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# Reuben Goodstein

Reuben Louis Goodstein (15 December 1912 in London – 8 March 1985 in Leicester) was an English mathematician with a strong interest in the philosophy and teaching of mathematics.

As a boy, he attended St Paul's School in London. He received his Master's degree from the University of 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 Wittgenstein and John Littlewood.

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, etc.).

See also

Goodstein's theorem

Primitive recursive arithmetic

External links

O'Connor, John J.; Robertson, Edmund F., "Reuben Goodstein", MacTutor History of Mathematics archive, University of St Andrews.

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