The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question.

The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains.

To me the potential beauty of this is that these tools might help us break through the increasing super specialization that humans in science have to go through today. Which in one hand is important on the other hand does limit the person in terms of the tooling and inspiration it has access to.

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efavdb an hour ago | parent | next [-]

It’s as if the body of human knowledge is our I’ve mind. It used to be expensive to access that, but no more.

Cool thing is now when someone contributes something to the hive mind, it can instantly be applied to any other problem people are working on.

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keyle 2 hours ago | parent | prev | next [-]

I think you're on point, and you've explained it very well.

As we're becoming hyper specialised, they become an invaluable tool to merge the horizon in, so to speak.

	▲	cpard an hour ago \| parent [-]
		I think traditionally engineering was supposed to be the discipline that brings the breadth that science has to give up. At least that’s how I rationalized the pain I had to go through in college studying EE. I don’t think that this model works anymore though. Also, I love the expression “merge the horizon in”. Being a non native speaker of a language is so nice some times. Thanks!

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

I’ve always been skeptical about the role of LLMs in mathematics, but this is the first time I’ve seen this argument, and I actually find it very compelling. Maybe LLMs will help us develop more horizontal understanding of the field.

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cpard 3 hours ago | parent [-]

It's up to us I think. We can use LLMs to generate web pages in candy crash style and end up dumper by outsourcing thinking to the machines or we can use it to expand our cognitive capabilities.

What makes me more of an optimist in this case is that people who today decide to go into these sciences are mostly people who are driven by intellectual activity so I feel they are the right ones to figure this out, probably more so than us the engineers.

	▲	Ar-Curunir 2 hours ago \| parent [-]
		Unfortunately, LLMs might lead to the demise of the primary institution that allows for people that are in it for the love of intellectual activity to do that activity, namely research universities. Certainly the people proposing the tech are quite opposed to the modern university.

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margorczynski 3 hours ago | parent | prev [-]

Yep. The thing is people (maybe because of our limited scope) just focus on the depth and not the breadth. Because this is a general purpose model - it also has PhD+ knowledge in Physics, Biology, History, etc.

I think we still don't really comprehend how much can be achieved by a single "mind" that has internalized so much knowledge from so many areas.

	▲	cpard 3 hours ago \| parent [-]
		there's so much opportunity on the breadth of things too! I think that you end up having different people focusing on different things though. Personally I'm a more of a breadth person and I could never compete with peers who where more of the depth type of person at college. But I get satisfaction from connecting things that feel irrelevant on first sight, that's what drives me.