Mathematicians: Let’s Surf This Wave

This post was written by Michael Freedman (Harvard CMSA & Logical Intelligence), and typeset by Milo Moses. Frontier models exhibit astonishing mathematical knowledge and power despite being in their infancy. They will surely strengthen further through routine maturation of the technology, and quite likely through future paradigm shifts in architecture and training. Where does this leave the human mathematician? Already, it has made us study harder than we have since school. The AIs speak to us in a broad language, equally at home in all fields, and we scurry to keep up. So those of us (not me) who were great students, are back in their natural environment, learning, interpreting, organizing knowledge as it flows in. The challenge of absorbing this knowledge will make good teachers into great ones. But what about those whose lives revolved around quiet hours struggling with an open problem, where do we go? My advice: lean in, let the AI’s teach you everything they can about the problem and its context; push them until they are stuck. One of the great feelings in research is the (rare) sense that you have at your command all the information relevant to the problem at hand, and all you need to do is to come up with your own idiosyncratic lens to see through it. Conversing with the AIs is often eye-opening on how much existing mathematics is out there and might be brought to bear. Let the AIs put you in this state of ideal preparation. If they flat out solve the problem on their own it means it was not hard enough. We (humans) should focus on the hardest problems and be creative in perturbing them into useful variants, stepping stones. I used to tell graduate students that if they worked on the central problem of the field, any progress they made would have to be absorbed - their work would have to be read. It makes little sense, now, to clean up loose ends - the AIs excel at this- we should be lost in meditation on the largest issues. There is a risk. Adi Shamir once