# Robinson, Abraham

- Joseph W. Dauben

Robinson, Abraham (1918–1974), mathematician, was born in Waldenburg, Lower Silesia, on 6 October 1918, the second, and posthumous, son of Abraham Robinsohn (1878–1918) and his wife, Hedwig Charlotte (Lotte; 1888–1947), daughter of Jakob Bähr. His father, a noted Zionist, writer, and secretary to David Wolfsohn, had died of a heart attack a few months earlier in Berlin, where he was working for the Jewish National Fund. His mother, formerly a schoolteacher, raised her two sons with the help of her father, in Breslau where the two were educated in a private school headed by the rabbi Max Simonson.

In April 1933, as the National Socialists came to power in Germany, Lotte Robinsohn fled with her sons to Palestine where they settled as illegal immigrants. After completing his high school education in Jerusalem, Robinsohn entered the Hebrew University in 1936, where he studied mathematics with Abraham Fraenkel. Robinsohn was also active in the Haganah, the illegal Jewish organization in Palestine during the British mandate. While still an undergraduate, he published his first contribution to symbolic logic, an article 'On the independence of the axioms of definiteness' (1939).

In 1939 Robinson was awarded a special scholarship by the French government for study in Paris at the Sorbonne, but within six months, as the Germans invaded France, he narrowly escaped via Bordeaux to Britain, where he enlisted as a member of de Gaulle's free French forces, and soon Anglicized his name to Robinson. Almost immediately his mathematical talent came to the attention of the Royal Air Force, for which he worked at the Ministry of Aircraft Production at the Royal Aircraft Establishment in Farnborough for the duration of the war. There he contributed primarily to the study of shock waves and material stress failures in aerofoils, as well as to the aeronautics of supersonic aircraft design.

In 1943 Robinson met Renée Rebecca Kopel, an actress from Vienna who was working as a dress designer in London; they were married on 30 January 1944 at Temple Fortune in Golders Green. After the war, Robinson joined the staff of the newly founded Royal College of Aeronautics in Cranfield as a senior lecturer. He not only taught courses on basic applied mathematics, but emphasized numerical and statistical methods as well, making use of the college's new computer facilities. He was interested in both theoretical and practical aspects of supersonic aeronautics, and devoted considerable amounts of his time to wind-tunnel experiments. Among his major contributions to wing theory (research he later continued at the University of Toronto in Canada) was the book he co-authored with his former student from Cranfield, John Laurmann. *Wing Theory* (1956) included both subsonic and supersonic aerofoil design, considered under conditions of both steady and unsteady flow, and included Robinson's own pioneering studies of the aerodynamics of delta wings. Meanwhile Robinson returned to his earlier study of pure mathematics, and enrolled in Birkbeck College where he studied with Richard Cooke and the Hungarian Paul Dienes, and wrote his dissertation, 'On the metamathematics of algebra'. This was devoted to 'the analysis and development of algebra by the methods of symbolic logic', and earned him his PhD in 1949 (he was awarded the DSc in 1957).

In 1951 Robinson accepted an offer from the University of Toronto to join its department of applied mathematics, teaching mainly differential equations, fluid mechanics, and aerodynamics. His first graduate students worked on aspects of mathematical physics, from the mathematics of quantum mechanics to supersonic aerofoil theory. Robinson maintained his interest in theoretical mathematics; his *Théorie métamathématique des idéaux* (1955) extended his earlier work on the 'metamathematics' of algebra, namely aspects of model theory. In other articles he dealt with aspects of ordered fields and definite functions. Robinson's research interests became increasingly devoted to mathematical logic and model theory. His *Complete Theories* (1956)—which used the idea of model completeness to determine the decidability of formal systems—was judged 'a milestone in the development of model theoretic algebra' (*Selected Papers*, 1.vi). Applying his ideas to algebraically closed fields, Robinson succeeded in establishing an abstract version of Hilbert's *Nullstellensatz*. Using his 'prime model test', he also established the completeness of different groups and fields.

From 1957 to 1962 Robinson was back in Jerusalem, having accepted the mathematics chair at the Hebrew University, formerly held by Abraham Fraenkel. In addition to serving as chairman of the department, he also published a significant paper on differential closed fields, a subject he may be said to have invented. In 1960, while on sabbatical leave at Princeton University, he made his best-known discovery, nonstandard analysis, which succeeds in rigorously defining infinitesimals in mathematics through an ingenious application of mathematical logic and model theory. This enabled him to enlarge the system of real numbers to include infinitely large as well as infinitely small elements. Back in Israel, he finished a revision of his earlier book, *On the Metamathematics of Algebra* (1951), which he retitled *Introduction to Model Theory and to the Metamathematics of Algebra* (1963). The last chapter, devoted to 'selected topics', included a brief introduction to nonstandard analysis.

