet no one cares. Everyone's busy watching Magnus Carlsen. We are human. This means we care about what other humans do. We only care about machines insofar as it serves us. This principle is broadly extensible to work and art. Humans will always have a place in these realms as long as humans are around.

magnus carlsen basically quit because computers ruined chess. As did kasparov. Fischer was probably the last great player who was unassisted by tools.

Carlsen plays still at the highest level. He just didn't want to do the world championship anymore, wasn't worth the effort after winning it so many times.

Re: AI solves International Math Olympiad problems at silver medal level

#285

To what extent is the training and structure of AlphaProof tailored specifically to IMO-type problems, which typically have short solutions using combinations of a small handful of specific techniques? (It's not my main point, but it's always worth remembering - even aside from any AI context - that many top mathematicians can't do IMO-type problems, and many top IMO medalists turn out to be unable to solve actual pr…

The last statement is largely correct (though idk what the imo medalists that are unable to solve actual problems most mathematicians can't solve most open problems). But i kind of disagree with the assessment of imo problems--the search space is huge if it were as you say it would be easy to search.

No, I don't mean that the search space is small. I just mean that there are special techniques which are highly relevant for IMO-type problems. It'd be interesting to know how important that knowledge was for the design and training of AlphaProof.

In other words, how does AlphaProof fare on mathematical problems which aren't in the IMO style? (As such exceptions comprise most mathematical problems)

Re: AI solves International Math Olympiad problems at silver medal level

#286

I'm seriously jealous of the people getting paid to work on this. Sounds great fun and must be incredibly satisfying to move the state of the art forward like that.

C'mon you're meant to be re-configuring 3,292,329 line of YML for K8s.

(/s)

Re: AI solves International Math Olympiad problems at silver medal level

#287

I'm seriously jealous of the people getting paid to work on this. Sounds great fun and must be incredibly satisfying to move the state of the art forward like that.

C'mon you're meant to be re-configuring 3,292,329 line of YML for K8s. (/s)

It's funny that if I could describe my entire career, it would probably be something similar to software janitor/maintenance worker.

I guess I should have pursued a PhD when I was younger.

Re: AI solves International Math Olympiad problems at silver medal level

#289
post #6

The problems were first converted into a formal language. So they were partly solved by the AI

Yes and it is difficult for me to believe that there is not useful human analysis and understanding involved in this translation that the AI is helpless without. But that I suppose is a problem that could be tackled with a different model...

It is vastly easier to do the formalization than to actually solve the problem. Any undergraduate with some lean familiarity could do it in minutes.

Re: AI solves International Math Olympiad problems at silver medal level

#290

Earlier quoted context omitted.

The linked page says > While the problem statements were formalized into Lean by hand, the answers within the problem statements were generated and formalized by the agent. However, it's unclear what initial format was given to the agents that allowed this step

So if Lean was used to find the answers, where exactly is the AI? A thin wrapper around Lean?

Think of problems in NP - you can check the answer efficiently, but finding the answer to check is the hard part... This is basically what we're looking at here: The proof checker can quickly evaluate correctness, but we need something to produce the proof, and that's the hard part.
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