1912 – 1985
Reuben Louis Goodstein was a British mathematician and philosopher of mathematics best known for Goodstein's theorem, a result in mathematical logic demonstrating a natural number-theoretic statement unprovable in Peano arithmetic. He contributed significantly to constructive mathematics, recursive arithmetic, and the philosophy of formal systems, advocating a finitist approach influenced by Wittgenstein.
Proved Goodstein's theorem (1944), a true arithmetical statement unprovable in Peano arithmetic
Developed primitive recursive arithmetic as a foundation for constructive mathematics
Authored influential texts including 'Constructive Formalism' and 'Recursive Number Theory'
Advanced finitist and constructivist approaches to the foundations of mathematics
Founded the mathematics department at the University of Leicester