Doctoral advisor Paul Dienes Fields Mathematics Role Mathematician | Name Abraham Robinson Known for Non-standard analysis | |
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Born October 6, 1918
Waldenburg, German Empire ( 1918-10-06 ) Institutions University of California, Los Angeles, Yale University, University of Toronto Alma mater Hebrew University, University of London Doctoral students Azriel Levy
A. H. Lightstone
Peter Winkler
Carol S. Wood Influences Gottfried Leibniz, Abraham Fraenkel Died April 11, 1974, New Haven, Connecticut, United States Education Hebrew University of Jerusalem, University of London Influenced by Gottfried Wilhelm Leibniz, Abraham Fraenkel People also search for Gottfried Wilhelm Leibniz, A. H. Lightstone, Larry Travis Books Nonarchimedean Fields and Asymptoti, Non‑standard analysis, Wing theory, The Repair of Vehicle Bodies, Complete theories | ||
Abraham Robinson’s legacy in model theory and (...) - L. Van den Dries - Workshop 3 - CEB T1 2018
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.
Contents
- Abraham Robinsons legacy in model theory and L Van den Dries Workshop 3 CEB T1 2018
- Biography
- Work in model theory
- Publications
- References
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". 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.