Live data from Hacker News

AI solves International Math Olympiad problems at silver medal level

deepmind.google

231–240 of 564 posts

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

#231
post #191

Is the score of 28 comparable to the score of 29 here? https://www.kaggle.com/competitions/ai-mathematical-olympiad...

IIUC the American Math Olympiad has 3 rounds. Wining the last one is almost a guaranty gold medal.

The link you posted has problems with a dificulty between the first and second round that are much easier.

I took a quik look at the recent list of problems in the first and second round. I expect this new AI to get a solid 50/50 points in this test.

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

#232
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.

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

#233

Earlier quoted context omitted.

The point isn't IMO rules. It's that we are living in a period of time where there are very real consequences of nearly a century of unchecked CO2 due to human industry. And AI (like crypto before it) requires considerable energy consumption. Because of which, I believe we (people who believe in AI) need to hold companies accountable by very transparently disclosing those energy costs.

What if at some point AI figures out a solution to climate change?

You mean new and incredibly effective ways to shape public opinion? I guess it might. But then someone would still have to use it for that purpose...

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

#234

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.

Sure but if an AI can prove e.g the Goldbach conjecture then that is a bfd.

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

#235

Theorem proving is a single-player game with an insanely big search space, I always thouht it would be solved long before AGI. IMHO, the largest contributors to AlphaProof were the people behind Lean and Mathlib, who took the daunting task of formalizing the entirety of mathematics to themselves. This lack of formalizing in math papers was what killed any attempt at automation, because AI researcher had to wrestle wi…

> Theorem proving is a single-player game with an insanely big search space, I always thouht it would be solved long before AGI.

This seems so weird to me - AGI is undefined as a term imo but why would you expect "producing something generally intelligent" (i.e. median human level intelligence) to be significantly harder than "this thing is better than Terrence Tao at maths"?

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

#236
post #48

Earlier quoted context omitted.

There's no energy limit in the IMO rules.

The point isn't IMO rules. It's that we are living in a period of time where there are very real consequences of nearly a century of unchecked CO2 due to human industry. And AI (like crypto before it) requires considerable energy consumption. Because of which, I believe we (people who believe in AI) need to hold companies accountable by very transparently disclosing those energy costs.

They are 100% accountable for paying the bill from their electricity provider.

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

#237
post #223
post #177

In 1997, machines defeated a World Chess Champion for the first time, using brute-force "dumb search." Critics noted that while "dumb search" worked for chess, it might not necessarily be a general strategy applicable to other cognitive tasks.[a] In 2016, machines defeated a World Go Champion for the first time, using a clever form of "dumb search" that leverages compute, DNNs, reinforcement learning (RL), and self-p…

If one of the lessons of LLMs was that much of "common sense" is covered in the written language corpus - that is, perhaps, basic human intelligence is covered by language. Then, should we expect less with mathematics where written language is the normal way knowledge is propagated, and where formal proofs are wanted? An important distinction here is the coupling of search (not LLM for this one), a formal math langua…

>that is, perhaps, basic human intelligence is covered by language.

It isn't. That's why LLMs are still terrible at basic reasoning tasks. The dataset doesn't contain the human intelligence, just the end results. Nobody is training their LLMs on brain scans.

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

#238

So I am extremely hyped about this, but it's not clear to me how much heavy lifting this sentence is doing: > First, the problems were manually translated into formal mathematical language for our systems to understand. The non-geometry problems which were solved were all of the form "Determine all X such that…", and the resulting theorem statements are all of the form "We show that the set of all X is {foo}". The do…

I as someone with a maths degree but who hasn't done this kind of thing for half a decade, was able to immediately guess the solution to (1) but actually proving it is much harder.

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

#239
post #177

In 1997, machines defeated a World Chess Champion for the first time, using brute-force "dumb search." Critics noted that while "dumb search" worked for chess, it might not necessarily be a general strategy applicable to other cognitive tasks.[a] In 2016, machines defeated a World Go Champion for the first time, using a clever form of "dumb search" that leverages compute, DNNs, reinforcement learning (RL), and self-p…

High efficiency "search" is necessary to reach AGI. For example, humans don't search millions of potentially answers to beat ARC Prize puzzles. Instead, humans use our core experience to shrink the search space "intuitively" and deterministically check only a handful of ideas. I think deep-learning guided search is an incredibly promising research direction.

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

#240
post #206

Earlier quoted context omitted.

> a lot of brute force search Don't dismiss search, it might be brute force but it goes beyond human level in Go and silver at IMO. Search is also what powers evolution which created us, also by a lot of brute forcing, and is at the core of scientific method (re)search.

What makes solving IMO problems hard is usually the limits of human memory, pattern-matching, and search, not creativity. After all, these are problems that are already solved, and it is expected that many people can solve the problems in about 1 hour's time. That makes it, in principle, similar or even easier than a champsionship-level chess move, which often take more than 1 hour for a professional human (with more…

Ok but if you read the actual solutions they aren't a bizarre mess of brute force.

They look like what a human would write if they were trying to come up with a formal proof (albeit it does some steps in a weird order).

Post reply on HN