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Abraham Robinson
Robinson in 1970
Born	(1918-10-06)October 6, 1918 Waldenburg, German Empire
Died	April 11, 1974(1974-04-11) (aged 55) New Haven, Connecticut, US
Alma mater	Hebrew University, University of London
Known for	Non-standard analysis
Scientific career
Fields	Mathematics
Institutions	University of California, Los Angeles, Yale University, University of Toronto
Doctoral advisor	Paul Dienes
Doctoral students	E. Mark Gold Azriel Lévy A. H. Lightstone Peter Winkler Carol S. Wood

Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics.

Biography

He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he emigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics and becoming an expert on the airfoils used in the wings of fighter planes.

After the war, Robinson worked in London, Toronto, and Jerusalem, but ended up at the University of California, Los Angeles in 1962.

Work in model theory

He became known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. He "introduced many of the fundamental notions of model theory". Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system that include infinite and infinitesimal numbers. Others, such as Wilhelmus Luxemburg, showed that the same results could be achieved using ultrafilters, which made Robinson's work more accessible to mathematicians who lacked training in formal logic. Robinson's book Non-standard Analysis was published in 1966. Robinson was strongly interested in the history and philosophy of mathematics, and often remarked that he wanted to get inside the head of Leibniz, the first mathematician to attempt to articulate clearly the concept of infinitesimal numbers.

While at UCLA his colleagues remember him as working hard to accommodate PhD students of all levels of ability by finding them projects of the appropriate difficulty. He was courted by Yale, and after some initial reluctance, he moved there in 1967. In the Spring of 1973 he was a member of the Institute for Advanced Study. He died of pancreatic cancer in 1974.

See also

• Influence of non-standard analysis
• Robinson's joint consistency theorem – Theorem of mathematical logic
• Transfer principle – Concept in model theory

Notes

1. O'Connor, John J.; Robertson, Edmund F., "Abraham Robinson", MacTutor History of Mathematics Archive, University of St Andrews
2. "Robinson biography". mathshistory.st-andrews.ac.uk/Biographies/Robinson/. Retrieved 2016-07-10.
3. Hodges, W: "A Shorter Model Theory", page 182. CUP, 1997
4. "Abraham Robinson, Institute for Advanced Study". Retrieved 2017-11-25.

Publications

• Robinson, Abraham (1963), Introduction to model theory and to the metamathematics of algebra, Amsterdam: North-Holland, ISBN 978-0-7204-2222-1, MR 0153570
• Lightstone, A. H.; Robinson, Abraham (1975), Nonarchimedean Fields and Asymptotic Expansions, North-Holland, ISBN 978-0-7204-2450-8
• Robinson, Abraham (1977) , Keisler, H. Jerome (ed.), Complete theories, Studies in Logic and the Foundations of Mathematics (2nd ed.), Amsterdam: North-Holland, ISBN 978-0-7204-0690-0, MR 0472504
• Robinson, Abraham (1979), Keisler, H. Jerome (ed.), Selected papers of Abraham Robinson. Vol. I Model theory and algebra, Yale University Press, ISBN 978-0-300-02071-7, MR 0533887
• Robinson, Abraham (1979), Luxemburg, W. A. J.; Körner, S. (eds.), Selected papers of Abraham Robinson. Vol. II Nonstandard analysis and philosophy, Yale University Press, ISBN 978-0-300-02072-4, MR 0533888
• Robinson, Abraham (1979), Young, A. D. (ed.), Selected papers of Abraham Robinson. Vol. III Aeronautics, Yale University Press, ISBN 978-0-300-02073-1, MR 0533889
• Robinson, Abraham (1996) , Non-standard analysis, Princeton Landmarks in Mathematics (2nd ed.), Princeton University Press, ISBN 978-0-691-04490-3, MR 0205854

References

• Dauben, J. W. (1998), Abraham Robinson: The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey, Princeton University Press, ISBN 0-691-03745-0
• Mostow, G. D. (1976), "Abraham Robinson 1918—1974", Israel Journal of Mathematics, 25 (1/2): 5–14, doi:10.1007/BF02756558, S2CID 123539367
• Young, A. D.; Kochen, S.; Körner, S.; Roquette, P. (1976), "Abraham Robinson", Bulletin of the London Mathematical Society, 8 (3): 307–323, doi:10.1112/blms/8.3.307, MR 0409084

External links

• Media related to Abraham Robinson at Wikimedia Commons
• Abraham Robinson — Biographical Memoirs of the National Academy of Sciences
• Kutateladze S.S., Abraham Robinson, the creator of nonstandard analysis

v t e Infinitesimals
History	Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle
Related branches	Nonstandard analysis Nonstandard calculus Internal set theory Synthetic differential geometry Smooth infinitesimal analysis Constructive nonstandard analysis Infinitesimal strain theory (physics)
Formalizations	Differentials Hyperreal numbers Dual numbers Surreal numbers
Individual concepts	Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity
Mathematicians	Gottfried Wilhelm Leibniz Abraham Robinson Pierre de Fermat Augustin-Louis Cauchy Leonhard Euler
Textbooks	Analyse des Infiniment Petits Elementary Calculus Cours d'Analyse

• 1918 births
• 1974 deaths
• 20th-century American mathematicians
• Alumni of the University of London
• 20th-century German mathematicians
• Jewish emigrants from Nazi Germany to Mandatory Palestine
• Jews who emigrated to escape Nazism
• German emigrants to the United States
• People from Wałbrzych
• University of California, Los Angeles faculty
• Yale University faculty
• Brouwer Medalists
• Mathematical logicians
• Model theorists
• Institute for Advanced Study visiting scholars
• Yale Sterling Professors