Reuben Louis Goodstein

Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with an interest in the philosophy and teaching of mathematics. He was educated at St Paul's School, London, and received his Master's degree from Magdalene College, Cambridge. He earned his PhD from the University of London in 1946. Goodstein also studied under Ludwig Wittgenstein, with Wittgenstein selecting him and others to take notes of his lectures, which later became *The Blue Book*. His research included work on finitism, the reconstruction of analysis from a finitistic viewpoint, and Goodstein's theorem, which was one of the earliest theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems. He also introduced a variant of the Ackermann function known as the hyperoperation sequence. Goodstein held the first professorial chair in mathematical logic in the UK and was keenly interested in the teaching of mathematics. He served as editor of *The Mathematical Gazette* from 1956 to 1962 and was an invited speaker at the International Congress of Mathematicians in Stockholm in 1962.