Raphael Mitchel Robinson (November 2, 1911, National City California - January 27, 1995. Berkeley California) was an American mathematician. November 2 is the 306th day of the year (307th in leap years) in the Gregorian Calendar, with 59 days remaining. ... 1911 (MCMXI) was a common year starting on Sunday (click on link for calendar). ... National City is the name of several places in the United States of America: National City, California National City, Illinois National City, Michigan National City Corporation. ... Official language(s) English Capital Sacramento Largest city Los Angeles Area  Ranked 3rd  - Total 158,302 sq mi (410,000 km²)  - Width 250 miles (400 km)  - Length 770 miles (1,240 km)  - % water 4. ... January 27 is the 27th day of the year in the Gregorian calendar. ... 1995 (MCMXCV) was a common year starting on Sunday of the Gregorian calendar. ... Berkeley is the name of several places, all eventually deriving from Berkeley Castle in Berkeley, Gloucestershire, UK, from whom the noble family of Berkeley derive their name, and for which several vessels of the British Royal Navy have been christened HMS Berkeley Castle. Any of the holders of several titles... Official language(s) English Capital Sacramento Largest city Los Angeles Area  Ranked 3rd  - Total 158,302 sq mi (410,000 km²)  - Width 250 miles (400 km)  - Length 770 miles (1,240 km)  - % water 4. ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ...

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 the University of California, Berkeley. His Ph.D. thesis, on complex analysis, was titled Some results in the theory of Schlicht functions. National City is a city located in San Diego County, California. ... Official language(s) English Capital Sacramento Largest city Los Angeles Area  Ranked 3rd  - Total 158,302 sq mi (410,000 km²)  - Width 250 miles (400 km)  - Length 770 miles (1,240 km)  - % water 4. ... The University of California, Berkeley (also known as the University of California at Berkeley, UC Berkeley, Cal, California, or Berkeley) is the oldest and flagship campus of the ten-campus University of California system. ... Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics. ... In complex analysis, de Branges theorem, named after Louis de Branges, formerly called the Bieberbach conjecture, after Ludwig Bieberbach, states a necessary condition on a holomorphic function to map the open unit disk of the complex plane injectively to the complex plane. ...

In 1941 Robinson married Julia Bowman who became his Berkeley colleague and the first woman president of the American Mathematical Society. For the movie, see 1941 (film) 1941 (MCMXLI) was a common year starting on Wednesday (the link is to a full 1941 calendar). ... Julia Hall Bowman Robinson (December 8, 1919 - July 30, 1985) was an American mathematician, born in Saint Louis, Missouri. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...

Robinson worked on mathematical logic, set theory, geometry, number theory, and combinatorics. In 1937, he published a paper setting out a simpler and more conventional version of John Von Neumann's 1923 axiomatic set theory. Soon after Alfred Tarski joined Berkeley's math department in 1942, Robinson began to do major work on the foundations of mathematics, proving a number of mathematical theories undecidable. He also examined Tarski's concept of "essentially undecidable," answering an important open question by constructing (Robinson 1950) an essentially undecidable theory having but a finite number of axioms. This theory was Robinson arithmetic, Q Like Peano arithmetic, Q is incomplete and undecidable, but lacks Peano arithmetic's axiom schema of induction and so is finitely axiomatized. Robinson coauthored an important 1953 monograph on undecidability with Tarski and Mostowski, establishing the undecidability of group theory, lattices, abstract projective geometry, closure algebras, among other theories. Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Table of Geometry, from the 1728 Cyclopaedia. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. ... John von Neumann in the 1940s. ... Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ... In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer. ... An axiom is a sentence or proposition that is taken for granted as true, and serves as a starting point for deducing other truths. ... In mathematics, Robinson arithmetic or Q arithmetic is a primitive axiomatization of number theory. ... In mathematics, the Peano axioms (or Peano postulates) are a set of first-order axioms proposed by Giuseppe Peano which determine the theory of Peano arithmetic (also known as first-order arithmetic). ... The term induction has more than one meaning in the English language. ... Group theory is that branch of mathematics concerned with the study of groups. ... The ordinary meaning of lattice is the basis for several technical usages A cherry lattice pastry A mathematical lattice that is a type of partially ordered set. ... Projective geometry is a non-metrical form of geometry that emerged in the early 19th century. ... In abstract algebra, an interior algebra is an algebraic structure of the signature <A, ·, +, , 0, 1, I> where <A, ·, +, , 0, 1> is a Boolean algebra and I is a unary operator, the interior operator, satisfying the identities: xI ≤ x xII = xI (xy)I = xIyI 1I = 1 xI is called the...

Robinson worked in number theory, even employing very early computers to obtain results. He coded the Lucas test for primality and tested whether 2n - 1 was prime for all prime n < 2304 on a SWAC computer. In 1954, 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 these Mersenne primes, the largest ones known at the time. To meet Wikipedias quality standards, this article or section may require cleanup. ... Lucas reagent is a solution of zinc chloride in concentrated hydrochloric acid, used to classify alcohols of low molecular weight. ... In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ... In mathematics, a Mersenne prime is a prime number that is one less than a prime power of two. ...

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 in 1949 and retired in 1973. He remained intellectually active until the very end of his long life. At 80 years of age, he published "Minsky's small universal Turing machine," describing a universal Turing machine with 4 symbols and 7 states. At age 83, he published "Two figures in the hyperbolic plane." An artistic representation of a Turing Machine . ...

References

• Leon Henkin, 1995, "In memoriam : Raphael Mitchell Robinson," Bull. Symbolic Logic 1: 340-43.
• "In memoriam : Raphael Mitchell Robinson (1911-1995)," Modern Logic 5: 329.

Leon Henkin is a logician, currently Emeritus Professor at the University of California at Berkeley. ...

External links

• John J. O'Connor and Edmund F. Robertson. Raphael Mitchell Robinson at the MacTutor History of Mathematics archive.
• Raphael M. Robinson at the Mathematics Genealogy Project