Elsewhere rafa was musing whether recent AI developments represent a paradigm shift in math and I argued that it’s probably not. I’m not a mathematician so this take is based on an old eulogy-assessment of Grothendieck (linked, 2014) that I found very compelling when I first read it. To quote myself

“Since approximately Grothendieck, the game in math has been a meta game. It’s not about grinding away at lots of obscure theorems of dubious significance but architecting large conceptual structures (“Grothendieckian mansions”) plus the handful of charismatic mega theorems (Riemann hypothesis, the clay prize problems) that are known to be strategically significant and/or of sentimental historic importance (for eg Fermat’s last theorem I think was not that important but had high sentimental value?).”

Curious if there are actual mathematicians here who might agree/disagree cc QC. Somehow I can’t bring myself to take all this grinding through math’s accumulated unprioritized to-do list very seriously. It’s sort of like chess or Go AI. The surprise factor is low because unprioritized “tactical grinding” math is similar to those games. It fits what Grothendieck characterized as effectively “mansion maintenance” rather than mansion-conceptualization. The writing has been on the wall for a decade that AIs were going to get utterly dominant at the mansion-maintenance level. It’s steam-shovel work currently done by John Henry mathematicians.

Notable that Grothendieck in his time didn’t work alone. He defined such compelling “mansion” visions, many other top mathematicians (including many John Henry’s presumably) dropped everything to help him build them. I think Terence Tao also acts as mansion-conceptualizer orchestrating other mathematicians. Today’s young, budding Grothendieck type geniuses will simply need far fewer humans to build their mansions.

I’m seeing the same distinction emerge in vibe-coding in the more math-y software domains. The architects (“mansion builders”) are having a great time. The John Henrys are not. The former have been super-leveraged. The latter have seen their dopamine loops and identities destroyed. In semiconductors (very math-y) for eg, you typically need an order of magnitude more people doing RTL, physical design, and verification compared to architects. But those downstream functions are getting automated steadily to the point architects might soon be able to tape out entire chips single-handedly. Now extrapolate to other fields with this structure (there’s not that many — other fields like say rocketry, and the harder kinds of robotics, the hard part moves downstream because it’s a lot more empirical than fields that resemble pure math in being closed and internal-logic driven).

“Single architect” problems are like social-graph single-shottable problems. Single-shotting I think is mostly silly stunts, but single-architecting (but with multiple shots) is a fascinating possibility. In many ways mansion-architect types are intellectual equivalents of Schmittian sovereign types in politics, who “decide the exceptions.” I think this intuition is what people are groping towards with taste discourse. Taste as such at John Henry level is anxious craft/grinder cope that AI will inevitably eat. Taste at mansion architect level is auteur-dictator schmittian sovereign authoritah. I’m not sure it’s even well-posed as a problem at an AI level yet.

This phenomenon btw is why I’m obsessed with automating writing to “good enough” so we can work at the “mansion” level with far fewer resources. Extended universes for both fiction and nonfiction are somewhere between math and highly empirical domains like say rocketry and other oozy-matter fields. Depending on the content, you might be able to architect ambitious mansions that then get actually built mostly by AI.