Biographical Memoirs Volume 82 (2003) / Chapter Skim
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Abraham Robinson
Abraham Robinson
Pages 242-285
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Abraham Robinson ABRAHAM ROBINSON WAS BORN on October 6, ~ 918, in the Prussian mining town of WaTclenburg (now Walbrzych) , PolancI.i His father, Abraham Robinsohn ( 1878-1918)
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to spencling their summers in Vienna with their uncle Isak Robinsohn, a prominent radiologist. In 1933, however, as Hitler and the National Socialists came to power in Germany, Lotte Robinsohn decided it was time to realize her lifelong ciream of settling in Palestine.
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When Robinson entered Hebrew University in 1936, the Mathematics Department (aciclec! to the faculty in 1927)
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to which he once gave a lecture on the zeta function. Robinson's first publication appeared in 1939 in the Journal of Symbolic Logic.
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PARIS: JANUARY-JUNE 1940 In Paris Robinson lived in a small pension in the Quartier Latin, not far from the Sorbonne. There is no record of what Robinson may have done with respect to his mathematical studies in Paris, apart from an enthusiastic letter of introduction Fracnkel wrote on Robinson's behalf to the philosopher of mathematics Leon Brunschvicg.
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LONDON ( 1940-1946) Thanks to the Jewish National League in London, Robinson eventually founcl a place to stay in Brixton, "a quarter of ill repute," as his cliary put it.
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The results were sufficiently impressive that the British government requested Robinson's transfer from the Free French to the Ministry of Aircraft Production at the Royal Aircraft Establishment in Farnborough, just southwest of Lonclon. Immecliately Robinson began to study aerodynamics in earnest en c!
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He also usecl the month he was there to work on a paper with his former instructor Theodore Motzkin, the result of which was "Characterization of Algebraic Plane Curves," published in the Duke Mathematical fournal the following year. Robinson returned to London, having accepted a position as senior lecturer at the newly founclecl College of Aeronautics at Cranfielcl (northwest of Lonclon)
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Paul Dienes. He originally thought to devote a cloctoral thesis to the syntax of algebra, but this eventually became "On the Metamathematics of Algebra." He reported some of the early results of his thesis in a brief abstract he sent to the Journal of Symbolic Logic in ~ 949: "Analysis en cl Development of Algebra by the Methods of Symbolic Logic." Even from this very concise note it was clear that his interests were much more mathematical in a strict sense than were those of other pioneers of the subject like Alfrecl Tarski en c!
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. As Abby and Renee sailed from Liverpool to Montreal on a Cunard liner in August of 1951, they not only went first class but in the course of the trip Robinson also completed the 25-page manuscript "On the Foundations of Dimensional Analysis." (The original manuscript dated "RMS Franconia, August/ September 1951" is preserved among Robinson's papers in the Yale University archives.)
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clifferential equations, the sort of courses he hacl been teaching at CranfielcI. He sometimes taught a graduate course on supersonic wing theory and also taught basic introductory courses as well, inclucling calculus en cl analytic geometry.
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to algebraically closed fields, real-closed ordered fields, and moclel completeness, all of which were clevelopecl in a book he published in 1955: Theorie metamathematique des ideates.
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Among the more important results Robinson publishecl while at Toronto was a paper he submitter! to Mathematische Annaten, "On Orclerecl Fielcis en cl Definite Functions." This proviclecl a moclel theoretic proof of Hilbert's seventeenth problem, that a positive definite real rational function is a sum of squares of rational functions.
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As a result, until the 1967 Six Day War, which wouIcl reunite all of Jerusalem, Hebrew University was scatterer! throughout West Jerusalem in a patchwork of builclings.
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his thesis on "Contributions to the Metamathematics of Set Theory." By then, coinciding with the tenth anniversary of the founcling of Israel, a new campus of Hebrew University was officially opened on Givat Ram, where Manchester House served both the departments of mathematics en cl of theoretical physics. In aciclition to his teaching at the university, Robinson was invited to teach a course on Quill dynamics at the Weizmann Institute (in Rehovot)
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The clifferentially closecl fielcis couIcl then be taken as models of the "closure" axioms associated with the completion. As George Seligman has said, reflecting the views of Angus Macintyre, "it wouIcl be appropriate to say that he invented differentially closed fields" (Seligman, 1979, p.
