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$10M AI Mathematical Olympiad Prize

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Re: $10M AI Mathematical Olympiad Prize

#51

Post by RandomLensman »

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…

What mathematics was AlphaGo solving? What do you mean by solving there?

Re: $10M AI Mathematical Olympiad Prize

#52

Post by ekianjo »

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…

> 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 instead of 5 on one hand, but this kind of mishaps break everything in Math.

Re: $10M AI Mathematical Olympiad Prize

#53

Post by Davidzheng »

magnio wrote: post #10
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…

That's 300 words for saying "in order for n to satisfy the requirements, it must satisfy the requirements." I tried an easier problem, extending Rolle's theorem to the multidimensional case with Poe.com: Prompt: Let U be an open subset of R^n with compact closure K. Suppose f: K → R is continuous on K, differentiable on U, and satisfies f(x) = 0, for all x in K \ U. Show that there exists a in U with grad f (a) = 0.…

https://chat.openai.com/share/f710b53c-1d87-4228-8940-f48ec6... GPT-4 for me solves it.

Re: $10M AI Mathematical Olympiad Prize

#54

Post by auggierose »

Davidzheng wrote: post #32
auggierose wrote: post #22

Earlier quoted context omitted.

I wouldn't worry. What this means is that mathematics as a skill is going to be back big time, because now you can actually use it everywhere. Mathematics departments have been closing down for a while now, I think. I think this trend will reverse now. Mathematics itself will change in the process, but for the better.

I don't think it's true that "math departments have been closing for a while now"

It's an impression I had, I don't know any hard data. For example:

https://www.reddit.com/r/math/comments/l7yyir/not_joking_uni...

https://www.reddit.com/r/math/comments/15of64l/rumor_west_vi...

Re: $10M AI Mathematical Olympiad Prize

#55

Post by eigenket »

magnio wrote: post #10
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…

That's 300 words for saying "in order for n to satisfy the requirements, it must satisfy the requirements." I tried an easier problem, extending Rolle's theorem to the multidimensional case with Poe.com: Prompt: Let U be an open subset of R^n with compact closure K. Suppose f: K → R is continuous on K, differentiable on U, and satisfies f(x) = 0, for all x in K \ U. Show that there exists a in U with grad f (a) = 0.…

> Now, let's define a new function g: K → R^n such that g(x) = (f(x), f(x), ..., f(x)) for all x in K. In other words, each component of g is equal to f(x) for all x in K.

That's hilarious

Re: $10M AI Mathematical Olympiad Prize

#56

Post by Davidzheng »

edf13 wrote: post #6
daoboy wrote: post #5

Anything you can do with a calculator is obviously trivial. Is there a clear point of departure when AI can no longer handle mathematical reasoning?

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…

GPT-4+code is surprisingly good. https://chat.openai.com/share/ad42d09a-b366-4b21-b701-782fc8... "This observation leads to a hypothesis: only the powers of prime numbers satisfy the given condition. To verify this hypothesis, we need to consider why powers of primes might uniquely satisfy the divisibility condition and then prove or disprove it."

Re: $10M AI Mathematical Olympiad Prize

#57

Post by sdenton4 »

Davidzheng wrote: post #32
auggierose wrote: post #22

Earlier quoted context omitted.

I wouldn't worry. What this means is that mathematics as a skill is going to be back big time, because now you can actually use it everywhere. Mathematics departments have been closing down for a while now, I think. I think this trend will reverse now. Mathematics itself will change in the process, but for the better.

I don't think it's true that "math departments have been closing for a while now"

Correct - math departments are doing fine. Not quite as fine as CS departments, which get showered with piles of money and their grad students poached to make money in industry. But so long as other university departments want their students to know some combination of calculus, linear algebra, and statistics, math departments will continue humming along.

Re: $10M AI Mathematical Olympiad Prize

#58

Post by skepticATX »

adhocmobility wrote: post #16
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 think its pretty clear that in the coming decade intelligence and cognitive labor is going to become very cheap. So your kid should develop some skills outside of that to stay competitive in the job market.

I think it's pretty clear that cognitive labor will become even higher value in the future, as our tools get better and allow us to become more productive.

Re: $10M AI Mathematical Olympiad Prize

#59

Post by anonylizard »

ekianjo wrote: post #52
anonylizard wrote: post #34

Earlier quoted context omitted.

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…

> 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 get a good user rating, it has to do 99 things right for every 1 thing it draws wrong.

Re: $10M AI Mathematical Olympiad Prize

#60

Post by Davidzheng »

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…

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?
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