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Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who is most widely known for development of non-standard analysis
Non-standard analysis

Non-standard analysis is a branch of mathematics that formulates mathematical analysis using a rigorous notion of an infinitesimal number.Non-standard analysis was introduced in the early 1960s by the mathematician Abraham Robinson....
, a mathematically rigorous system whereby infinitesimal
Infinitesimal

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....
 and infinite
Transfinite number

Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite set numbers, yet not necessarily absolutely infinite....
 numbers were incorporated into mathematics.

He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Walbrzych
Walbrzych

Walbrzych is a city in Lower Silesian Voivodeship in south-western Poland, with 125,773 inhabitants . From 1975–1998 it was the capital of Walbrzych Voivodeship; it is now the seat of Walbrzych County....
, in Poland
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian Enclave and exclave, to the north....
.






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Abraham Robinson
Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who is most widely known for development of non-standard analysis
Non-standard analysis

Non-standard analysis is a branch of mathematics that formulates mathematical analysis using a rigorous notion of an infinitesimal number.Non-standard analysis was introduced in the early 1960s by the mathematician Abraham Robinson....
, a mathematically rigorous system whereby infinitesimal
Infinitesimal

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....
 and infinite
Transfinite number

Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite set numbers, yet not necessarily absolutely infinite....
 numbers were incorporated into mathematics.

He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Walbrzych
Walbrzych

Walbrzych is a city in Lower Silesian Voivodeship in south-western Poland, with 125,773 inhabitants . From 1975–1998 it was the capital of Walbrzych Voivodeship; it is now the seat of Walbrzych County....
, in Poland
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian Enclave and exclave, to the north....
. Robinson was in France when the Nazis
Nazi Germany

Nazi Germany and the Third Reich are the colloquial English names for Germany under the regime of Adolf Hitler and the Nazi Party , which established a Totalitarianism dictatorship that existed from 1933 to 1945....
 invaded during World War II
World War II

World War II, or the Second World War , was a global military conflict which involved a Participants in World War II, including all of the great powers, organised into two opposing military alliances: the Allies of World War II and the Axis powers....
, 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
Free French Air Force

The Free French Air Force were the air arm of Free French Forces during the Second World War....
 and contributed to the war effort by teaching himself aerodynamics
Aerodynamics

Aerodynamics is a branch of Dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them....
 and becoming an expert on the airfoil
Airfoil

An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section.An airfoil-shaped body moved through a fluid produces a force perpendicular to the motion called lift ....
s used in the wings of fighter planes.

After the war, Robinson worked in London
London

London is the capital of both England and the United Kingdom, and the most populous municipality in the European Union. An important settlement for two millennia, History of London goes back to its founding by the Roman Empire....
, Toronto
Toronto

Toronto is the List of the 100 largest municipalities in Canada by population in Canada and the Provinces and territories of Canada Provincial and territorial capitals of Canada of Ontario....
, and Jerusalem
Jerusalem

Jerusalem is the capital of Israel and its List of Israeli cities in both population and area, with a population of 747,600 residents over an area of if Positions on Jerusalem East Jerusalem is included....
, but ended up at University of California, Los Angeles
University of California, Los Angeles

The University of California, Los Angeles is a public research university located in Westwood, Los Angeles, California, California, United States....
 in 1962. He become known for his approach of using the methods of mathematical logic
Mathematical logic

Mathematical logic is a subfield of mathematics and logic with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics....
 to attack problems in analysis
Mathematical analysis

Mathematical analysis, which mathematicians refer to simply as 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....
 and abstract algebra
Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as group , ring , field , module , vector spaces, and algebra over a field....
. He "introduced many of the fundamental notions of model theory
Model theory

In mathematics, model theory is the study of mathematical Structure such as Group , fields, graph , or even models of set theory, using tools from mathematical logic....
". 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 ultrafilter
Ultrafilter

In the mathematics 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 ....
s, 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
Gottfried Leibniz

Gottfried Wilhelm Leibniz was a Germany polymath who wrote primarily in Latin and French language.He occupies an equally grand place in both the history of philosophy and the history of mathematics....
, 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
Doctor of Philosophy

Doctor of Philosophy, abbreviated Ph.D. or PhD for the Latin , meaning "teacher of philosophy", is an postgraduate academic degree awarded by University....
 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
Yale University

Yale University is a private university in New Haven, Connecticut. Founded in 1701 as the Collegiate School, Yale is the Colonial Colleges institution of higher education in the United States and is a member of the Ivy League....
, and after some initial reluctance, he moved there in 1967. He died of pancreatic cancer
Pancreatic cancer

Pancreatic cancer is a cancer of the pancreas. Each year in the United States, about 37,680 individuals are diagnosed with this condition and 34,290 die from the disease each year....
 in 1974.

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