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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

#11

Post by tossandthrow »

noFaceDiscoG668 wrote: post #5
tossandthrow wrote: post #3

Earlier quoted context omitted.

I do think it is time to start questioning whether the utility of ai solely can be reduced to the quality of the training data. This might be a dogma that needs to die.

I tried. I don't have the time to formulate and scrutinise adequate arguments, though. Do you? Anything anywhere you could point me to? The algorithms live entirely off the training data. They consistently fail to "abduct" (inference) beyond any language-in/of-the-training-specific information.

It is a gradual thing. Presumably the models are inferring things on runtime that was not a part of their training data.

Anyhow, philosophically speaking you are also only exposed to what your senses pick up, but presumably you are able to infer things?

As written: this is a dogma that stems from a limited understanding of what algorithmic processes are and the insistence that emergence can not happen from algorithmic systems.

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

#14

Post by asddubs »

aithrowawaycomm wrote: post #9

I am fairly optimistic about LLMs as a human math -> theorem-prover translator, and as a fan of Idris I am glad that the AI community is investing in Lean. As the author shows, the answer to "Can AI be useful for automated mathematical work?" is clearly "yes." But I am confident the answer to the question in the headline is "no, not for several decades." It's not just the underwhelming benchmark results discussed in…

it can take my math and point out a step I missed and then show me the correct procedure but still get the wrong result because it can't reliably multiply 2-digit numbers

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

#16

Post by croes »

tossandthrow wrote: post #3
noFaceDiscoG668 wrote: post #2

"once" the training data can do it, LLMs will be able to do it. and AI will be able to do math once it comes to check out the lights of our day and night. until then it'll probably wonder continuously and contiguously: "wtf! permanence! why?! how?! by my guts, it actually fucking works! why?! how?!"

I do think it is time to start questioning whether the utility of ai solely can be reduced to the quality of the training data. This might be a dogma that needs to die.

If not bad training data shouldn’t be problem

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

#17

Post by kergonath »

croes wrote: post #16
tossandthrow wrote: post #3

Earlier quoted context omitted.

I do think it is time to start questioning whether the utility of ai solely can be reduced to the quality of the training data. This might be a dogma that needs to die.

If not bad training data shouldn’t be problem

There can be more than one problem. The history of computing (or even just the history of AI) is full of things that worked better and better right until they hit a wall. We get diminishing returns adding more and more training data. It’s really not hard to imagine a series of breakthroughs bringing us way ahead of LLMs.

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

#18

Post by fifilura »

asddubs wrote: post #14
aithrowawaycomm wrote: post #9

I am fairly optimistic about LLMs as a human math -> theorem-prover translator, and as a fan of Idris I am glad that the AI community is investing in Lean. As the author shows, the answer to "Can AI be useful for automated mathematical work?" is clearly "yes." But I am confident the answer to the question in the headline is "no, not for several decades." It's not just the underwhelming benchmark results discussed in…

it can take my math and point out a step I missed and then show me the correct procedure but still get the wrong result because it can't reliably multiply 2-digit numbers

Better than an average human then.

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

#19

Post by jampekka »

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 on multiplying matrices with mismatching dimensions.

O1 is a lot better at spotting its errors than 4o but it too still makes a lot of really stupid mistakes. It seems to be quite far from producing results itself consistently without at least a somewhat clueful human doing hand-holding.

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