Raphael M. Robinson

Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician. Born in National City, California, Robinson was the youngest of four children of a lawyer and a teacher. He earned his BA (1932), MA (1933), and Ph.D. (1935) in mathematics from the University of California, Berkeley. His doctoral thesis focused on complex analysis, specifically on Schlicht functions. In 1941, Robinson married Julia Bowman, a former student who later became a prominent mathematician and the first woman president of the American Mathematical Society. Robinson's research spanned mathematical logic, set theory, geometry, number theory, and combinatorics. He contributed to axiomatic set theory by providing a more conventional formulation of John von Neumann's system. Working with Alfred Tarski, Robinson made significant contributions to the foundations of mathematics, proving the undecidability of various mathematical theories. In 1950, he demonstrated that an essentially undecidable theory does not necessarily require an infinite number of axioms by introducing Robinson arithmetic Q. His work on undecidability was further showcased in a joint publication with Tarski and Mostowski, which established the undecidability of group theory, lattice theory, projective geometry, and closure algebras. Robinson also explored number theory, utilizing early computing technology. He employed the Lucas–Lehmer primality test on the SWAC computer to identify Mersenne numbers, discovering five new Mersenne primes. His later work included research on tilings of the plane, simplifying the theory of undecidability and nonperiodicity. Robinson became a full professor at Berkeley in 1949, retired in 1973, and continued to publish on topics like universal Turing machines and hyperbolic geometry.