Mathematicians Need to Act • Hacker News Board

Re: Mathematicians Need to Act

#11

Post by dare944 » Tue, Aug 04, 2026, 12:21 AM UTC

brianwawok wrote: post #2

In the goal of the math problems to get the answers or think for years on a complicated topic? It’s the same Q developers have. Are they paid to type code or create programs? As a not math person, seems strictly good that AI can solve more problems. If they were important, it can maybe unlock new science. If they had no useful purpose, why did we think about them for years?

> If they had no useful purpose, why did we think about them for years?

I don't see a 'we' here. By your own admission you didn't spend years thinking about complicated math topics. So maybe you simply don't see the "purpose". Or maybe no one sees the purpose yet because for some math practical applications take years to discover.

Re: Mathematicians Need to Act

#12

Post by tmhn2 » Tue, Aug 04, 2026, 1:11 AM UTC

brianwawok wrote: post #2

In the goal of the math problems to get the answers or think for years on a complicated topic? It’s the same Q developers have. Are they paid to type code or create programs? As a not math person, seems strictly good that AI can solve more problems. If they were important, it can maybe unlock new science. If they had no useful purpose, why did we think about them for years?

> Are they paid to type code or create programs?

The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the former case you have a point, but not so much in the latter. We really need both modes of work going on.

> As a not math person, seems strictly good that AI can solve more problems.

As a math person I think that's probably true, though it's not that simple. We do still have to understand the solutions to the problems, and take time to explore. That's how we figure out what problems should be solved in the first place. Cognitive debt is bad enough in your codebase, but you don't really want it to overwhelm entire academic disciplines.

Re: Mathematicians Need to Act

#13

Post by freehorse » Tue, Aug 04, 2026, 4:10 AM UTC

ianbicking wrote: post #10

freehorse wrote: post #7

> I believe in chasing fantastic scientific and mathematical progress with the help of LLMs, we risk imperiling our institutions, our professional norms, and human mathematical understanding I don't think that defending institutions and professional status is a great image for a largely publicly funded academia. Academia should not be about reproducing itself firstmost. This may be a bit less pronounced in mathematic…

Maintaining human understanding in the face of fast progress is a big unsolved problem. If you are worried about there being nothing left when LLMs tear their way through a topic then the presence of a big unsolved problem should be comforting! And it seems legitimately like an important problem for mathematics (and other areas), one which is deeply academic in the best sense: mathematicians spend much more time tran…

The futures I predict, out of my ass, for when the LLM wildfire spreads enough:

1. We are in a situation that the pace crumbles, in which situation we are left with classes of problems LLMs simply cannot touch because they have exhausted the "low hanging fruits" that their training and architecture was optimised for solving. In this scenario there is still stuff for the mathematicians to do, but the way young research mathematicians get trained has to be adjusted.

2. Or we simply see some slowdown, but it is still fast enough that it overtakes human capacities and produces novel mathematics that are harder and harder to understand, as LLMs are adapting to solve more and more types of problems faster than humans, while more and more fields are transcribed into lean. I guess if that happens the main role would be to clean up the llms' work, trying to get some gist out of it to build theories, and guide the llms for those with access to them. But not sure how many mathematicians will have access to these advanced LLMs to work with, so this may create big issues. Until now funding of mathematical work was somewhat trivial, they would only have expenses for traveling, conferences, and phds and postdocs, compared to other fields that need labs, equipment, high compute and/or research assistants to function.