# Abraham Robinson

### Quick Info

Waldenburg, Germany (now Wałbrzych, Poland)

New Haven, Connecticut, USA

**Abraham Robinson**was a Polish-born mathematician best known for the development of non-standard analysis.

### Biography

We should note at the outset that in fact**Abraham Robinson**'s family name was Robinsohn rather than Robinson, but we shall refer throughout this article to Robinson, the version which he used after 1940. Abraham Robinson's father was also named Abraham Robinson and his mother was Hedwig Lotte. He was the second child of the family, his older brother Saul Robinson also went on to have an outstanding career; he became an expert on comparative education. Abraham Robinson senior was also a highly talented man. After studying chemistry he became an important writer and philosopher but Abraham junior never knew his father for he died shortly before Abraham junior was born.

It was a Jewish family and although Abraham Robinson senior was a Zionist he had never been to Palestine but he had accepted the position of head of the Hebrew National Library in Jerusalem just before he died. Hedwig Robinson was a teacher and she brought up her two sons in Germany until 1933 when Abraham was fourteen years old. Although little is known of Abraham during these years, some notebooks which he owned have survived [18]:-

... containing poems and plays, suggesting a sensitive observant child with an ambition to write.Clearly the family had always been attracted to Jerusalem but the anti-Jewish legislation introduced into Germany in 1933 indicated very clearly that it was time to leave. On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the schools and universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. Hedwig, Abraham and Saul Robinson avoided the problems that Jews would have in Germany from 1933 by starting a new life in Palestine.

There Robinson completed his schooling and, in 1935, began studying mathematics under Fraenkel and Levitzki at the Hebrew University of Jerusalem. Robinson was a brilliant student and, after graduating in 1939, he was awarded a scholarship to allow him to study at the Sorbonne in Paris. After only a few months of study he was forced to flee when the Germans invaded France. After reaching England on one of the last small boats from Bordeaux to evacuate refugees, he changed his name from Robinsohn.

As an undergraduate at the Hebrew University Robinson has been interested in both algebra and mathematical logic. However, once in England he enlisted in the Free French Air Force and, because he was a mathematician, he was sent in 1941 to the Royal Aircraft Establishment at Farnborough where he became a Scientific Officer. Rapidly he became an expert in aerodynamics and for the rest of World War II he worked on delta wings and supersonic flow. He was sent to Germany in 1945, still in his role as Scientific Officer, and then in 1946 he was appointed as a senior lecturer at the College of Aeronautics at Cranfield. Young writes in [20]:-

At Cranfield his interests in the aerodynamic theory of wings, both in subsonic and supersonic flow, broadened and became increasingly comprehensive.By now Robinson was a world leading authority in aerodynamics yet he continued with his interest in mathematical logic. In 1946 he was awarded a Master's Degree from the Hebrew University in Jerusalem and, following this, he began research at London University receiving a Ph.D. from London in 1949 for pioneering work in model theory and the metamathematics of algebraic systems.

He went to the University of Toronto in 1951 to take up a chair of applied mathematics but left for Jerusalem in 1957 to fill Fraenkel's chair at the Hebrew University. He was Chairman of the Mathematics Department there until 1962 when he accepted the professorship of Mathematics and Philosophy at the University of California, Los Angeles. In 1967 he moved again, but remaining in the United States he went to Yale University as Professor of Mathematics. Other than changing his chair to the Sterling Professor of Mathematics at Yale in 1971 he remained there until his death. He was diagnosed as having cancer of the pancreas in 1973, underwent an operation in November of that year, but died a few months later. A collection of papers

*Model theory and algebra*was published in 1975 as a memorial tribute to Robinson. The editors' foreword states:-

The sudden fatal illness of Abraham Robinson came as a great shock to many people around the world. For Robinson was more than an excellent mathematician. He was also a person whom one came very quickly to like very much. Those swift sad months of November 1973-April 1974 were for those at Yale tinged with a sense of unreality. He was gone before anyone could come to grips with what was happening. We sought a way of expressing our respect and our sense of personal loss. This volume was the best way we knew.Robinson was a leading expert in remarkably different areas of mathematics. The article [20] lists 130 papers and nine books which he wrote. Let us examine first his contributions to applied mathematics. Only one of his books deals with applied mathematics but it may surprise mathematicians who think of Robinson only as a mathematical logician to realise that almost half his papers are on applied mathematics, particularly on aerodynamics. The one applied mathematics book is

*Wing theory*written jointly with J A Laurmann and published in 1956. Lighthill, reviewing the work, wrote:-

This is an admirable compendium of the mathematical theories of the aerodynamics of aerofoils and wings. Almost all the important results are referred to, even though there can be only a brief reference to literature in connection with the more difficult topics. ... It should be an invaluable introduction to wing aerodynamics for mathematically-minded students, as well as a solid stand-by for purposes of reference for all workers in this and allied fields.Robinson is best known, however, for his work on mathematical logic. His doctorate from the Hebrew University in 1949 was

*The metamathematics of algebraic systems*and this became his first book published in 1951. He published

*Complete theories*in 1956 which was written to study the properties of model-completeness and bounding transform. He applied these two concepts to the elementary theories of certain mathematical structures. Robinson's contributions to model theory were developed during his time at the University of Toronto. He weaved his many contributions and papers into a treatise

*Introduction to model theory and to the metamathematics of algebra*published in 1963. Engeler wrote:-

This is ... the first attempt to write a connected exposition of the new subject of model theory. The main body of the work consists of rewritten versions of the author's main contributions to the subject, which are brought into a smooth and eminently readable sequence. ... there results as complete a survey as can be expected at this time from any single author.Robinson's most famous invention was non-standard analysis which he introduced in 1961. Kochen writes in [20]:-

