High-payoff Tedium

A few weeks ago, OpenAI made a splashy announcement: With the help of ChatGPT, mathematicians had found a counterexample to a famous conjecture by mathematician Paul Erdős. If you're into combinatorial geometry, this is kind of a big deal.

I want to focus on a particularly neat observation that has a lesson for all of us working with AI. In Cal Newport's recent reporting on the achievement (on his AI Reality Check podcast) he explains why the AI succeeded where other mathematicians have failed:

First, the conjecture was widely believed to be true, so most mathematicians were spending time and effort looking for a proof, not for counterexamples, because a proof would have been an even bigger deal.

Second, constructing the counterexample was straightforward but very tedious. In Cal's words, "you wouldn't even want a grad student working on this." You have to do lots of relatively straightforward exploration with lots of annoying symbolic manipulation and then check and double-check your math. The opportunity cost is just too high since there are almost certainly higher-profile higher-payoff higher-chance-of-success problems you'd want to spend your time on.

What AI offers here is a lower opportunity cost to exploring lots of approaches. I'm seeing this directly in my own work, where I knew that a certain codebase should have the testing framework rearchitected, but I recoiled from it because it would be boring, tedious work that I wouldn't even want to hand off to a junior. Claude Code did it for me in an afternoon.

I'm expecting more of these results in math (and computer science) where the AI makes a breakthrough not because it is smarter, but because it doesn't fatigue. And I like this prospect, because it means we can set our sights even higher.