Name Reuben Goodstein Role Mathematician | ||
 | ||
Born 15 December 1912
London ( 1912-12-15 ) Institutions University of Leicester
University of Cambridge Alma mater Birkbeck, University of London Thesis An axiom-free equation calculus (1946) Doctoral students Alan Bundy
S. Barry Cooper
Raymond Cuninghame-Green
Martin Lob
Paul Stanford
H. P. (Paul) Williams Known for Goodstein's theorem
Primitive recursive arithmetic Died March 8, 1985, Leicester, United Kingdom Books Recursive Number Theory: A Development of Recursive Arithmetic in a Logic-free Equation Calculus Education St Paul's School, London, University of London, University of Cambridge | ||
Doctoral advisor Ludwig Wittgenstein Notable students Alan Bundy, Martin Lob | ||
Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with a strong interest in the philosophy and teaching of mathematics.
Contents
Education
Goodstein was educated at St Paul's School in London. He received his Master's degree from Magdalene College, Cambridge. After this, he worked at the University of Reading but ultimately spent most of his academic career in the University of Leicester. He earned his PhD from the University of London in 1946 while still working in Reading.
Goodstein also studied under Ludwig Wittgenstein.
Research
He published many works on finitism and the reconstruction of analysis from a finitistic viewpoint, for example "Constructive Formalism. Essays on the foundations of mathematics." Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems (such as second order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the naming convention now used for these operations (tetration, pentation, hexation, etc.).
Besides mathematical logic (in which he held the first professorial chair in the U.K.), mathematical analysis, and the philosophy of mathematics, Goodstein was keenly interested in the teaching of mathematics. From 1956 to 1962 he was editor of the Mathematical Gazette. In 1962 he was an invited speaker at the International Congress of Mathematicians (with an address on A recursive lattice) in Stockholm. Among his doctoral students are Martin Löb and Alan Bundy.