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$10M AI Mathematical Olympiad Prize

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Re: $10M AI Mathematical Olympiad Prize

#91

Post by larodi »

anonylizard wrote: post #59
ekianjo wrote: post #52

Earlier quoted context omitted.

> Art isn't an easier problem than math Not sure. Art is about approximate pattern recognition and if you have a large enough dataset it seems that you can definitely reproduce some of that. For math... it involves consistent reasoning from A to Z - which does not allow for any kind of mistake in the way. In Art you won't feel too bad if the shadows or the lights are a little weird or if a character has 7 fingers ins…

Fingers are already mostly solved. The latest models draw hands better than most human artists. I think artists would disagree with your assessment of 'approximate pattern recognition'. Its more like： 1. Given a set of words describing what the user wants. 2. Arrange pixels in a grid 3. That maximizes the user rating On one hand it is tolerant of small errors. On the other hand its an extremely broad problem. Also to…

Well this thing about fingers, etc in drawings. Lets put it this way - for us mere mortals the generative images look very much okay. To artists and people who actually draw something, well ... they very often spot inconsistencies in the whole production, including how fingers, arms, overall body posture, etc is presented. So it is exactly what we can expect - good enough on average, but actually a mediocre result of commonality. Thing is the wide audience chews in mediocrity all the time, and nobody seems to have been able to change this for ages...

Re: $10M AI Mathematical Olympiad Prize

#92

Post by haltist »

WhitneyLand wrote: post #67

Winning a gold medal here will really be a leap forward for AI creativity and deep insight into problem solving. AI already is already contributing in substantial ways to research. What’s tantalizing here is this next level would take a huge step toward accelerating the pace of advancements in many fields. It will be a milestone in moving past AI being a mere tool in scientific progress to something much greater.

I sense you are a techno-optimist.

Re: $10M AI Mathematical Olympiad Prize

#93

Post by k2enemy »

falcor84 wrote: post #69
dimask wrote: post #62

Earlier quoted context omitted.

Proving that the first player has a winning strategy, or the optimal strategy for both players leads to draw.

Just to nitpick, while unlikely, it is theoretically possible that the second player has a winning strategy

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.

Re: $10M AI Mathematical Olympiad Prize

#94

Post by haltist »

machiaweliczny wrote: post #38
singularity2001 wrote: post #7

Maybe the recently announced 1T Parameter Scientific AI will be trained on mathematical papers as well and picks up reasoning on the fly: https://news.ycombinator.com/item?id=38391923 Or at least maybe it will be a good foundation model to be fine-tuned for reasoning?

Picks up reasoning on the fly seems like wishful thinking. On the other hand in nature there also is split into people who get math and those who don’t so maybe there are 2 different ways of bootstrapping brain to be functional and luck is all we need. Anyone knows more on this?

It's just a matter of scale because when you add more floating point numbers magical things happen. The magic is called emergence, as in if you have a big enough computer then it can do anything if you prompt it the right way. As a techno-optimist I believe that thinking is simply very complicated arithmetic and by adding enough numbers we can solve any problem.

Re: $10M AI Mathematical Olympiad Prize

#95

Post by daxfohl »

andyjohnson0 wrote: post #15

As the parent of a young adult currently half way through their maths undergrad, this kind of fills me with foreboding. I know that proof assistants etc have existed for quite a while now, but what with this and the murmours about OAI's Q* model, I do wonder what will happen to maths as a human endeavour - and as a enabling skill for jobs that can financially support people like my child.

In a way, all math proofs already exist. Humans just have to determine what is worth looking for and uncover them. AI will help us do the latter. But we still have to do the former ourselves.

It will still require sound mathematical knowledge and understanding, to know what are the interesting questions to ask. Even if AI knows all the answers, it doesn't change anything because the answers already exist anyway.

Re: $10M AI Mathematical Olympiad Prize

#96

Post by japoco »

anonylizard wrote: post #34
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.

Art isn't an easier problem than math. An artbot would have sounded more sci-fi than a mathbot only 2 years ago. Yet it only took the AI world 1.5 years to go from drawing child scribbles to replicating top artists with like 90% similarity (I can barely tell the difference between AI and human drawn art anymore with the new NovelAI model). It won't be long before AI starts to go superhuman in art skills. It won't tak…

I think art is much easier for LLM-style AI models to do compared to writing. To make a nice picture you just need to place pixels near each other in a way that looks good, and we all know LLMs are phenomenal at this. Good text on the other hand is not just text that has a good flow and fits the prompt. It must follow a line of thought, and LLMs don’t do that by design, even though we could argue wether they have that capability as an emergent one, but I don't believe that at all.

Re: $10M AI Mathematical Olympiad Prize

#97

Post by daveguy »

falcor84 wrote: post #69
dimask wrote: post #62

Earlier quoted context omitted.

Proving that the first player has a winning strategy, or the optimal strategy for both players leads to draw.

Just to nitpick, while unlikely, it is theoretically possible that the second player has a winning strategy

I would assume this is possible for any sufficiently complex game. Would you mind answering a few questions from someone near-completely ignorant about Go?

Does second mover in Go have some sort of artificial benefit in scoring or playing? As in -- is there something to compensate for moving second?

On the face it seems like first mover would have an advantage in any turn-based game. But maybe, in some games, seeing an opponent's strategy is more helpful than executing the strategy.

Also, are there examples of real games where second mover can always win? (Real as in, not made up with weird rules just to demonstrate it's possible.)

Re: $10M AI Mathematical Olympiad Prize

#98

Post by Davidzheng »

kevinbuzzard wrote: post #83
Davidzheng wrote: post #60

Earlier quoted context omitted.

https://chat.openai.com/share/ad42d09a-b366-4b21-b701-782fc8... . Will you re-evaluate how far GPT4 is from it from the fact that it can guess it's powers of primes?

Do we really know for sure that GPT4 has not seen this problem already?

It's a good point. The knowledge cut-off says Jan 2022, but in the past there's been reasons to suspect some data after the cut-off is in the model too. There's also the possibility that it has seen the problem somewhere else before Jan 2022.

Nevertheless, I think the more important question is whether GPT-4 is capable of

1) Listing all solutions less than 100

2) Figuring out the commonalities of the solutions

For 1) I have no doubt that the answer is yes based on its coding skills, in fact it is much stronger at coding than this. For 2) my subjective feeling in playing around with it is it's not consistent at similar problems but it can do it sometimes. Maybe in this case it has seen the list of prime powers <100 so it's very easy for it.

Re: $10M AI Mathematical Olympiad Prize

#99

Post by falcor84 »

Davidzheng wrote: post #84
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).

I don't think research math is that accessible! Granted theoretically it's possible to just read papers and do research--and possibly it's theoretically as accessible as possible. In practice people learn better with teachers and access to experts at the research level. If this pans out, we can commoditize access to experts (or even experts).

But even in 1913 a brilliant mathematician from the middle of nowhere could access a world class mentor. I would assume that this is so much easier these days. What would stand in the way of a modern day math prodigy from getting accepted into a good program?

Or is it about making this more accessible to students who are "merely good" rather than brilliant?

Re: $10M AI Mathematical Olympiad Prize

#100

Post by c7b »

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…

I'm sure lots of people have been thinking/working along that direction. I think the idea of combining LLMs with formal verification/proof assistant tools (Lean, Coq, Isabelle,...) is particularly interesting. Anyone is aware of any major groups working on open source solutions for this?
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