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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

#91

Post by haolez »

swalsh wrote: post #87

Every profession seems to have a pessimistic view of AI as soon as it starts to make progress in their domain. Denial, Anger, Bargaining, Depression, and Acceptance. Artists seem to be in the depression state, many programmers are still in the denial phase. Pretty solid denial here from a mathematician. o3 was a proof of concept, like every other domain AI enters, it's going to keep getting better. Society is CLEARLY…

I think it's a little of both. Maybe generative AI algorithms won't overcome their initial limitations. But maybe we don't need to overcome them to transform society in a very significant way.

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

#92

Post by WanderPanda »

swalsh wrote: post #87

Every profession seems to have a pessimistic view of AI as soon as it starts to make progress in their domain. Denial, Anger, Bargaining, Depression, and Acceptance. Artists seem to be in the depression state, many programmers are still in the denial phase. Pretty solid denial here from a mathematician. o3 was a proof of concept, like every other domain AI enters, it's going to keep getting better. Society is CLEARLY…

Or is it just white collar workers experiencing what blue collar workers have been experiencing for decades?

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

#93

Post by lordnacho »

jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

The only thing I've consistently had issues with while using AI is graphs. If I ask it to put some simple function, it produces a really weird image that has nothing to do with the graph I want. It will be a weird swirl of lines and words, and it never corrects itself no matter what I say to it.

Has anyone had any luck with this? It seems like the only thing that it just can't do.

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

#94

Post by red75prime »

Someone wrote: post #28
est wrote: post #13

At this stage I assume everything having a sequencial pattern can and will be automated by LLM AIs.

I think that’s provably incorrect for the current approach to LLMs. They all have a horizon over which they correlate tokens in the input stream. So, for any LLM, if you intersperse more than that number of ‘X’ tokens between each useful token, they won’t be able to do anything resembling intelligence. The current LLMs are a bit like n-gram databases that do not use letters, but larger units.

The follow-up question is "Does it require a paradigm shift to solve it?". And the answer could be "No". Episodic memory, hierarchical learnable tokenization, online learning or whatever works well on GPUs.

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

#95

Post by esafak »

WanderPanda wrote: post #92
swalsh wrote: post #87

Every profession seems to have a pessimistic view of AI as soon as it starts to make progress in their domain. Denial, Anger, Bargaining, Depression, and Acceptance. Artists seem to be in the depression state, many programmers are still in the denial phase. Pretty solid denial here from a mathematician. o3 was a proof of concept, like every other domain AI enters, it's going to keep getting better. Society is CLEARLY…

Or is it just white collar workers experiencing what blue collar workers have been experiencing for decades?

So will that make society shift to the left in demand stronger of safety nets, or to the right in search of a strongman to rescue them?

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

#96

Post by lcnPylGDnU4H9OF »

alphan0n wrote: post #64

As far as ChatGPT goes, you may as well be asking: Can AI use a calculator? The answer is yes, it can utilize a stateful python environment and solve complex mathematical equations with ease.

There is a difference between correctly stating that 2 + 2 = 4 within a set of logical rules and proving that 2 + 2 = 4 must be true given the rules.

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

#97

Post by [deleted] »

jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

[deleted]

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

#98

Post by gmadsen »

voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

I hear these arguments a lot from law and philosophy students, never from those trained in mathematics. It seems to me, "literary" people will still be discussing these theoretical hypotheticals as technology passes them by building it.

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

#99

Post by beng-nl »

Someone wrote: post #28
est wrote: post #13

At this stage I assume everything having a sequencial pattern can and will be automated by LLM AIs.

I think that’s provably incorrect for the current approach to LLMs. They all have a horizon over which they correlate tokens in the input stream. So, for any LLM, if you intersperse more than that number of ‘X’ tokens between each useful token, they won’t be able to do anything resembling intelligence. The current LLMs are a bit like n-gram databases that do not use letters, but larger units.

It’s that a bit of an unfair sabotage?

Naturally, humans couldn’t do it, even though they could edit the input to remove the X’s, but shouldn’t we evaluate the ability (even intelligent ability) of LLM’s on what they can generally do rather than amplify their weakness?

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

#100

Post by KeplerBoy »

lordnacho wrote: post #93
jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

The only thing I've consistently had issues with while using AI is graphs. If I ask it to put some simple function, it produces a really weird image that has nothing to do with the graph I want. It will be a weird swirl of lines and words, and it never corrects itself no matter what I say to it. Has anyone had any luck with this? It seems like the only thing that it just can't do.

You're doing it wrong. It can't produce proper graphs with it's diffusion style image generation.

Ask it to produce graphs with python and matplotlib. That will work.

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