Practice Makes Perfectoid

Comparing my historical account of the early years of Laurent Schwartz’s theory of distributions with number theorist Michael Harris’s narrative of the early years of Peter Scholze’s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the social and political conditions and implications of mathematical research and the communities that practice it.