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.^[1]

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".^[2] 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

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 

See also

• Influence of non-standard analysis

References

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

External links

• O'Connor, John J.; Robertson, Edmund F., "Abraham Robinson", MacTutor History of Mathematics archive, University of St Andrews .
• Abraham Robinson at the Mathematics Genealogy Project
• Abraham Robinson — Biographical Memoirs of the National Academy of Sciences

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