In 1962 Robinson moved on to the University of California at Los Angeles, where until 1967 he held a joint appointment in mathematics and philosophy. There his most impressive result was achieved and published with his graduate student, Alan Bernstein, when they succeeded in proving an invariant subspace theorem for Hilbert space, a result that 'instantly rocked the mathematical world' (Dauben, *Odyssey*, 327). In 1965 Robinson published a general, undergraduate introduction to algebra, *Numbers and Ideals*, which he hoped would illustrate the power of abstract algebra and such concepts as groups, rings, primes, and ideals, all with an eye to showing the 'beauty of the subject' (*Numbers and Ideals*, 62–3). The following year he also published another major work, *Nonstandard Analysis* (1966). Meanwhile he was becoming increasingly dissatisfied with the unmanageable size of the University of California system and the deteriorating academic climate, with continuing campus turmoil over political, social, economic, and academic issues; in 1967 he accepted an offer to join the prestigious department of mathematics at Yale University.

While at Yale, Robinson served as president of the Association for Symbolic Logic (1968–70), and actively sought to promote symbolic logic abroad, notably in Japan and Latin America. He also began to extend his interests in model theory and applications of nonstandard analysis to a variety of different subjects, including economics and quantum physics. Perhaps most promising of all was nonstandard number theory, on which he co-authored an important paper with Peter Roquette devoted to Diophantine equations and the Siegel–Mahler finiteness theorem. Robinson also pioneered a method of forcing in model theory (a variant of Paul Cohen's method of forcing in set theory). The generic models Robinson constructed using this method are closely related to his earlier results on model-completions, and served to create 'new interest in model-completeness and suggested many questions in particular areas of algebra' (*Selected Papers*, 1.431–2).

Meanwhile interest in Robinson's nonstandard analysis was growing and he participated in the first meeting on the subject held at the Mathematical Research Institute in Oberwolfach, Germany, in 1970. The following year he was named Sterling professor at Yale University. In 1973 he was invited to the Institute for Advanced Study by Kurt Gödel, who hoped that Robinson would eventually succeed him, and in the same year he was awarded the prestigious Brouwer medal by the Dutch Society of Mathematicians. However, in November he was diagnosed with cancer of the pancreas, of which he died at the Yale University Hospital in New Haven on 11 April 1974; he was buried in Jerusalem, on Givat Shaul, overlooking the hills of Judea. His wife survived him.

### Sources

- J. W. Dauben,
*Abraham Robinson**: the creation of nonstandard analysis, a personal and mathematical odyssey*(1995) *Selected papers of Abraham Robinson*, ed. H. J. Keisler and others (1979)- J. W. Dauben, ‘Robinson, Abraham’,
*DSB*, suppl. - J. W. Dauben, ‘Abraham Robinson and nonstandard analysis: history, philosophy, and foundations of mathematics’,
*History and philosophy of modern mathematics*, ed. W. Aspray and P. Kitcher (1988), 177–200 - S. Kochen, ‘The pure mathematician: on Abraham Robinson's work in mathematical logic’,
*Bulletin of the London Mathematical Society*, 8 (1976), 312–15

W. A. J. Luxemburg,

*Nonstandard analysis: lectures on A. Robinson's theory of infinitesimals and infinitely large numbers*, rev. edn, 1964 (1962)Find it in your libraryGoogle PreviewWorldCat

- M. Machover and J. Hirschfeld,
*Lecture notes on nonstandard analysis*(1969) - A. Macintyre, ‘Abraham Robinson, 1918–74’,
*Bulletin of the American Mathematical Society*, 83 (1977), 646 - H. Sinaceur,
*Corps et modèles, essai sur l'histoire de l'algèbre réelle*(1991) - A. D. Young, ‘Abraham Robinson: the applied mathematician’,
*Bulletin of the London Mathematical Society*, 8 (1976), 308–12 - H. Barreau, ed.,
*La mathématique non-standard*(1989) - private information (2004)

### Archives

- Jewish National and University Library, Jerusalem

- Princeton University, Gödel MSS

#### Film

- Mathematical Association of America, ‘Nonstandard analysis’, film (1970, 1 hour)

### Likenesses

- R. F. Zallinger, oils, repro. in Dauben,
*Abraham Robinson*; priv. coll. - photographs and slides, repro. in Dauben,
*Abraham Robinson*; priv. coll.