Feller book: "[In 1940s] few mathematicians outside the USSR recognized probability as a legitimate branch of math" And Doob "Feller & 20th century probability" seems to make a handful of references to probability and 'respectable established topics' being at odds in 30s & 40s ?
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?
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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
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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
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