Kenneth Chang

yes, probability was entirely mainstream in mid-century, embraced as an important method by prestigious folks in many places, including in Labourie's France. It was important in both pure and applied work (a distinction that was being actively re-negotiated in this period).

Yes, and Labourie said that most mathematicians looked down on it, just as physicists think of engineering as a lesser academic discipline because it's just "applied physics." Probability is and was of course of great use, but it wasn't for most mathematicians.

yes, I, a professional historian of 20th century mathematics, am telling you that Labourie's claim is wrong. He has no evidence that "most mathematicians looked down on it" because most did not. The comparison to physics/engineering is also flawed, but that's another story

Who used dynamical systems for a number theory or group theory proof?

Kolmogorov, among others

Ok, I get your point, but think Labourie has a valid point too even if you don't like how he phrased it. How would describe how Furstenberg's and Margulis's work differed in nature from what proceeded it.

I mean, no phrasing would make Labourie's point historically correct, but I agree it's an interesting mark of some current mathematicians' *perception* of that history, and it's valuable to report from that perspective

fwiw I asked another current mathematician’s (and contemporary of the subjects of the piece) view on Labourie’s point today, and he said: “he is dead wrong. Pompous ass.”