Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an

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mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

with a strong interest in the philosophy and

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of mathematics.

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 The University of Reading is a public university in Reading, Berkshire, England. It was founded in 1892 as University College, Reading, a University of Oxford extension college. The institution received the power to grant its own degrees in 192 ...

but ultimately spent most of his academic career at the

University of Leicester , mottoeng = So that they may have life , established = , type = public research university , endowment = £20.0 million , budget = £326 million , chancellor = David Willetts , vice_chancellor = Nishan Canagarajah , head_lab ...

. He earned his PhD from the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree ...

in 1946 while still working in Reading. Goodstein also studied under Ludwig Wittgenstein.

Research

He published many works on finitism and the reconstruction of mathematical analysis, 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 Formal system, logical systems (such as second-order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation, 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.

Publications

* Fundamental concepts of mathematics, Pergamon Press, 1962, 2nd edn. 1979 * Essays in the philosophy of mathematics, Leicester University Press 1965 * Recursive Analysis, North Holland 1961, Dover 2010 * Mathematical Logic, Leicester University Press 1957 * Development of mathematical logic, London, Logos Press 1971 * Complex functions, McGraw Hill 1965 * Boolean Algebra, Pergamon Press 1963, Dover 2007 * Recursive number theory - a development of recursive arithmetic in a logic-free equation calculus, North Holland 1957 * Constructive formalism - essays on the foundations of mathematics, Leicester University College 1951 * with E. J. F. Primrose: Axiomatic projective geometry, Leicester University College 1953

References

{{DEFAULTSORT:Goodstein, Reuben Louis English mathematicians 1912 births 1985 deaths People educated at St Paul's School, London Alumni of the University of London Academics of the University of Reading Academics of the University of Leicester 20th-century British mathematicians Alumni of Magdalene College, Cambridge