Reuben Goodstein

Reuben Louis Goodstein was an English mathematician with an interest in the philosophy and teaching of mathematics, born on 15 December 1912. He was educated at St Paul's School, London and at Magdalene College, Cambridge, worked at the University of Reading, and spent most of his academic career at the University of Leicester, earning his PhD from the University of London in 1946. He also studied under Ludwig Wittgenstein, who selected him and others to take notes of his lectures. Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems. He introduced a variant of the Ackermann function now known as the hyperoperation sequence, with the naming convention of tetration and pentation, and from 1956 to 1962 he edited The Mathematical Gazette. He died on 8 March 1985.