Terence Tao on doing math with AI
Here is Matteo Wong's interview1 with Terence Tao about math and generative AI. It's both interesting in its own right and useful as a source of metaphors for building software with AI. Here are some of Tao's claims:
- AI has produced impressive results in part by cherry-picking unexpectedly easy Erdős problems.
- Even when AI solves problems by straightforwardly applying known techniques, an expert can still learn something from those solutions. As Tao says, "maybe it uses a trick from some paper from 1960 that I wasn’t aware of."
- Experts find ways to work around tedious computations, but AI will "just happily blast through" them.
- AI will enable large-scale math, enabling studies in the style of scientific population surveys instead of case studies.
- The "obsession with push-of-a-button, completely autonomous workflows" is misplaced, and the best tools for enabling AI-human collaboration would have a form that doesn't exist yet.
Some closely related software notes:
- It's hard to assess the epistemic value of (to simplify a bit) check which of N proof techniques can be used to solve any of M open problems. It might be easier to assess the value of getting rid of the easiest ticket in your backlog (meaningful, if often small).
- Relatedly: I suspect that there are two groups of agentic coders out there, those who do and don't find ways to continually prompt the AI to "solve another task" or "find a bug and fix it" or similar. If you have the credits, there's really no reason not to. That you would not want to do this work over and over is not a reason not to have it do so.
- Even Terence Tao sometimes just learns "a trick from 1960" and gets a little better at what he does. I suspect that this sort of mechanism is an underrated aspect of high-level cognitive performance. I know that I've filled plenty of little gaps in my software knowledge with AI, but now I'm tempted to track how often this happens.
- I share the desire for AI tools with other human-AI communication models. I don't yet have a clear idea what those might be.
Or possibly "interview notes."↩