I'm watching how Tao uses AI, and it's interesting.

Expand the entire expression, then change the representation to find the core axis. You can't see the axis from just one perspective, so you change the representation. In programming terms, it's like applying multiple domain models. Then break it down into small contract units. Why is it a Jacobian monomial? Why does x satisfy a cubic equation? And so on.

Then swap out the modeling under a hypothesis, assemble it all back together, and verify it through the equation.

This feels similar to modeling in programming.

Observe the whole -> explore better modeling -> decompose local problem -> verify independently -> reason about the highre level structure -> integrate back into the original problem.

This feels similar to when I receive work from a client and write a programming proposal