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$10M AI Mathematical Olympiad Prize

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Re: $10M AI Mathematical Olympiad Prize

#191

Post by supernewton »

nojvek wrote: post #170
lupire wrote: post #158

This is an embarrassing overreach. We don't even have models that can win the far easier AMC, let alone AIME, USAMO, and then IMO.

What is AMC AIME, USAMO ?

They're the feeder contests in the U.S. that determine who gets to represent the U.S. in the IMO.

AMC = multiple choice test, open to all grade school students.

AIME = open response test, all answers are numerical, open to students who score high enough on AMC only.

USAMO = USA Math Olympiad. IMO-style proof problems. Open only to top N scorers on AMC and AIME.

Re: $10M AI Mathematical Olympiad Prize

#193

Post by singularity2001 »

quirino wrote: post #153
haltist wrote: post #94

Earlier quoted context omitted.

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.

Depends a lot on how this scales though. If you need 10x as many parameters to get 1% better results for instance, then even if this works it could be impractical.

Very valid point. The last papers I read on the subject conclusively show that all current networks do not hit a limit in scaling though. Bill Gates said that GPT five will not be much better than GPT four so maybe things change

Re: $10M AI Mathematical Olympiad Prize

#194

Post by Yhippa »

BeetleB wrote: post #109
Yhippa wrote: post #68

I'm asking this question out of ignorance: if you were able to do this, why would you make it public for $10MM instead of keeping it private and exploiting it. Say, in algorithmic trading models?

I see no reason to believe such a machine would be helpful for algorithmic trading. Why should it? How well do current gold medalists do in trading?

I was curious as to why an algorithmic trading firm is sponsoring this. What's in it for them?

Re: $10M AI Mathematical Olympiad Prize

#195

Post by EVa5I7bHFq9mnYK »

auntienomen wrote: post #180
antoinexp wrote: post #85

Earlier quoted context omitted.

Might depend on the terms you have in mind, but current consensus seems to be more like 4-5 years as we speak on https://www.metaculus.com/questions/6728/ai-wins-imo-gold-me...

That's 4-5 years for solving Olympiad problems. Those are just very tricky high school math problems. They have solutions and can generally be solved by applying some combination of standard tricks. It's very much the sort of thing an LLM should be good at. Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, st…

We can look at it this way: there are ~1000 chess Grandmasters and one World Champion. It took very short time for AI to go from beating an average GM to beating World Champion.

There are ~1000 MO winners and 1 (one) Millenial problem solver ...

Re: $10M AI Mathematical Olympiad Prize

#196

Post by gorkish »

jacobr1 wrote: post #142
anonylizard wrote: post #30

Earlier quoted context omitted.

I don't think the actual winning algorithm itself was used, because real world systems have more constraints/requirements than what the recommender was trained on. But that was in 2009, pre deep-learning/AI summer, and $1 mil clearly helped stimulate interest in that area. Today we see multiple billion dollar recommender systems, like Tiktok. Netflix ironically benefits the least from recommenders due to the nature o…

My understanding was that their research on what drove engagement shifted quite a bit. Things like social proof, and product patterns like auto-loading the next episode to binge drove engagement metrics. Recently there were some articles about their team custom-identifying which cuts of a video to show as a trailer maximized engagement on a personal level. In some sense that is a recommendation, but it is a broader p…

I have a more cynical take; the recommendations declined when Netflix started producing their own content. Prior to this, what constituted a "good recommendation" was aligned between Netflix and the customer, but afterwards not so much.

Today Netflix is in the "how do we get our customers to use our service as little as possible but still pay us every month" phase of their mediacom hypocracy. From a business standpoint, that is their best optimization. They are AOL/TW from 20 years ago.

Re: $10M AI Mathematical Olympiad Prize

#197

Post by auntienomen »

EVa5I7bHFq9mnYK wrote: post #195
auntienomen wrote: post #180

Earlier quoted context omitted.

That's 4-5 years for solving Olympiad problems. Those are just very tricky high school math problems. They have solutions and can generally be solved by applying some combination of standard tricks. It's very much the sort of thing an LLM should be good at. Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, st…

We can look at it this way: there are ~1000 chess Grandmasters and one World Champion. It took very short time for AI to go from beating an average GM to beating World Champion. There are ~1000 MO winners and 1 (one) Millenial problem solver ...

We can. But doing so frames math research as the same sort of activity as math problem solving.. it's not. Many imo champions struggle to do any successful math research. And many successful math researchers (e.g., all of the most recent batch of Fields medallists) never did the Oympiad at all.

Re: $10M AI Mathematical Olympiad Prize

#198

Post by EVa5I7bHFq9mnYK »

dxbydt wrote: post #175
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.

Perhaps this might cheer you up - https://statmodeling.stat.columbia.edu/2015/03/17/1980-math-... Or perhaps not. In that blog, Gelman speaks of Gregg, who ended up as a GS VP, and says - math olympiad = high school basketball star pro mathematician = NBA player Goldman Sachs VP = sports hustler I actually worked with Gregg in fixed income at that time :) Gelman's blogpost received sufficient notoriety, atleast withi…

Yet GS VPs salary is closer to NBA player's salary, while math pro's salary is closer to sports hustlers' ...

Re: $10M AI Mathematical Olympiad Prize

#199

Post by paulddraper »

Enginerrrd wrote: post #132
eddtries wrote: post #125

Earlier quoted context omitted.

I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon

Yeah, millennium problems almost certainly require truly novel nontrivial ideas to solve. That's a tough thing for AI to do. On the other hand, Terrence Tao had an interesting article on his blog a while back where he was trying to solve a problem and asked chatGPT about it in a high-level strategy sense. ChatGPT suggested several reasonable approaches, one of which turned out to work. That's nowhere near solving a m…

Ask yourself what mathematicians do today...

They decompose problems, solve specialized subsets, examine more general cases, use existing proofs, do some numerical analysis, etc.

Re: $10M AI Mathematical Olympiad Prize

#200

Post by lacker »

openquery wrote: post #116

Can automated theorem provers solve mathematical olympiad problems in a reasonable time given enough compute? LLMs are quite good at generating semantically correct language. I remember reading a paper about extending the planning capabilities of GPT-4 by using a Planning Domain Definition Language [0]. By that same logic could an LLM not translate the olympiad problem into a form suitable for a theorem prover? [0] h…

No, IMO problems are much too hard for the current generation of theorem provers.
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