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Can AI do maths yet? Thoughts from a mathematician

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Re: Can AI do maths yet? Thoughts from a mathematician

#171

Post by riku_iki »

nebulous1 wrote: post #39

There was a little more information in that reddit thread. Of the three difficulty tiers, 25% are T1 (easiest) and 50% are T2. Of the five public problems that the author looked at, two were T1 and two were T2. Glazer on reddit described T1 as "IMO/undergraduate problems", but the article author says that they don't consider them to be undergraduate problems. So the LLM is already doing what the author says they woul…

> So the LLM is already doing what the author says they would be surprised about.

that's if you unconditionally believe in result without any proofreading, confirmation, reproducability and even barely any details (we are given only one slide).

Re: Can AI do maths yet? Thoughts from a mathematician

#172

Post by lern_too_spel »

bongodongobob wrote: post #156
Radim wrote: post #150

Earlier quoted context omitted.

> don't trust Nobel laureates or even winners Nobel laureate and winner are the same thing. > Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel. Can you be more specific, what garbage? And which Nobel prize do you mean – Pauling got two, one for chemistry and one for peace.

Eugenics and vitamin C as a cure all.

If Pauling's eugenics policies were bad, then the laws against incest that are currently on the books in many states (which are also eugenics policies that use the same mechanism) are also bad. There are different forms of eugenics policies, and Pauling's proposal to restrict the mating choices of people carrying certain recessive genes so their children don't suffer is ethically different from Hitler exterminating people with certain genes and also ethically different from other governments sterilizing people with certain genes. He later supported voluntary abortion with genetic testing, which is now standard practice in the US today, though no longer in a few states with ethically questionable laws restricting abortion. This again is ethically different from forced abortion.

https://scarc.library.oregonstate.edu/coll/pauling/blood/nar...

Re: Can AI do maths yet? Thoughts from a mathematician

#173

Post by joe_the_user »

nebulous1 wrote: post #39

There was a little more information in that reddit thread. Of the three difficulty tiers, 25% are T1 (easiest) and 50% are T2. Of the five public problems that the author looked at, two were T1 and two were T2. Glazer on reddit described T1 as "IMO/undergraduate problems", but the article author says that they don't consider them to be undergraduate problems. So the LLM is already doing what the author says they woul…

The reddit thread is ... interesting (direct link[1]). It seems to be a debate among mathematicians some of whom do have access to the secret set. But they're debating publicly and so naturally avoiding any concrete examples that would give the set away so wind-up with fuzzy-fiddly language for the qualities of the problem tiers.

The "reality" of keeping this stuff secret 'cause someone would train on it is itself bizarre and certainly shouldn't be above questioning.

https://www.reddit.com/r/OpenAI/comments/1hiq4yv/comment/m30...

Re: Can AI do maths yet? Thoughts from a mathematician

#174

Post by nyrikki »

ComplexSystems wrote: post #162
nyrikki wrote: post #153

Earlier quoted context omitted.

What LLMs can do is limited, they are superior to wet-wear in some tasks like finding and matching patterns in higher dimensional space, they are still fundamentally limited to a tiny class of problems outside of that pattern finding and matching. LLMs will be tools for some math needs and even if we ever get quantum computers will be limited in what they can do. LLMs, without pattern matching, can only do up to abou…

"LLMs, without pattern matching, can only do up to about integer division, and while they can calculate parity, they can't use it in their calculations." - what do you mean by this? Counting the number of 1's in a bitstring and determining if it's even or odd?

Yes, in this case PARITY is determining if the number of 1s in a binary input is odd or even

It is an effect of the complex to unpack descriptive complexity class DLOGTIME-uniform TC0, which has AND, OR and MAJORITY gates.

http://arxiv.org/abs/2409.13629

The point being that the ability to use parity gates is different than being able to calculate it, which is where the union of the typically ram machine DLOGTIME with the circuit complexity of uniform TC0 comes into play.

