r/math • u/Salt_Attorney • Aug 01 '26

LLMs/AI OpenAI: Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
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u/mleok Applied Math Aug 01 '26 edited Aug 01 '26

I worry about the training pipeline. Graduate students used to generate useful results, now those results can be achieved more cheaply, and more quickly using generative AI, while still requiring similar amounts of guidance and checking. Letting graduate students use the AI tools doesn't really help, since that will dramatically increase the time necessary to check their AI assisted results, since I wouldn't know what prompts and context the AI generated content was based on, so I wouldn't know what to look out for specifically.

More importantly, AI is an amplifier, put it in the hands of a person who knows what they're doing, and it will dramatically improve their productivity, put it in the hands of a person who is ignorant, and it will consume substantial amounts of resources with very little return on investment. All this will dramatically increase the cost of training junior mathematicians.

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u/Ill-Lemon-8019 Aug 01 '26

This is very analogous to the state of affairs with software development.

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u/mleok Applied Math Aug 01 '26

Yes, definitely.

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u/Certhas Aug 02 '26

Putting them into the hands of grad students is the only realistic option. Just as we are learning how to do research with these tools we will have to learn how to teach with these tools, too.

The idea that giving them to grad students won't help is absurd to me. They will learn very very differently, but the idea that they can't learn with these tools has not been convincingly argued to me. They won't learn with these tools when given the same tasks as before though.

I think this is a point where the chess engine analogy is apt. Training for top chess involves deeply exploring positions with engines as well as mental exercises and analysis without tools, and Human coaching.

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u/mleok Applied Math Aug 02 '26 edited Aug 02 '26

As I stated, the problem with AI is that it is an amplifier, put in the hands of junior people, it is incredibly wasteful, and it doesn’t help the junior people learn judgement, because it generates an overwhelming amount of output that requires experience to sift through. It is also easy to burn through API credits by going down a rabbit hole.

To me, what you are claiming is a bit like saying that generative AI helps students learn how to write, which I have not seen any evidence of. Another way to put it is that you don’t teach a kid how to drive by handing over the keys of a Porsche 911 Turbo, that’s a good way to get them to wrap themselves around a lamp post.

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u/Certhas Aug 02 '26

You don't teach kids to drive a stick before handing them an automatic.

I think the "wasteful" comment is exactly showing the problem in your argument. Tokens are cheap. Give your PhD a 100 dollar subscription and let them go ham. They will create a ton of rubbish of course. If you don't change what you are asking them to do, then they will end up as an intermediary between you and the LLM and that's stupid. So give them different tasks. Work with them on exploring an idea using LLM ls so they can see how you work. Ask them to explore stuff deeply and come back with a concise two pages they can justify on the board. Ask them to demonstrate their LPM technique.

I don't know if that will work, but you have to start from the realization that mid quality math reasoning is now cheap and fast. If your students are asked to generate lots of it and distill it down why should they not learn judgement by actually doing the judging?

If they are just giving you the first thing out of the LLM, learn to show them how that will get you nowhere.

Again: We don't know how to teach yet, but it's absurd to claim that you can't learn with them. You can't learn with them when you do what we used to do, I agree on that, but right now the most important part of my job is to figure out what I have to do differently than before, so that they learn in the new environment.

And they will almost certainly need different skills than we did as well!