Abraham Robinson

Abraham Robinson

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

Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard 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 (according to MacTutor).

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 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".^[1] 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. He died of pancreatic cancer in 1974.

Notes

↑ Hodges, W: "A Shorter Model Theory", page 182. CUP, 1997

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
Robinson, Abraham (1977) [1956], 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 533887
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 533888
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 533889
Robinson, Abraham (1996) [1966], Non-standard analysis, Princeton Landmarks in Mathematics (2nd ed.), Princeton University Press, ISBN 978-0-691-04490-3, MR 0205854

References

J. W. Dauben, Abraham Robinson: The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey, Princeton, NJ: Princeton University Press, 1998

External links

Infinitesimals

History	Adequality Leibniz's notation Integral symbol Criticism of non-standard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle Method of indivisibles

Related branches	Non-standard analysis Non-standard calculus Internal set theory Synthetic differential geometry Constructive non-standard 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

Scientists	Gottfried Wilhelm Leibniz Abraham Robinson Pierre de Fermat Augustin-Louis Cauchy Leonhard Euler

Textbooks	Analyse des Infiniment Petits Elementary Calculus Cours d'Analyse

Authority control	WorldCat VIAF: 59260725 LCCN: n50049281 ISNI: 0000 0001 1064 8730 GND: 11860158X SUDOC: 033972702 BNF: cb13621822s (data) MGP: 15886

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