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the bright iclea of taking the same approach to the real numbers R He soon proviclecl a much fuller account of nonstanciarcl analysis in his book Introduction to Model Theory (see below)
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rectify. When Introduction to Model Theory and to the Metamathematics of Algebra appearecl in 1963, the second half was almost entirely new en c!
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In the Mathematics Department he also taught a one-year course on axiomatic set theory en c! another on applications of logic to analysis.
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in a paper Robinson publishecl the following year in the Pacific Journal of Mathematics. Shortly after his arrival at UCLA Robinson's book Introduction to Model Theory and to the Metamathematics of Algebra appeared in the spring of 1963, and was describec!
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204~. Later that summer Robinson also participated in the International Congress for Logic, Methoclology, en cl PhiTosophy of Science, hell!
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Primarily responsible for acivising the university's president, Clark Kerr, one of the council's major concerns that year was the Berkeley Free Speech Movement, set against the background of both the Civil Rights Movement en cl the Vietnam War. This eventually pitted faculty and students against the administration, which also hac!
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Infinitesimals, Robinson insisted, "appeal naturally to our intuition." Using nonstanciarcl analysis, he proved a wicle variety of results, inclucling basic theorems from the calculus, clifferential geometry, nonmetric topological spaces, Lebesgue measure, Schwartz distributions, complex nonstanciarcl analysis, analytic theory of polynomials, entire functions, linear spaces (inclucling Hilbert space) , along with nonstanciarcl spectral theory of compact operators, topological groups, and Lie groups.
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He thus gave up his position in philosophy, and moved full-time to the Mathematics Department. Meanwhile, he hacl been invited by John CrossTey to visit St.
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When he returnee! to UCLA for the fall term, Robinson taught a course on set theory, another on lattice theory and Boolean algebras, and a three
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by the American Mathematical Society en cl the Association for Symbolic Logic, with financial support from the National Science Founciation. The meeting was cleclicatec!
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. YALE UNIVERSITY, 1967-1974 At Yale Robinson joined a clistinguishecl faculty in the Department of Mathematics, which at the time incluclecI, among others, Walter Felt, Nathan Jacobson, Shizuo Kakutani, William Massey, George Mostow, Oystein Ore, Charles Rickart, en cl George Seligman.
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By then the Six Day War hacl reunited Jerusalem, and Abby and Renee were pleased to spend most of August back in Israel. At the end of the month Robinson presided over a two-day meeting of the Association for Symbolic Logic in Warsaw, during a week's conference clevotecl to "Construction of Moclels for Axiomatic Systems." From Polancl they went on to Italy for a meeting at Varenna, where Robinson gave a one-week introduction to moclel theory.
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Heyting he chose to consoler in partly historical terms the "ultimate foundation" for mathematics. lust as nonEucliclean geometry clestroyocl faith in Eucliclean geometry as the one true geometry of space, so too, Robinson helcI, clicl the results of Goclel en cl Cohen destroy any faith one might have hacl in the existence of a single, absolutely true set theory.
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about recent clevelopments clue to "Infinite Forcing in Moclel Theory." What Robinson clicl was to clevelop Paul Cohen's methoc! of forcing in set theory within the context of mocle!
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At the end of the summer Robinson not only cleliverecl the twentieth series of Hedrick lectures at the summer meeting of the Mathematical Association of America (on "Nonstanciarcl Analysis en cl Nonstanciarcl Arithmetic") but he also attended the Fourth International Congress for Logic,
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. ciation for Symbolic Logic in 1973, he was askocl to give an hour lecture at its annual meeting, which he clevotec!
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Of the "metamathematical problems" Robinson hacl raiser! in his Association for Symbolic Logic presiclential aciciress, he now turned to answer some of the questions he _ ~ rat · ~ .
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424~. From Heiclelberg Robinson flew to Bristol for a European meeting of the Association for Symbolic Logic, where
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ABRAHAM ROBINSON 277 he cliscussec! problems of foundations.
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When Robinson returned to Yale in the fall of 1973, he hac! been experiencing stomach pains en c!
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ABRAHAM ROBINSON 279 career was the perfect counter-example to the oic! myth that mathematicians clo their best work before they are 30, at the beginning of their careers.
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1973. Studies in model theory." Stud.
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In Selected Papers of Abraham Robinson, vol.
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1954 On predicates and algebraically closed fields.
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On some applications of model theory to algebra and analysis.
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20:18893. 1971 Infinite forcing in model theory.
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