Peter Scholze is recognised as the leading mathematician of his generation in the field of arithmetic geometry. He has introduced new ideas to this field, most notably the theory of perfectoid spaces. His point of view has enabled him to make progress on some of the best known problems in this and neighbouring fields. In particular his ideas have become extremely important in the construction of Galois representations, in p-adic Hodge theory, and in the theory of automorphic forms. He has very broad interests and influence in mathematics. He was awarded the Fields medal in 2018.