Centaur Math

In the past, new PhD students would ask how they could succeed when they had to compete with the likes of say, Richard Karp or Avi Wigderson. I would say Karp and Wigderson have limited bandwidth and you can work on problems they don't work on, or think deeper about a problem than Karp or Wigderson has time to.Now we get the same question but with names like Claude and ChatGPT and it's hard to make the same bandwidth argument. What do we tell them as we get closer to Math AGI?What even is Math AGI? It's not that every math problem gets solved. I don't expect P vs NP to be solved anytime soon. It would require a completely new approach, and AI doesn't (yet) think outside the box, though it has a very large box.Math AGI means that with rare exceptions, if AI can't solve a math problem then no human could either. If you need a proof, you'd have to pay for more cycles, or wait for the next new and improved model. Like the Turing test, we'll only truly realize we've reached Math AGI once…