Ok, here’s a 2x2 that captures a lot of the variation in OP:
abstract/concrete x intuitive/methodical.
Intuitive vs. Methodical is what Atiyah, Klein, and Poincare are talking about. Abstract vs Concrete is what Gowers, Rota, and Dyson are talking about.
Abstract and intuitive is like Grothendieck.
Concrete and intuitive is like geometry or combinatorics.
Concrete and methodical is like analysis.
Abstract and methodical — I don’t know what goes in this space.
This seems good. I was definitely getting the sense there were at least two axes, and these seem to capture a lot of it.
Could Abstract/Methodical be something like Russell and Whitehead’s Principia Mathematica?
Also, I’m interested that Concrete/Methodical is analysis, given the Corn post. I would have expected it to be Intuitive? (I don’t actually do higher math, so I don’t know from personal experience.)
Ok, here’s a 2x2 that captures a lot of the variation in OP:
abstract/concrete x intuitive/methodical.
Intuitive vs. Methodical is what Atiyah, Klein, and Poincare are talking about. Abstract vs Concrete is what Gowers, Rota, and Dyson are talking about.
Abstract and intuitive is like Grothendieck.
Concrete and intuitive is like geometry or combinatorics.
Concrete and methodical is like analysis.
Abstract and methodical — I don’t know what goes in this space.
This seems good. I was definitely getting the sense there were at least two axes, and these seem to capture a lot of it.
Could Abstract/Methodical be something like Russell and Whitehead’s Principia Mathematica?
Also, I’m interested that Concrete/Methodical is analysis, given the Corn post. I would have expected it to be Intuitive? (I don’t actually do higher math, so I don’t know from personal experience.)