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$10M AI Mathematical Olympiad Prize

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Re: $10M AI Mathematical Olympiad Prize

#72

Post by andyjohnson0 »

slibhb wrote: post #23
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.

I wouldn't worry about it. We're going to need humans with specialized mathematical training in the loop. Besides, these things have a way of surprising us. Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

> Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

That analogy occurred to me too. But I'm not sure what the corresponding higher-level domain is that mathematicians might have to migrate to - in the way that assembly programmers started using high level languages. Writing prompts for maths LLMs, or wrangling teams of them, is hardly going to be well paid enough to facilitate a decent life in this era of late capitalism, or even pay uni fees.

And even if there are such higher-level domains, its not certain that they are compatable with available human cognitive ability or limits.

Lots of maths grads currently go into tech/finance/lifescience/whatever. I'm a dev and I can see those fields being eaten alive by this stuff. I don't want my kid to end up as a 2030-equivalent of a fully qualified assembly language programmer.

Re: $10M AI Mathematical Olympiad Prize

#74

Post by spi »

spi wrote: post #48
edf13 wrote: post #6

Earlier quoted context omitted.

The IMO are a bit more involved... e.g. IMO 2023: > Problem 1. Determine all composite integers n > 1 that satisfy the following property: if d1, d2, . . . , dk are all the positive divisors of n with 1 = d1 Although ChatGPT 4 makes a pretty decent start on this already: > To determine all composite integers \( n > 1 \) that satisfy the given property, we need to closely examine the condition set forth: for a composi…

A decent start? It says absolutely nothing about how to solve it, except repeating the question. The part where it tries out the few first numbers is entirely wrong, given that 6 does _not_ satisfy the condition (2 does not divide 3+6=9) and 8 _does_ (2 does divide 4+8=12). Amusingly, the list of the integers Given that GPT4 is not a model but a full product, behind the scenes it probably coded up and ran a small pyt…

(I'm also replying myself concerning the problem itself).

Unless I'm getting myself completely wrong, this also seems to be a very unusually simple problem for IMO's standards. I don't think I ever got myself solving one of them when I tried in the past, but if I'm not fooling myself the most natural approach for this one seems to bring to the solution:

1) Look at the two smallest divisors 1 q = ap, which is impossible because p divides neither p+1 nor q.

2) So, for n not to be a power of p, it must be 1 Gosh I feel like a grumpy old man saying "those youngsters, on my days we used to have harder problems than this" ;-)

Re: $10M AI Mathematical Olympiad Prize

#76

Post by tromp »

anonylizard wrote: post #49
RandomLensman wrote: post #42

Earlier quoted context omitted.

AlphaGo solved Go?

"Superhuman at solving" != "solved". AlphaGo didn't solve go (Ie, can the first mover guarantee a win?). However, it understood go at a far, far superior level to any human. A mathbot doens't have to solve math in general. It merely has to be better at solving math than any human mathematician to be considered ASI. And it only has to be better than the 'average' human mathematician to be extremely useful in accelerat…

> solve go (Ie, can the first mover guarantee a win?).

Solving Go means determining by what margin the first player can win, or equivalently, at what komi for white the game is a theoretical draw.

That also makes it dependent on the exact rule set used.

E.g. 2x2 go is a +1 first player win with the Tromp-Taylor rules of Go, while the Japanese rules are not even sufficiently formalized to allow scoring a 2x2 game.

Re: $10M AI Mathematical Olympiad Prize

#77

Post by Davidzheng »

spi wrote: post #65
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?

Good to know it can do that, in the pasted chat above it didn't. To be honest, it surprised me it couldn't, this isn't exactly a very hard guess given the computation results. It doesn't convince me GPT4 is anywhere close to winning the IMO, though :-)

True. I let it continue and even prompted it with hints but it cannot find the proof that non-prime powers fail. It can however prove prime powers work.

Re: $10M AI Mathematical Olympiad Prize

#78

Post by falcor84 »

Davidzheng wrote: post #37
slibhb wrote: post #23

Earlier quoted context omitted.

I wouldn't worry about it. We're going to need humans with specialized mathematical training in the loop. Besides, these things have a way of surprising us. Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

It's highly unclear to me what will happen. Probably learning math will be more accessible. But it's unclear how many humans will be involved at the forefront of math research. For example you can imagine a situation where in some parts of math large communities work in a direction guided by a few "visionaries". This sort of thing will not really happen after the commodization of theorem provers. Like instead of an a…

>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).

Re: $10M AI Mathematical Olympiad Prize

#79

Post by nathanfig »

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?

Some private enterprises would undoubtedly ignore this prize, but a lot of academic researchers (including students) would be more than motivated by this prize.
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