Raphael Robinson

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Raphael Robinson

Raphael Mitchel Robinson (born November 2, 1911 in National City , California , † January 27, 1995 in Berkeley , California) was an American mathematical logician and mathematician .


Raphael Robinson was the youngest of four children by a teacher and a lawyer, but left the family early. He studied mathematics at the University of Berkeley with a bachelor's degree in 1932, a master's degree in 1933 and a doctorate from John McDonald a year later in 1934 (Some results in the theory of simple functions). During the time of the Depression , he only found a low-paying job as an instructor at Brown University and went through tough times. His situation improved in 1937 when he became an instructor at Berkeley. It was there that he met his future wife Julia Robinson in 1939 , who was his student and who later became a respected logician. They married in December 1941. Robinson stayed in Berkeley for the rest of his career, becoming a professor there in 1949. He was known as a good teacher, but retired early in 1973. That meant a bitter financial loss; but he could now devote himself entirely to research. His wife died in 1985. Robinson remained mathematically active into old age and published at the age of 83. He died after a stroke.

In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Intervals containing infinitely many sets of conjugate algebraic units ).


At first he dealt with function theory and number theory and after the Second World War he was one of those who used computers for number theoretic purposes early on, so he found some new Mersenne prime numbers . For this purpose, he wrote in his office, without ever having seen the computer, an executable program for the SWAC (Standards Western Automatic Computer) , which worked without any errors right away without testing.

Robinson is best known for working on the fundamentals of mathematics. In 1937 he published a simplified version of John von Neumann's axiomatization of set theory. He also dealt with recursive functions and recursively enumerable sets.

He proved the undecidability of some mathematical theories and took up the concept of essential undecidability from Alfred Tarski , who was in Berkeley from 1942 and with whom he published a book on undecidability. In 1950 he showed that Robinson arithmetic , a part of Peano arithmetic that can be represented by a finite number of axioms (without induction), is essentially undecidable . He showed that essentially undecidable theories do not require an infinite number of axioms. In his book with Tarski and Mostowski he showed the undecidability of further mathematical theories (theory of associations, group theory, projective geometry). Robinson later dealt with the question of the decidability of tiling problems, a problem area originally initiated by Hao Wang .

His wife Julia Robinson was also a logician (she did her PhD under Tarski) and worked in similar fields, but they never published together.


Web links

Individual evidence

  1. ^ Proc. American Mathematical Society 1954
  2. ^ Leo Corry: Hunting prime numbers from human to electronic computers. (PDF file; 545 kB) p. 64
  3. ^ Robinson: The theory of classes: a modification of von Neumann's system , Journal of Symbolic Logic, Volume 2, 1937, pp. 29-36
  4. Robinson: An essentially undecidable axiom system , Proc. International Congress of Mathematicians, 1950, pp. 729-730. Also shown in the 1953 book with Tarski and Mostowski.
  5. ^ Robinson: Undecidability and non periodicity of tilings in the plane , Inventiones Mathematicae, Volume 12, 1971, pp. 177-209. Undecidable tiling problems in the hyperbolic plane , Inventiones Mathematicae, Volume 44, 1978, pp. 259-264