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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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.
The “we’s” are different. Some of us will use AI to replace human relationships and our own decision making, others of us will use it to make amazing art and invent new things.
How does an AI finding a proof of a question that someone asked very long ago, is going to improve anyone's cognitive capabilities?
Human cognition improves the more you practice it. Not when you outsource it to machines that do the "cognition" for you.
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.
What little intelect we have can be directed to other parts of the vast endless ocean of unknown things.
I hear some specialists (specially multi-disiplinary ones) write things they know few or no one can read. (Which is the most ironic reason for being rejected by a journal)
I recall a funny moment on irc where a truly helpful guy moaned that no one helped him when he had a (programming) question. He was very good at many programming languages and worked in some mix of high level physics and mathematics. He posted SO questions that rarely got an appologetic response from someone able to understand the code and the physics but couldnt wrap around the math. lol I hope he finally gets some help with his wizardry.
You’re making some generalizations here, but I do agree that one of the primary dangers of LLMs is destruction of institutions of higher education. If thinking power becomes cheap, who will pay the money that universities demand?