“Is Mathematics over?” is how this week will begin. It will end with “How are mathematicians going to cope?”

If you haven’t been following [congrats!], OpenAI’s internal version of Astra looks to have solved 10 open problems in Mathematics. Here is the August 1st release: https://lnkd.in/gErbmW3m

The problems themselves aren’t the story. It’s that they’ve been open and now they are solved. That’s an accomplishment. No small feat.

There are existential threads (not threats) to pull on while keeping the backdrop of marketing in mind.

Mathematics research isn’t just pen and paper toil. And it doesn’t work the way it’s depicted in the movies: two mathematicians doing a “proof duel” on a chalkboard completing each other’s symbolism. Mathematics research can be a solitary experience. At the same time, math research is a social exercise if you can find the right social group of experts. Experiences vary.

The LLM dynamic is interesting because it can feel like deep technical partnership. I’m not going to pretend to know if interaction at OpenAI was a lengthy, detailed prompt and then let the machine churn until it solves it, or if there was a chalkboard-esque back and forth.

Math research is also about a LOT of wandering and walking into dead ends. This is what learning is when there is no path that’s already been found [school math vs research math]. You kind of just have to get lost. After emerging from the proverbial woods, the mathematician has gained a deeper understanding of the problem and its peripheries. Who gets lost with LLM-assist? Walking through a proof is one thing, wandering and retracing one’s steps and finding a way out, is altogether different.

Professional math research is a livelihood. You choose the problems that can turn into papers. If you have spare cycles or have escaped the publish-perish loop, you go fish or start working on a tough nut. So what does it mean for a problem to be open for 90 years? How much actual time was spent by mathematicians on such a problem for the last 90 years? 1 million hours? A few thousand hours? How many mathematicians?

I think part of the exposure here is, yes, these are hard problems, but not worth the gamble on one’s livelihood. Time is precious.

Do we know which other problems were attempted and went nowhere? Riemann Hypothesis? This is the marketing end: volume of success vs success rate. The success rate will determine how “over” Mathematics is. Does every problem get solved or only those that were ignored because of academic survival politics, triage [there are many other problems], etc.?

As for coping, to each their own, but if I were working on a problem and an LLM came through with a proof, then whatever time-saving I achieved, I would spend getting lost in the woods. I wouldn’t want to lose that experience. If you want a data point, I have tried this with my old research. The LLM’s suggestions were dead ends I had already explored.