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$10M AI Mathematical Olympiad Prize

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Re: $10M AI Mathematical Olympiad Prize

#211

Post by mlengineerio »

gregdoesit wrote: post #2

I was recently in Palo Alto, and bumped into a newly founded startup (I don't remember the name unfortunately) who set themselves the grand the vision of exactly this: winning a gold medal on the international Olympiad using AI. Their plan was to build mostly on LLMs as a start, and iterate as they go. In their barebones office space, they had a poster with a countdown of the number of weeks till the event: it was 36…

Can you share the name of the startup? I'm also in Palo Alto and tinkering LLM for Match competition too (math.llmlab.io).

Re: $10M AI Mathematical Olympiad Prize

#212

Post by dimask »

bilater wrote: post #182
dimask wrote: post #29

Earlier quoted context omitted.

Their current ambition is to be able to solve school math, which is quite far away from solving unsolved conjectures or math olympiads. I really doubt that any of this is within LLM/transformer scope, except maybe in some auxiliary sense to other, much different architectures.

Exponential progress. Hard to wrap your mind around. An analogy: If it takes 20 years to create AGI equivalent to the village idiot. It take another couple of hours to go from that to Einstein.

I don't disagree, as in that if we achieve school math in a way that is not mere overfitting over a language-based training set, going to more advanced mathematics is definitely conceivable. My problem is that people are talking about solving unsolved conjectures while we are not even in a point where we know how to tackle math at all.

Imo we are not currently in the beginning of an exponential curve re solving math with AI, and def not on the path of AGI. I understand that if one believes that we are on the path to AGI soon then we shall have these math-AI advancements quite soon, but I disagree with the premise.

Re: $10M AI Mathematical Olympiad Prize

#213

Post by recursivecaveat »

godelski wrote: post #183
k2enemy wrote: post #93

Earlier quoted context omitted.

To nitpick a little further, it actually is not possible that the second player has a winning strategy. For that to be the case, P2 would need a winning path of play no matter what P1's first move is. Suppose that P1 passes on their first move (which is a valid move). Then P2 has a winning path of play in which they put down the first stone. But P1 could have made that move and then they would be on the winning path.

I'm not a game theorist, in RL, nor a big Go player; but I am having a hard time finding this argument convincing. Isn't the whole reason Go is impressive is because the enormous set of possible moves? Like we know that no computer could run ever game in the lifetime of the universe were it to even perform millions of moves a second. So of the I understand this number to be north of 10^500 for possible legal and play…

It's a proof by contradiction, like the halting problem proof. It doesn't rely on the actual playable games at all, but what the existence of a winning strategy would imply. If there was a guaranteed winning strategy for player 2 it would be contradictory because player 1 could execute it by passing their first turn then using the winning P2 strategy. In that game both players can't be guaranteed to win, so there must be some flaw in P2's supposed guaranteed win strategy. https://en.m.wikipedia.org/wiki/Strategy-stealing_argument

Re: $10M AI Mathematical Olympiad Prize

#214

Post by ShamelessC »

haltist wrote: post #121
WhitneyLand wrote: post #110

Earlier quoted context omitted.

Maybe somewhat, but is anything I said that much of a leap? Do you consider AI to have already considered substantially to the advancement of science? For example AlphaFold, Weather forecasting, Algorithm optimization, etc

I believe the universe is a computer executing an algorithm. In fact, the universe is AI. This is a common belief among many techno-optimist church goers. People themselves are basically just numbers, aka algorithms, so future AI/numbers (people) will definitely contribute to scientific progress.

Are you serious?

edit: you’re either trolling or mentally ill. If it’s the latter, I sincerely apologize. Hope things get better for you soon.

edit edit: I saw your comments about the art project. Thank God. I didn’t want to live in a world where someone like that existed.

Re: $10M AI Mathematical Olympiad Prize

#215

Post by godelski »

recursivecaveat wrote: post #213
godelski wrote: post #183

Earlier quoted context omitted.

I'm not a game theorist, in RL, nor a big Go player; but I am having a hard time finding this argument convincing. Isn't the whole reason Go is impressive is because the enormous set of possible moves? Like we know that no computer could run ever game in the lifetime of the universe were it to even perform millions of moves a second. So of the I understand this number to be north of 10^500 for possible legal and play…

It's a proof by contradiction, like the halting problem proof. It doesn't rely on the actual playable games at all, but what the existence of a winning strategy would imply. If there was a guaranteed winning strategy for player 2 it would be contradictory because player 1 could execute it by passing their first turn then using the winning P2 strategy. In that game both players can't be guaranteed to win, so there mus…

I am familiar with strategy stealing and things like tit-for-tat. But even the wiki article you linked suggests that Go is not a symmetric game, which is the requisite condition for strategy stealing to work (which was my underlying belief albeit (very) poorly worded). The wiki suggests both ladder and ko fights create an asymmetry as well as central control. Not to mention Komi explicitly making it asymmetric.

