Kenneth Chang

Ok, blame me. He meant the hierarchy of the “difficulty” or prestige of the different areas, e.g. theoretical particle physicists think they do the most pure physics, followed by condensed matter, etc. That doesn’t imply solid state physics (and all the tech) is insignificant.

And thus for many of the top people in the field, these other areas are not worth their personal time and attention. Many theoretical physicists have this view even though the March APS meeting is huge.

I don't think mathematicians generally thought what Kolmogorov, Levy, Feller, Tukey, etc. were doing was not difficult or worth attention relative to work in other fields, at least judging by their recognitions, involvement in organisations, etc.

Again, Labourie’s point was not that they thought the work was not difficult or that it wasn’t useful. He meant they thought it wasn’t relevant, in the same way a particle theorist might likely think the latest solid state idea has no implications for a unified theory.

I think I've given plenty of indications so far for why even this watered-down view is historically incorrect and anachronistic. The quote tells us a lot more about biases in later years than about mid-century math.

Ok, I’m not convinced that probabilistic methods were in the toolkit of most mid-century algebraists and geometers. The “central” part of Labourie’s quote is arguing that now they are. Would the Terry Tao of that day have been using ergodic theory to tackle prime numbers?

literally yes: Damodar Kosambi (a member of the 1950 Fields Medal Committee) spent the 1950s using probability methods to tackle the Riemann Hypothesis and prime numbers

Erdős was already using probability in the theory of prime numbers in the 1940s and 50s, and a big reason Tao uses this combination now is the legacy of the "Hungarian school" from that time