Comment by yaqubroli
5 hours ago
> “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathematics, teach mathematics and do mathematics together.”
I am not a mathematician, but this seems like an entirely non-problematic answer to me. Mathematics is ultimately the discovery of relations and their consequences, so of course large language models were eventually going to catch up. But precisely what they do lack is ability to appreciate these relations.
The author says mathematics is a spiritual pursuit.[1] I have asked LLMs about theological topics before and they have also been able to produce perfectly cogent answers (even heavy questions like “how did Aquinas view Pseudo-Dionysius’ negation-laden description of God”). I am not the least bit shaken by this, because it is still on me to evaluate and understand, and appreciate these answers.[2] The author seems to think LLM’s pattern recognition makes redundant human understanding and appreciation, which is a logical leap that doesn’t make sense to me. Maybe the author is conflating utility and purpose? I feel bad, and hope the author takes care of themself, but I really think the author is taking a massive leap here. It is not that deep.
[1] I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
[2] I of course wouldn’t consult an LLM if I actually wanted to educate myself or reason about these topics. Not only do I want to reason through them myself, but when it comes to issues in philosophy/theology/heavy stuff, you need to take in to account the perspective and experiences of the human writing them. LLMs muddle everyone’s perspective together.
I think what people find "spiritual" about mathematics is the process, with its creativity and brilliance, ratjer than the final answer. I'd also think it's rather incomparable to a vegetable garden as the amount of effort required and complexity, which drive "spirituality", are of much grander scales. The author believes that llms make mathematics so trivial that mathematicians will no longer be the ones proving but the ones teaching and commentating, taking the "fun" part away in service of money. People will still do what they wabt to do, but one can no longer get by by indulging in what they like to do (math).
I am a mathematician, and I agree with you here. I do not feel at all threatened by LLMs, because for me the joy of mathematics is in constructing the theories and beholding their beauty! I know other people are different from me here. I find having to prove theorems a rewarding part of the whole, but I am also not going to weep if an LLM can unstuck me on difficult proofs.
I am really excited if LLMs means more of mathematics will be formalised. Once we have all of mathematics formalised, I think we will start to see real great progress!
I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
The thing is, if someone had the option to press a button and cause their garden to be weeded and growing perfectly, if most gardeners were using that button instead of growing normally, maybe some people would keep gardening for the spiritual part but they'd certainly feel like the rug had been pulled out from under them.
Edit: As another example, Robert Pirsig in his famous book described motorcycle maintinence as a spiritual enterprise. However, the quality that gave it this was the patience required-for and the uncertainty involved-in the enterprise. And again, if all you have to do is press a button, the spiritual part kind of goes away.
> feel like the rug had been pulled out from under them.
Which makes absolutely 0 sense, regardless of where attempt is made to apply the argument. If one really prefers to do X manually, they always can. Even if everyone else around them has fully automated X away.
Except agricultural automation does exist. And people do choose to do it by hand because... It's a hobby and efficiency isn't the point