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Abraham Robinson
Abraham Robinson (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 incorporated into mathematics.

He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Walbrzych, in Poland. Robinson was in France when the Nazis invaded, 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. 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 UCLA in 1962. He was becoming well known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. In particular 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, which include infinite and infinitesimal numbers. Others, such as Wim 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 1965. 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.

Robinson was at UCLA during the height of the Free Speech Movement and the movement against the Vietnam War. Although he was basically in sympathy with both, he didn't feel at home 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, but he was also unsatisfied with the quality of the graduate students at UCLA. He was courted by Yale, and after some initial reluctance, he moved there in 1967. He died of pancreatic cancer in 1974.

References

  • J. W. Dauben, Abraham Robinson: The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey, Princeton, NJ: Princeton University Press, 1998
1. ^ Hodges, W: "A Shorter Model Theory", page 182. CUP, 1997

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1971 1972 1973 - 1974 - 1975 1976 1977

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mathematician is a person whose primary area of study and research is the field of mathematics.

Problems in mathematics

Some people incorrectly believe that mathematics has been fully understood, but the publication of new discoveries in mathematics continues at an immense
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Non-standard analysis is a branch of mathematics that formulates analysis using a rigorous notion of infinitesimal, where a nonzero element of an ordered field F is infinitesimal if and only if its absolute value is smaller than any element of F of the form 1/
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Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. For everyday life, an infinitesimal object is an object which is smaller than any possible measure, whether we measure size, time, chemical concentration, etc.
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Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite
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Historical Jewish languages
Hebrew, Yiddish, Ladino, others
Liturgical languages:
Hebrew and Aramaic
Predominant spoken languages:
The vernacular language of the home nation in the Diaspora, significantly including English, Hebrew, Yiddish, and
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Zionism is an international political movement that supports a homeland for the Jewish People in the Land of Israel.[1] Although its origins are earlier, the movement was formally established by Austrian journalist Theodor Herzl in the late nineteenth century.
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Waldenburg is the name of several places:
  • Waldenburg, Saxony, Germany
  • Waldenburg, Baden-Württemberg
  • Waldenburg, Switzerland
  • the former German name for Walbrzych, Poland
  • Waldenburg, Arkansas, USA
Waldenburg is also a surname:

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Anthem
"Das Lied der Deutschen" (third stanza)
also called "Einigkeit und Recht und Freiheit"
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Mazurek Dąbrowskiego   (Polish)
Dąbrowski's Mazurek
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The Free French Forces (French: Forces Françaises Libres, FFL) were French fighters in World War II, who decided to continue fighting against Axis forces after the surrender of France and subsequent German occupation.
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airfoil (in American English, or aerofoil in British English) is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section.

An airfoil shaped body moved through a fluid produces a force perpendicular to the motion called lift.
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Jerusalem (Hebrew: יְרוּשָׁלַיִם   (help info ) , Yerushaláyim; Arabic:
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Bruins, NCAA Division I
Affiliations AAU
Pac 10
Nobel laureates 10
Website www.ucla.edu
The University of California, Los Angeles (generally known as UCLA) is a public research university located in Los Angeles, California, United States.
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Mathematical logic is a branch of mathematics, which grew out of symbolic logic. Subfields include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic has contributed to, and been motivated by, the study of foundations of mathematics, but
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Analysis has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function.
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Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. Most authors nowadays simply write algebra instead of abstract algebra.
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This article discusses model theory as a mathematical discipline and not the informally used term mathematical model as used in other parts of mathematics and science.

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In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure.
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Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz
Born July 1 (June 21 Old Style) 1646
Leipzig, Electorate of Saxony
Died November 14 1716
Hannover, Hanover
Nationality German
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The Free Speech Movement (FSM) was a student protest which began in the 1964-1965 school year on the campus of the University of California, Berkeley under the informal leadership of students Mario Savio, David Goines, Suzanne Goldberg, Bettina Aptheker, Jackie Goldberg, and others.
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Total dead: ~314,000
Total wounded: ~1,490,000 North Vietnam and NLF
dead and missing: ~1,100,000 [1] [2] [3] [4]
wounded: ~600,000+ [5]
People's Republic of China
dead: 1,446
wounded: 4,200

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Yale University is a private university in New Haven, Connecticut. Founded in 1701 as the Collegiate School, Yale is the third-oldest institution of higher education in the United States and is a member of the Ivy League.
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Pancreatic cancer
Classification & external resources

ICD-10 C 25.
ICD-9 157

OMIM 260350
DiseasesDB 9510
MedlinePlus 000236
eMedicine med/1712  
MeSH D010190 Pancreatic cancer
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The MacTutor History of Mathematics archive is an award-winning website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland.
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