First player does not always have the advantage. Nim is the best example where the setup can either be the first player winning game (nim-sum of the sizes of the heaps is not zero) or the second. My understanding is also that Chess (another perfect information turn-based game) is not shown solved or even has proven first player advantage (though in practice it looks so).

So I get the argument, I just don't buy it. I would be inclined to lean towards that direction, but it's a tough claim theoretically and probably not meaningful in practice (unless a generalized strategy such as strategy stealing can be employed otherwise a lookup table is impractical as it'd contain more bits than atoms in the universe even for 100 move games).

I think we have to consider far more than strategy-stealing which is not even a generalizable strategy to two-person perfect information turn-based games.

https://en.wikipedia.org/wiki/Nim#Proof_of_the_winning_formu...

Re: $10M AI Mathematical Olympiad Prize

#216

Post by supergirl »

not sure there is much point to this. currently no model is even at the level of primary school math. it will take decades until it can win a gold medal in maths. it won't happen overnight. it will happen slowly. will they still give out the prize in 20 years from now, when it won't seem like such a breakthrough?

Re: $10M AI Mathematical Olympiad Prize

#217

Post by [deleted] »

ShamelessC wrote: post #214
haltist wrote: post #121

Earlier quoted context omitted.

I believe the universe is a computer executing an algorithm. In fact, the universe is AI. This is a common belief among many techno-optimist church goers. People themselves are basically just numbers, aka algorithms, so future AI/numbers (people) will definitely contribute to scientific progress.

Are you serious? edit: you’re either trolling or mentally ill. If it’s the latter, I sincerely apologize. Hope things get better for you soon. edit edit: I saw your comments about the art project. Thank God. I didn’t want to live in a world where someone like that existed.

[deleted]

Re: $10M AI Mathematical Olympiad Prize

#218

Post by queuebert »

alecco wrote: post #187
queuebert wrote: post #139

Earlier quoted context omitted.

While I get your point and agree, there apparently is no Dunning-Kruger effect. It was determined to be yet another case of faulty data analysis in behavioral psych.[1] 1. https://economicsfromthetopdown.com/2022/04/08/the-dunning-k...

I don't think that's a mainstream take. But I can settle with: https://en.wikipedia.org/wiki/Overconfidence_effect Or even https://en.wikipedia.org/wiki/Grandiose_delusions

That first article cites more behavioral psych research, which has the absolute worst track record of data analysis. After so many retractions and scandals, I find it difficult to know what to believe anymore.

Re: $10M AI Mathematical Olympiad Prize

#219

Post by c-cube »

michaelt wrote: post #189
falcor84 wrote: post #78

Earlier quoted context omitted.

>Probably learning math will be more accessible. I'm not quite sure what you mean. Isn't math already pretty much the most accessible thing that could be imagined? I can't think of any story of someone in the past century who wanted to study math but was unable to, except for reasons prohibiting any sort of academic study whatsoever (e.g. girls in Taliban controlled areas).

Some people imagine AI will soon be a bit like being able to go to a university professor's office hours to ask questions and get detailed expert advice on any part of the undergraduate curriculum you're struggling with. Except it'll be available 24/7 and you won't have to pass exams, spend $$$$, attend full time, and live in dorms and be in your late teens or early 20s to get access.

And you'll have to fact check every answer to make sure it's not a "hallucination".

Re: $10M AI Mathematical Olympiad Prize

#220

Post by recursivecaveat »

godelski wrote: post #215
recursivecaveat wrote: post #213

Earlier quoted context omitted.

It's a proof by contradiction, like the halting problem proof. It doesn't rely on the actual playable games at all, but what the existence of a winning strategy would imply. If there was a guaranteed winning strategy for player 2 it would be contradictory because player 1 could execute it by passing their first turn then using the winning P2 strategy. In that game both players can't be guaranteed to win, so there mus…

I am familiar with strategy stealing and things like tit-for-tat. But even the wiki article you linked suggests that Go is not a symmetric game, which is the requisite condition for strategy stealing to work (which was my underlying belief albeit (very) poorly worded). The wiki suggests both ladder and ko fights create an asymmetry as well as central control. Not to mention Komi explicitly making it asymmetric. First…

The passing is the important part. In chess you can't pass so going first might be bad, you could be the first to reach a forced zugzwang. If you have the option of passing your first turn, then having a turn before the 2nd player gets to go is at worst neutral for you. Likewise in Nim you can't pass and taking your turn might be bad for you unlike Hex.
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