I want to emphasise that non-standard analysis was not a sudden tangential direction in which Robinson moved. Rather, it was the systematic application of the same viewpoint which he earlier applied to algebra to the study of analysis.Fenyo has explained the ideas behind the theory:-

[Robinson's] theory is based on the metamathematical fact that the system of real numbers is incomplete. Thus, there exist extensions of the field of real numbers that possess all the properties of the system of real numbers that are formulated in the lower predicate calculus in terms of some given set of relations. Proper extensions of noncomplete theories are often referred to as non-standard models. A non-standard model for the system of real numbers has the feature of being a non-Archimedean totally ordered field which contains a copy of the real number system.In 1966 Robinson published his famous text

*Non-standard analysis*. Kreisel wrote:-

This book, which appeared just 250 years after Leibniz's death, presents a rigorous and efficient theory of infinitesimals obeying, as Leibniz wanted, the same laws as the ordinary numbers.We end this biography by giving some comments on Robinson's personality. In [20] this appreciation is given:-

He had the humility and the kindness of the truly great, he was interested in people and he found it easy to like them and he patronised no-one. He was deeply concerned with most forms of human culture and creativity, and on all he could converse with the fascinating combination of logic, insight and knowledge that characterised his mathematics.Macintyre, in [18], writes:-

Robinson was a gentleman, unfailingly courteous, with inexhaustible enthusiasm. He took modest pleasure in his many honours. He was much respected for his willingness to listen, and for the sincerity of his advice.Finally let us quote from Korner's tribute to Robinson during the memorial service at Yale University on 15 September 1974:-

When one considers the wealth, profundity and diversity of his interests and the continuous interplay in his thinking of pure mathematics, applied mathematics, logic and philosophy one is constantly reminded of Leibniz to whom he felt a natural affinity and for whom he had the deepest admiration. The one Leibnizian idea in which he could see little merit was Leibniz's 'principe de meilleur' according to which the world is the best of all possible worlds. I remember his asking me more than once in his gently ironic way whether I could make any sense of this principle. Today I should like to offer a partial answer: It cannot be a wholly bad worlds in which an Abraham Robinson could live and think; in which his wife and friends are able to cherish his memory; and in which his life's work will be remembered as long as logic, mathematics and philosophy matter to mankind.

### References (show)

- J W Dauben, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - J W Dauben,
*Abraham Robinson. The creation of nonstandard analysis. A personal and mathematical odyssey*(Princeton, NJ, 1995). - A Robinson,
*Selected papers of Abraham Robinson. Vol. I. Model theory and algebra*(New Haven, Conn., 1979). - A Robinson,
*Selected papers of Abraham Robinson. Vol. II. Nonstandard analysis and philosophy*(New Haven, Conn., 1979). - A Robinson,
*Selected papers of Abraham Robinson. Vol. III. Aeronautics*(New Haven, Conn., 1979). - A provisional bibliography of Robinson's works. Model theory and algebra (a memorial tribute to Abraham Robinson),
*Lecture Notes in Math.***498**(Berlin, 1975), 4-13. - Abraham Robinson - a biographical note, in
*Developments in nonstandard mathematics, Aveiro, 1994*(Harlow, 1995), iv-vi. - H Benis-Sinaceur, La théorie d'Artin et Schreier et l'analyse non-standard d'Abraham Robinson,
*Arch. Hist. Exact Sci.***34**(3) (1985), 257-264. - Biography of Abraham Robinson. Model theory and algebra (a memorial tribute to Abraham Robinson),
*Lecture Notes in Math.***498**(Berlin, 1975), 1-3. - J W Dauben, Abraham Robinson and nonstandard analysis: history, philosophy, and foundations of mathematics, in
*History and philosophy of modern mathematics, Minneapolis, MN, 1985*(Minneapolis, MN, 1988), 177-200. - J W Dauben, Abraham Robinson : les infinitésimaux, l'analyse non standard, et les fondements des mathématiques, in
*La mathématique non standard*(Paris, 1989), 157-184. - J W Dauben, Abraham Robinson : the man and his mathematics (Spanish),
*Mathesis***8**(1) (1992), 73-108. - J W Dauben, Mathematics at the University of Toronto : Abraham Robinson in Canada (1951-1957), in
*History of mathematics*(San Diego, CA, 1996), 93-136. - V Gómez Pin, The ontology and history of calculus (the work of Abraham Robinson) (Spanish),
*Theoria (San Sebastián)*(2)**2**(4) (1986/87), 97-119. - A Heijting, Address to Professor A Robinson. At the occasion of the Brouwer memorial lecture given by Prof A Robinson on the 26th April 1973,
*Nieuw Arch. Wisk.*(3)**21**(1973), 134-137. - W A J Luxemburg, Book review of 'Abraham Robinson',
*Nieuw Arch. Wisk.*(4)**15**(1-2) (1997), 103-111. - W A J Luxemburg, Robinson's nonstandard analysis and its influence on mathematics, in
*Rechnen mit dem Unendlichen*(Basel, 1990), 13-21. - A J Macintyre, Abraham Robinson, 1918-1974,
*Bull. Amer. Math. Soc.***83**(4) (1977), 646-666. - G D Mostow, Abraham Robinson, 1918-1974,
*Israel J. Math.***25**(1-2) (1976), 4-14. - A D Young, S Kochen, S Körner and P Roquette, Abraham Robinson,
*Bull. London Math. Soc.***8**(1976), 307-323.

### Additional Resources (show)

Other pages about Abraham Robinson:

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### Honours (show)

Honours awarded to Abraham Robinson

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update July 2000

Last Update July 2000