Comment by SpicyLemonZest
12 hours ago
> Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct?
Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you can build based solely on OpenAI's construction, because analytic solutions to the Navier-Stokes equations are not used for practical purposes in fluid dynamics. The problems and their proofs are only interesting to the degree that they help us better understand how the math works.
IIUC the Navier-Stokes proof is understandable by human beings, but if it weren't it would be no more useful than a proof that 3 dimensional florg-complete entry seams have no durdle-nodes.
So...why can't an AI do the exact same thing? Make AI so it understands math better for future math to understand more math.
Unless your argument is that mathematicians are effectively useless?
I am assuming that's not your point though.
> Unless [...] mathematicians are effectively useless?
It's always been a bit bizarre that this isn't the case. Mathematicians are almost always working on problems that there is no good reason to expect to have utility in the real world... problems they selected because of their elegance or whatever... yet there is a strong historical trend of their work having huge importance after the fact. Sometimes in fields that weren't even invented yet at the time of the work.
There's something to be said for the idea that disrupting a system that is working well for no apparent reason is a bad idea.
So solving and discovering math is or is not the core value a mathematician provides?
If AI can perfectly replicate their work but faster and better then what?
SWE have nobody crying for them as they've been massively disrupted.
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Math academia was not working well at all. Almost every single graduated from my PhD program wound up working in ads or finance.
The gatekeeping in math academia is extremely unfair, or should I say objectively fair but personally unfair. I won’t cry crocodile tears.
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Perhaps an AI could! Today they do not, because the people driving them understand constructing the proof rather than understanding the proof to be "the problem".
(I suppose it's possible that in some distant AI future there might be no value in people understanding theoretical math, but I'm pretty skeptical of that; to me it seems like the same error as thinking nobody needs to understand multiplication because you can ask the computer to solve any multiplication problem.)