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Comment by bunderbunder | Hacker News Reader

I'm no mathematician, but my impression as someone who at least does a lot of applied work with maths is that the main thing that's changed is that the yardstick by which academics earn recognition is being re-assessed.

But from my perspective proofs have never been the most interesting part of maths. What really interests me is the intuition that leads to new applications, and to new questions. Newton, for example, gets more credit for calculus than Leibniz because he's the one who demonstrated how darned useful it is. Erdos is arguably more famous for asking interesting questions than for answering them.

I still don't see LLMs seriously contributing to that facet of mathematics any time soon. Every so often I ask one to suggest a good binomial confidence interval for a particular application, and it still tends to just suggest one of the subpar options that everyone learns in a first year stats course.

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Proving theorems is one of the main ways that mathematicians turn math into money.

The recent barf-out done by LLM companies is useful if what are you are interested in is an unreadable mess and someone giving you the final answer. You might be able to extract some new "aha!" moments out of it, but we will have to wait and see what happens once people go through it. I would hypothesize the LLM output will be good at hinting at some non-obvious relationships and patterns, but I doubt it will yield anything of substance in its own right.

Historically, proving difficult theorems required mathematicians to sometimes invent new fields, new ways of looking at problems, the discovery of which itself yielded incalculable contributions to both mathematics and other fields. It is this that is the greater contribution of and to mathematics.

> Proving theorems is one of the main ways that mathematicians turn math into money.

Mathematicians working at universities are paid to teach, to engage in the politics and business of government contracting, and only in very rare circumstances to play prestige games on famous problems.

It is unlikely that Congress will decide to slash budget for NSF's MPS directorate on account of AI getting good at proving theorems. That's just not how Congress works.

It is also unlikely that LLMs will be able to do, in the near future, do the sort of applied mathematics that happens in the context of occasional NIH or DoD funding that flows into Mathematics departments, for a variety of complex sociological reasons I'm happy to expound upon.

And it's unlikely Engineering degree programs will stop requiring calculus sequences, since being able to do the computation was has not been the actual point of teaching calc since he late 20th century (if ever).

So, the good news is that I doubt any of this will have much of an effect on the job market for Mathematicians who want to prove theorems for a living. The bad news, of course, is that the job market for Mathematicians who want to prove theorems for a living was already pretty horrendous.

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