The research field of mathematics is obviously so different with these frontier models that to describe it has being laid waste is nonsensical.

It’s like saying the power loom laid waste to the field of textiles.

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Loquebantur 6 hours ago | parent | next [-]

The bottleneck now is human understanding.

Ironically, that has been that way for most people since forever.

Comparing with the situation in programming, where code evaluation (obviously analogous to "understanding") is that bottleneck now, should get people the idea of being in the same boat.

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JumpCrisscross 5 hours ago | parent | next [-]

I’d say it’s understanding in general. We currently have zero evidence the AI models can understand mathematical breakthroughs in a productive way. (When they intuit a new technology or theory from a mathematical construct, we’ll be along that way.)

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achierius 4 hours ago | parent | prev | next [-]

What is that the bottleneck for, though? Certainly, it's tautologically the bottleneck for "humans understanding math"; but what about things like using math to drive discoveries in other fields, or for practical work in CS, or applications elsewhere? I fear that practically those aren't bottlenecked on human understanding.

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zer00eyz 5 hours ago | parent | prev [-]

Putting asside the stolen research -

It is my understand that there isnt a lot of innovation here. Rather the (broad) field of mathematics got mined for solutions that already existed within the corpus.

It implies "We didn't know we already knew how to solve these problems". How is that a good look for mathematics as a field?

	▲	JumpCrisscross 5 hours ago \| parent [-]
		> the (broad) field of mathematics got mined for solutions that already existed within the corpus I think we’re still trying to figure this out. Once the proposed proofs are verified and deciphered I think we’ll have a better answer.

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reasonableklout 6 hours ago | parent | prev [-]

Did you read any of the explanations from mathematicians over the last month? What part of them do you disagree with?

For example [1]:

> In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align.

Or [2]:

> Use of AI tools, when done responsibly, can support not just the initial generation of a solution, but all of the valuable followup activities that traditionally flow out of that solution. But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.

> ...

> solutions to open problems are now being harvested at large scale in an unsustainable fashion, leaving entire fields of mathematics much less fertile than when such problems were solved in the traditional "Math 1.0" fashion.

[1]: https://mathandai.org/

[2]: https://mathstodon.xyz/@tao/117395268130901862

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monideas 6 hours ago | parent | next [-]

> prompters who have no interest in the broader field itself once their initial target is "solved"

This applies to all fields and pursuits where AI is effective. Yes I think about this with regards to various things I’m working on.

This is just the nature of things, you need to adapt and not throw a tantrum like a child. You need to not behave like Terrance Tao who is essentially like a child in an adult’s body in terms of his behavior and lack of wisdom, and keep in mind he was a child prodigy so this isn’t a knock at all or statement about his intelligence, only his development as a man.

You can mourn, as I have for the field of programming as I knew it which I have loved since I was a child, but you need to move on.

	▲	JumpCrisscross 5 hours ago \| parent [-]
		> but you need to move on If AI can actually replicate mathematicians, sure. We don’t have evidence it can. We have evidence it can do useful stuff once promoted by human mathematicians. But if all the Terence Taos “move on,” we won’t have those in America anymore. (The irony of ironies would be the mathematicians prematurely moving on causing American AI progress to stall in the future.)

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HDThoreaun 5 hours ago | parent | prev [-]

I completely reject the idea that releasing proofs is bad for the field of mathematics. Yes, it holistically changes the role for mathematicians, and they might not like where the change leaves them, but I do not think it harms the field overall.

Best I can tell the biggest complaints are really just that the future of their career is largely combing through lean and they don’t want to do that. Too bad. Adapt or get off the pot.

Mathematicians need to completely rethink the prestige paradigm. Counting proofs no longer works. That doesn’t mean there’s nowhere for them to go. Now it’s about gleaning human understanding from the lean. Maybe in the future LLMs can do that too and it’ll be all about formulating new conjectures.