Reuben Goodstein Explained

Reuben Goodstein
Birth Date:1912 12, df=y
Birth Place:London, England
Death Place:Leicester, England
Workplaces:University of Leicester
University of Cambridge
Alma Mater:Magdalene College, Cambridge (MA)
Birkbeck, University of London (PhD)
Thesis Title:An axiom-free equation calculus
Thesis Year:1946
Academic Advisors:Ludwig Wittgenstein[1] [2]
Doctoral Students:Alan Bundy
S. Barry Cooper
Martin Löb
Known For:Goodstein's theorem
Primitive recursive arithmetic

Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with an interest in the philosophy and teaching 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 but ultimately spent most of his academic career at the University of Leicester. He earned his PhD from the University of London in 1946[3] while still working in Reading.

Goodstein also studied under Ludwig Wittgenstein.[1] [2]

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.

Publications

Notes and References

  1. Nuno Venturinha, The Textual Genesis of Wittgenstein’s Philosophical Investigations, Routledge, 2013, p. 39.
  2. In Goodstein . R. L. . Mathematical Systems . 10.1093/mind/XLVIII.189.58 . . 58–73 . 1939 . 48 . 189 ., at p. 58, Goodstein refers to Wittgenstein as his former teacher.
  3. Goodstein . R. L. . Function Theory in an Axiom-Free Equation Calculus . s2-48. 10.1112/plms/s2-48.1.401 . . 401–434 . 1945 .
  4. Rogers, Hartley. Hartley Rogers Jr.. Review: R. L. Goodstein, Mathematical logic. Bull. Amer. Math. Soc.. 1958. 64. 1. 32–35. 10.1090/s0002-9904-1958-10141-x. free.