Masayoshi Nagata

Masayoshi Nagata (1927 to 2008) was a Japanese mathematician best known for his work in commutative algebra and its links to algebraic geometry. He was celebrated for building intricate counterexamples to statements that seemed plausible, which earned him the nickname Mr. Counterexample. His compactification theorem shows that algebraic varieties can be embedded in complete varieties, and the Chevalley-Iwahori-Nagata theorem describes the quotient of a variety by a group. In 1959 he gave a counterexample to the general case of Hilbert's fourteenth problem on invariant theory. His 1962 book on local rings contains further counterexamples, among them a commutative Noetherian ring that is not catenary and a commutative Noetherian ring of infinite dimension. Two open problems carry his name: Nagata's conjecture on plane curves of given multiplicities at given points, and Nagata's conjecture on wild automorphisms of polynomial algebras in three variables, the second of which has since been settled in the affirmative.