From manifolds to reasoning

People sometimes ask how I went from doing geometry on manifolds to working on machine reasoning, as if the two are far apart. To me they never felt that way.

Geometry trains a very specific instinct: that the right coordinates — the right way of looking at a thing — turn an impossible problem into an obvious one. Most of the work is finding that view.

A lot of what I find compelling about reasoning systems is the same instinct, pointed at a different object. What representation lets a model see the structure of a problem? When does it get the coordinates right, and when does it flail?

This is a placeholder post — more to come. But the throughline, if there is one, is that I keep chasing the same thing: the change of perspective that makes the hard part disappear.