Reuben Goodstein

Reuben Louis Goodstein (* December 15, 1912 in London, † March 8, 1985 in Leicester ) was a British mathematician who has been dealing with mathematical logic and philosophy and foundations of mathematics.

Goodstein went to the St. Paul 's School in London, where he won a mathematics prize and a scholarship. From 1931 he studied mathematics at Cambridge University ( Magdalene College ), where he graduated in 1933 made ​​( with a specialization in Analysis ) and then under John Edensor Littlewood research on transfinite cardinal numbers. 1934/35 he was one of the students who were allowed to work out Ludwig Wittgenstein 's lectures ( Blue Book ). In 1935, he received his master's degree and taught at the University of Reading, where he took over a significant portion of the Mathematical teaching in particular during the Second World War. In 1946 he received his doctorate from the University of London and in 1948 professor at University College, Leicester, where he remained until his retirement in 1977. 1966 to 1969 he was Vice- Chancellor of the University.

Goodstein is today mainly for the Goodstein sequence is known ( 1944). An associated set can be formulated in Peano arithmetic, but does not prove to her how Jeff Paris and Laurie Kirby showed. He dealt with recursive arithmetic and finitistischer foundations of mathematics and refined in 1954, the logic - free formulation of the Skolem -founded primitive recursive arithmetic ( first shown by Haskell Curry 1941). In addition to mathematical logic ( in which he had the first chair in the UK) and Philosophy of Mathematics and Analysis, he was also interested in didactics of mathematics. 1956 to 1962 he was editor of the Mathematical Gazette.

In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm (A recursive lattice ).

Among his pupils was Martin Loeb.

Writings

  • Fundamental concepts of mathematics, Pergamon Press, 1962, 2nd edition 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 EJFPrimrose: Axiomatic projective geometry, Leicester University College 1953
Goodstein's theorem Finitism Thoralf Skolem
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