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Comment by SpicyLemonZest | Hacker News Reader

> 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.

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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.

Mathematicians provide two complementary services bundled together.

1. Proving theorems - what AI can apparently replicate faster and better.

2. Creating definitions and new theorems from those definitions to prove, selecting which of the possible statements to work on. I.e. developing the "language" of mathematics. So far there is no evidence that LLM can do this at all well. And there's some reason to think that mathematicians won't be as good at this if they aren't also doing the first part.

The value to society only comes when they do both "well", and it's 2 which is really the black magic where we don't understand why they've been so useful to us.

Fair take.

So I totally agree if AI also cannot do the second part better than a person.

Honestly though, I wouldn't want to take that bet. I never thought that the first thing AI would become super human AGI like is math.

You ask me 10years ago and I'd think the opposite. I think we all would have said we'd have super human HR employees before a super human mathematician.

But here we are.

We don't understand why? Reality is mathematical. As evidenced by lawful physics.

Think of it like software going from programmers understanding every instruction, knowing where every byte of memory was being used and why, and using this knowledge to build optimised systems

During the process of optimising and understanding the programmer might learn something new or have some kind of "aha" moment of insight that might lead them down a new path of study where fantastic new technologies and capabilities can be realised

Fast forward to 2026

Most web pages take several seconds to load

Applications crash often for no apparent reason

A vast majority of programmers have no idea what their applications are actually really even doing anymore, so they stack bloat on top of bloat and if something breaks, well I guess that's someone elses problem cos I have no idea what's going on anymore

There's something to be said about levels of abstraction being useful, but abstracting away understanding of the task itself is not the path to generating useful knowledge or applications for humanity

We might be gaining the "what" but we are losing the "why" and the "how" and these are generally fundamentally more important

The answer is 42 but what is the question?

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.

> wound up working in ads or finance

Because there's lots and lots of money in that and there's not in funding pure math. It sounds like your problem is with the people holding the purse strings.

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.)

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