Notes
I'm speculating about a style of math research that might be satisfying and productive over the next few years (but not beyond that). If on target, then likely obvious.
Some caveats: I'm not a research mathematician, and I have had almost no training along those lines. My recent experience is with software with AI on all levels, but I'm skeptical of possible parallels.
Point of departure: There will still be plenty of math for people to do. Obviously, the blend of activities will change.
Should still happen some. Why?
- Fun
- AIs don't know everything
- Personal learning
- Healthy for maintaining and building skills and knowledge
- The devil can be in the details: potential to gain novel insights
- Distill to a research note that has expository and even artistic/literary value
- Figure out WTF some LLM just did at interesting points or overall
"garXiv" = "generative arXiv"
"jarXiv" = "Jamie's arXiv"
Some AI work gets special attention and is promoted to something like a personal arXiv. You will have your own editorial standards, which presumably the AIs can meet and review (etc.). Maybe these personal arXivs are made public. Maybe you keep a private garXiv and a public one.
Your garXiv could become something you discuss like any other work product (like papers and talks). Maybe like a gallery, or maybe like a large knowledge base. Or perhaps one garXiv for each.
More or less like a normal principal investigator with a team and budget. This role includes serious technical, perhaps ad hoc, dynamic investigations (with AI assistance, as always) to steer the team, as well as research that is integral to specific lines of inquiry that have been elevated to longer-running efforts.
By "tools" I mean LLM-called tools. These days, AIs can have full computer use and, of course, web search, so they should be able to find and use (say) GAP or PARI/GP. These days, it's easy to have an AI write a state-of-the-art, specialized tool. We might want more of that.
By "skills" I mean the usual LLM skills. This whole notion has a questionable future, but at least for now, distilling some approaches into something conveniently reproducible is productive.
Low-level traces of LLM sessions can be extremely valuable. (Sadly, and not coincidentally, the instructions to agents that the big labs' harnesses generate are obfuscated. The raw thinking is actually encrypted to prevent you from seeing it. But your overall session is, of course, available to you. For some models, open harnesses like opencode and pi might work well. However, models from the big labs are tuned for their harnesses.) Researchers should collect and manage these sessions diligently.
- Would a "math harness" be worth exploring? Probably not and for the same reason that previous math-oriented AI micromanagement fails relative to Big Lab efforts (basically The Bitter Lesson).