Caltech Mathathon – first hackathon ever devoted to research level mathematics • Hacker News Board

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#111

Post by maths_math » Thu, Sep 10, 2026, 9:47 PM UTC

tim-kt wrote: post #68

lovasoa wrote: post #65

Earlier quoted context omitted.

steam engines solved a problem people had

If mathematicians aren't solving problems people are having (which your comment seems to imply), then putting them out of their job with AI is not a bad thing. Of course mathematicians are solving problems, just in a very different way than other professions.

Steam engines actually replaced what a horse does with a machine that could do the same job. So far LLMs aren't doing this - they're producing Lean proofs but very little to actually aid in understanding (again so far pretty much all of these proofs have been extremely difficult optimizations of known techniques). Mathematicians do solve a problem that people have: they build theories that explain the world and give us mental models to navigate questions in science, technology, etc., this just isn't a problem that LLMs solve.

So the issue isn't so much that LLMs will replace mathematicians, but that AI companies bragging constantly about how their machines "solve math" will convince people who don't understand the value of math research to no longer fund it, or students who don't yet understand why learning math is useful for developing their brains that it's a waste of time. That could put mathematicians out of a job without providing a useful replacement.

Motto: a mathematician's job isn't to solve the Hodge conjecture, it's to understand why the Hodge conjecture is or isn't true, and turn that understanding into something that makes it easier for the next person to grasp/use/enjoy.

LLMs absolutely have the potential to make this job easier, but the way in which these companies are using them right now risks being antithetical to that goal.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#112

Post by maths_math » Thu, Sep 10, 2026, 9:56 PM UTC

brian-bfz wrote: post #79

reasonableklout wrote: post #74

Earlier quoted context omitted.

It’s a noble goal to change the incentives, but how will you prevent the headlines from this event being “students prove Collatz conjecture with Claude” and instead be “students give great explanation of Collatz conjecture proof”?

You're right that we can't. We'll be responsible in our press releases and award prizes based on explanation, but we don't control the headlines. However, this is already an improvement over the current state, where results are announced by headlines alone.

As I've commented elsewhere in this thread - if your goal is really to have people use LLMs to further mathematical understanding for humanity, instead of to brag about "solving" open problems, then why is there an explicit push for the Marathon to involve open problems at all? The whole thing could explicitly be about generating pedagogical content, or writing mathematical theories that simplify known results (example project idea: Kevin Buzzard wrote a lovely article on the issues that he had formalizing Grothendieck's definition of a scheme. They have since been wildly successful using AI to do formalization all the way to FLT, but no one has gone back and written a new Hartshorne that takes the insights from the formalism into account, and writes a clearer introduction to schemes that is simultaneously formally rigorous in ZFC. Using an LLM to attempt this would certainly contribute far more to human understanding of math than writing a new arxiv paper would).

I suspect you will find there is less appetite at the funding level for this kind of thing though, because what your funders really care about is generating headlines in front of their IPOs, and this kind of thing wouldn't generate the same headlines. I would be pleasantly surprised to be proved wrong of course.

EDIT: A more cynical point that I should add - I also suspect your funders would have less appetite for this kind of marathon because LLMs don't seem to be very good at this yet, which kind of points to the whole problem: so far, LLMs seem good at producing Lean proofs but not very good at the rest, but that fact is being lost in the media narrative, and "the rest" is actually the part that matters.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#113

Post by maths_math » Thu, Sep 10, 2026, 10:10 PM UTC

a2ff6eeb0 wrote: post #64

ktallett wrote: post #62

Earlier quoted context omitted.

I get your point and agree to some extent, but you can't understand the proof without significant background in Maths so it will just allow mathematicians to solve issues faster than not have the opportunity at all.

Why do people need to understand proofs? If Amazon improves package routing with new advances in graph theory, my cat doesn't need to understand it to benefit from better shipments of cat food. Similarly, humans don't need to be involved in scientific advances to benefit. We just need an aligned AI to take over the scientific thought for us. AI is already better than all but the top tier of humans at doing mathematic…

> humans don't need to be involved in scientific advances to benefit.

I agree with you on this point in isolation, but I think it's missing an enormous amount of context. Humans can absolutely benefit from science they weren't involved in and don't understand - I have no idea what a "histimine" is but I benefit from my allergy medication in the springtime.

That said, we're already living through a time where, on the whole, measures of intelligence, literacy, critical thinking, etc. are falling (at least in the US). That is a problem, which risks being exacerbated by AI, and the broader point is that we should be figuring out how to use these tools to produce knowledge that benefits humanity while also maintaining incentives for people to use their brains. Going back to my allergies: while I don't understand how my allergy meds work, my life is better, and I'm a better spouse/parent/friend/citizen etc., because I've taken the time to understand how other parts of the scientific and mathematical world that do interest me work. The current AI push to just throw out LLM-generated Lean proofs of everything under the sun to get headlines and pump up their IPO valuations (which this Marathon seems, intentionally or not, to be participating in), doesn't appear to be considering this alignment between what we get from AIs and how we can maintain our incentives to do human science. It seems more like measuring you-know-whats while risking that the message the broader public takes away is that math "has been automated" so what's the point in using your brain anymore?