- Raphael M. Robinson
Raphael Mitchel Robinson (
November 2 1911 ,National City California -January 27 1995 . BerkeleyCalifornia ) was an Americanmathematician .Born in National City,
California , Robinson was the youngest of four children of a lawyer and a teacher. He was awarded the BA (1932), MA (1933), and Ph.D. (1935), all in mathematics, and all from theUniversity of California, Berkeley . His Ph.D. thesis, oncomplex analysis , was titled "Some results in the theory ofSchlicht function s".In 1941 Robinson married his former student Julia Bowman. She became his Berkeley colleague and the first woman president of the
American Mathematical Society .Robinson worked on
mathematical logic ,set theory ,geometry ,number theory , andcombinatorics . Robinson (1937) set out a simpler and more conventional version ofJohn Von Neumann 's 1923 axiomatic set theory. Soon afterAlfred Tarski joined Berkeley's mathematics department in 1942, Robinson began to do major work on thefoundations of mathematics , building on Tarski's concept of "essential undecidability," by proving a number of mathematical theories undecidable. Robinson (1950) proved that an essentially undecidable theory need not have an infinite number ofaxiom s by coming up with a counterexample: Robinson arithmetic "Q". "Q" is finitely axiomatizable because it lacksPeano arithmetic 's axiom schema ofinduction ; nevertheless "Q", like Peano arithmetic, is incomplete and undecidable in the sense of Gödel. Robinson's work on undecidability culminated in his coauthoring Tarski et al (1953), which established, among other things, the undecidability ofgroup theory ,lattice theory , abstractprojective geometry , andclosure algebra s.Robinson worked in
number theory , even employing very early computers to obtain results. For example, he coded theLucas-Lehmer primality test to determine whether 2"n" − 1 was prime for all prime "n" < 2304 on aSWAC (computer) . In 1952, he showed that these Mersenne numbers were all composite except for 17 values of "n" = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281. He discovered the last 5 of theseMersenne prime s, the largest ones known at the time.Robinson wrote several papers on tilings of the plane, in particular a clear and remarkable 1971 paper "Undecidability and nonperiodicity for tilings of the plane" simplifying what had been a tangled theory.
Robinson became a full professor at Berkeley in 1949 and retired in 1973. He remained intellectually active until the very end of his long life. He published at age:
* 80 "Minsky's small universal Turing machine," describing a universalTuring machine with 4 symbols and 7 states;
* 83 "Two figures in the hyperbolic plane."References
* Robinson, R. M., 1937, "The theory of classes: A modification of Von Neumann's system," "Journal of Symbolic Logic 2": 29-36.
* ------, 1950, "An Essentially Undecidable Axiom System." "Proceedings of the International Congress of Mathematics": 729-30.
*Alfred Tarski ,A. Mostowski , and R. M. Robinson, 1953. "Undecidable theories". North Holland.
*Leon Henkin , 1995, " [http://www.math.ucla.edu/~asl/bsl/0103-toc.htm In memoriam : Raphael Mitchell Robinson,] " "Bull. Symbolic Logic 1": 340–43.
* "In memoriam : Raphael Mitchell Robinson (1911–1995)," "Modern Logic 5": 329.External links
*. The source for much of this entry.
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