PARITY, MAJ, AND, and OR are all symmetric, and are in TCO, but PARITY is not in DLOGTIME-uniform TC0, which is first-order logic with Majority quantifiers.

Another path, if you think about symantic properties and Rice's theorem, this may make sense especially as PAC learning even depth 2 nets is equivalent to the approximate SVP.

PAC-learning even depth-2 threshold circuits is NP-hard.

https://www.cs.utexas.edu/~klivans/crypto-hs.pdf

For me thinking about how ZFC was structured so we can keep the niceties of the law of the excluded middle, and how statistics pretty much depends on it for the central limit and law of large numbers, IID etc...

But that path runs the risk of reliving the Brouwer–Hilbert controversy.

Re: Can AI do maths yet? Thoughts from a mathematician

#176

Post by obastani »

joe_the_user wrote: post #173
nebulous1 wrote: post #39

There was a little more information in that reddit thread. Of the three difficulty tiers, 25% are T1 (easiest) and 50% are T2. Of the five public problems that the author looked at, two were T1 and two were T2. Glazer on reddit described T1 as "IMO/undergraduate problems", but the article author says that they don't consider them to be undergraduate problems. So the LLM is already doing what the author says they woul…

The reddit thread is ... interesting (direct link[1]). It seems to be a debate among mathematicians some of whom do have access to the secret set. But they're debating publicly and so naturally avoiding any concrete examples that would give the set away so wind-up with fuzzy-fiddly language for the qualities of the problem tiers. The "reality" of keeping this stuff secret 'cause someone would train on it is itself bi…

It's not about training directly on the test set, it's about people discussing questions in the test set online (e.g., in forums), and then this data is swept up into the training set. That's what makes test set contamination so difficult to avoid.

Re: Can AI do maths yet? Thoughts from a mathematician

#177

Post by reshlo »

sebzim4500 wrote: post #74
reshlo wrote: post #43

Earlier quoted context omitted.

Nobody said you have to do it in your head.

That's the equivalent to what we are asking the model to do. If you give the model a calculator it will get 100%. If you give it a pen and paper (e.g. let it show it's working) then it will get near 100%.

Citation needed.

Re: Can AI do maths yet? Thoughts from a mathematician

#178

Post by a3w »

Filligree wrote: post #44
glimshe wrote: post #27

Earlier quoted context omitted.

Isn't Wolfram Alpha a better "ChatGPT of Math"?

Wolfram Alpha is better at actually doing math, but far worse at explaining what it’s doing, and why.

Is the explanation a pro feature? At the very end it says "step by step? Pay here"

Re: Can AI do maths yet? Thoughts from a mathematician

#179

Post by busyant »

pfisherman wrote: post #145
busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

I used to do bench top work too; and was blessed with “the golden hands” in that I could almost always get protocols working. To me this always felt more like intuition than deductive reasoning. And it made me a terrible TA. My advice to students in lab was always something along the lines of “just mess around with it, and see how it works.” Not very helpful for the stressed and struggling student -_- Digression asid…

> blessed with “the golden hands” in that I could almost always get protocols working.

Very funny. My friends and I never used the phrase "golden hands" but we used to say something similar: "so-and-so has 'great hands'".

But it meant the same thing.

I, myself, did not have great hands, but my comment was more about the intellectual process of conducting research.

I guess my point was that:

* I've already dealt with more talented researchers, but I still contributed meaningfully.

* Hopefully, the "AI" will simply add another layer of talent, but the rest of us lesser mortals will still be able to contribute.

But I don't know if I'm correct.

Re: Can AI do maths yet? Thoughts from a mathematician

#180

Post by TheRealPomax »

busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

What part do you think is going to become obsolete? Because Math isn't about "working out the math", it's about finding the relations between seemingly unrelated things to bust open a problem. Short of AGI, there is no amount of neural net that's going to realize that a seemingly impossible probabilistic problem is actually equivalent to a projection of an easy to work with 4D geometry. "Doing the math" is what we have computers for, and the better they get, the easier the tedious parts of the job become, but "doing math" is still very much a human game.
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