Robinson and Grice on the infinite

Speranza

Abraham Robinsohn was courted by Yale. Grice wasn't.

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

Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) is a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.

 

Robinsohn 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.

Robinsohn 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, Robinsohn 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, Robinsohn worked in London, Toronto, and Jerusalem, but ended up at University of California, Los Angeles in 1962.

 

Robinsohn become known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra.

Robinsohn introduced many of the fundamental notions of model theory.

 Using these methods, Robinsohn finds a way of using formal logic to show that there are self-consistent nonstandard models of the real number system which include infinite and infinitesimal numbers.

Others, such as Wilhelmus Luxemburg, showed that the same results could be achieved using ultrafilters, which made Robinsohn's work more accessible to mathematicians who lacked training in formal logic.

Robinsohn's book Non-standard Analysis was published in 1966.

Robinsohn 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.

He meant it 'metaphorically', he later explained ("as if "per implicatura"").

While at UCLA Robinsohn's colleagues remember him as working hard to accommodate PhD students of all levels of ability by finding them projects of the appropriate difficulty.

Robinsohn was courted by Yale, and after some initial reluctance, he moved there in 1967.

He died of pancreatic cancer in 1974.

Notes

1. ^ 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 

See also[edit]

• Influence of non-standard analysis

References[edit]

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

External links[edit]

• 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

[hide] v t e Infinitesimals History Adequality Infinitesimal calculus Leibniz's notation Integral symbol Criticism of non-standard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle Related branches Non-standard analysis Non-standard calculus Internal set theory Synthetic differential geometry Constructive non-standard analysis 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 Physics Engineering Infinitesimal strain theory Infinitesimal oscillations of a pendulum Textbooks Analyse des Infiniment Petits Elementary Calculus

Authority control VIAF: 59260725

Persondata
Name	Robinson, Abraham
Alternative names
Short description	American mathematician
Date of birth	October 6, 1918
Place of birth	Waldenburg (Wałbrzych), Germany
Date of death	April 11, 1974
Place of death	New Haven, Connecticut

      

Categories:

• Mathematics of infinitesimals
• 1918 births
• 1974 deaths
• 20th-century mathematicians
• Alumni of the University of London
• American mathematicians
• German mathematicians
• German Jews
• German emigrants to the United States
• American people of German-Jewish descent
• People from Wałbrzych
• University of California, Los Angeles faculty
• Yale University faculty
• Mathematical logicians
• Model theorists
• Institute for Advanced Study visiting scholars