Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...

. Born in National City, California, Robinson was the youngest of four children of a lawyer and a teacher. He was awarded from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

in mathematics: the BA (1932), MA (1933), and Ph.D. (1935). His Ph.D. thesis, on complex analysis, was titled ''Some results in the theory of

Schlicht function In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was ...

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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Robinson worked on

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal sy ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathe ...

, and combinatorics. In 1937 he set out a simpler and more conventional version of the

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

1923

axiomatic set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

. Soon after

Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician a ...

joined Berkeley's mathematics department in 1942, Robinson began to do major work on the

foundations of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...

, building on Tarski's concept of essential undecidabilility, by proving a number of mathematical theories undecidable. In 1950 Robinson proved that an essentially undecidable theory need not have an infinite number of

axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...

s by coming up with a counterexample: Robinson arithmetic ''Q''. ''Q'' is finitely axiomatizable because it lacks

Peano arithmetic In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly u ...

's axiom schema of induction; 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 of

group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...

lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper boun ...

, abstract projective geometry, and closure algebras. Robinson worked in

, even employing very early computers to obtain results. For example, he coded the Lucas–Lehmer primality test to determine whether 2^''n'' − 1 was prime for all prime ''n'' < 2304 on a SWAC. 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 five of these

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...

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, retired in 1973, and remained active in his educational interests for the duration of his life having published late in his life: * (age 80 years) '' Minsky's small universal Turing machine'', describing a

universal Turing machine In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simu ...

with four symbols and seven states; * (age 83 years) ''Two figures in the

hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

''.

References

* . * . *

, A. Mostowski, and R. M. Robinson, 1953. ''Undecidable theories''. North Holland. *

Leon Henkin Leon Albert Henkin (April 19, 1921, Brooklyn, New York - November 1, 2006, Oakland, California) was an American logician, whose works played a strong role in the development of logic, particularly in the theory of types. He was an active scholar ...

, 1995,
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. * {{DEFAULTSORT:Robinson, Raphael M. 1911 births 1995 deaths People from National City, California 20th-century American mathematicians American logicians Set theorists University of California, Berkeley alumni University of California, Berkeley faculty

See also

References

External links