Peter Scholze introduces in 2011, in his master's thesis completed at age 22 at the University of Bonn, the concept of perfectoid spaces, a new class of geometric objects that allows problems in arithmetic geometry in characteristic zero to be translated to a characteristic-positive setting, where they are often more tractable, and vice versa. The tool would prove decisive for a new proof of Deligne's weight-monodromy conjectures and for numerous later developments in p-adic arithmetic geometry. Scholze obtained a full professorship at the University of Bonn at age 24, one of the earliest ages recorded in mathematics for such an appointment, and received the Fields Medal in 2018.