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Abraham Robinson

Abraham Robinson: The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey

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    Abraham Robinson
    Book Description:

    One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first biography of Robinson, Joseph Dauben reveals the mathematician's personal life to have been a dramatic one: developing his talents in spite of war and ethnic repression, Robinson personally confronted some of the worst political troubles of our times. With the skill and expertise familiar to readers of Dauben's earlier works, the book combines an explanation of Robinson's revolutionary achievements in pure and applied mathematics with a description of his odyssey from Hitler's Germany to the United States via conflict-ridden Palestine and wartime Europe.

    Robinson was born in Prussia in 1918. As a boy, he fled with his mother and brother Saul to Palestine. A decade later he narrowly escaped from Paris as the Germans invaded France. Having spent the rest of World War II in England, at the Royal Aircraft Establishment in Farnborough, he began his teaching career at the Royal College of Aeronautics. Subsequently he moved to universities in Canada, Israel, and finally the United States. A joint appointment in mathematics and philosophy at UCLA led to a position at Yale University, where Robinson served as Sterling Professor of Mathematics until his untimely death at the age of fifty-five.

    Originally published in 1998.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6409-6
    Subjects: Mathematics

Table of Contents

    (pp. ix-xii)
    BENOIT B. MANDELBROT and Abraham Robinson

    Abraham Robinson’s life was extraordinary in many ways, if only because his professional work spanned three significant fields: airplane design, symbolic logic, and mathematical analysis. His untimely death was a blow to many people worldwide, and I was one of them; in fact, Robinson and I had hoped to work together on a presentation of fractals in terms of nonstandard analysis (unfortunately, he was on sabbatical when I spent a term at Yale in 1970). This direct personal link, in addition to both my friendship with Renée Robinson and being the Robinson Professor at Yale, made me treasure the invitation...

    (pp. xiii-2)
    Joseph W. Dauben
  3. CHAPTER ONE Family and Childhood: Germany 1918–1933
    (pp. 3-32)

    Abraham Robinson was born early in October 1918 in the small Silesian mining town of Waldenburg (Prussia), now Walbrzych in Poland. By the end of the year the First World War had been won by the Allies at a cost of eight-and-a-half million soldiers killed, another twenty-one million wounded, and an estimated seven-and-one-half million taken prisoner or otherwise missing in action. In the aftermath of the war a worldwide influenza epidemic claimed an additional twenty-two million lives. Oswald Spengler’sThe Decline of the West,which first appeared in 1918, must have struck contemporary readers as a grim prophecy that, if...

  4. CHAPTER TWO Life in Palestine: 1933–1939
    (pp. 33-58)

    Despite the euphoria the Robinsohns must have felt at having reached the promised land, it was clear from the beginning that life in Palestine would not be easy. From Haifa, where Lotte Robinsohn and her two sons had disembarked in early April 1933, the family moved to Tel Aviv, where they settled shortly after their arrival in Palestine.²

    Tel Aviv, in the 1930s, never failed to make an impression. Arthur Koestler, correspondent and author living in Palestine at the time, viewed it with a rather jaundiced eye:

    There was a main street named after Dr. Herzl with two rows of...

  5. CHAPTER THREE Robinson in Paris: January–June 1940
    (pp. 59-90)

    Hitler’s Armies invaded Poland on September 1, 1939, having annexed Austria and taken Slovakia the year before.² On September 3, to make good their treaty obligations with the Poles, England and France simultaneously declared war on Germany. But instead of war, only diplomatic skirmishes followed, and neither the English nor the French offered more than token opposition, thereby allowing the German army to occupy and subdue Poland. For the next six months, Europeans tried to persuade themselves that the world could live with totalitarian, expansionist Germany and still return to peace.

    Meanwhile thedrdle de guerre(or “phony war” as...

  6. CHAPTER FOUR Robinson and the War: London 1940–1946
    (pp. 91-130)

    In June of 1940, as France fell prey to the Germans and their Vichy collaborators, England braced herself for an invasion from across the channel. Britain, as Churchill said, was now alone. After the desperate yet heroic evacuation of troops from Dunkirk, the military at home was in disarray, “almost unarmed except for rifles.”² On July 19, bold from his victories in Western Europe, Hitler delivered a triumphant speech in the Reichstag. He was looking forward to the speedy collapse of Britain and the capitulation of the British. Throughout July, however, a steady stream of American armaments poured into England....

  7. CHAPTER FIVE Robinson after the War: London 1946–1951
    (pp. 131-184)

    Although the end of World War II did not immediately mean freedom for Abraham Robinson—at least not from his military service at the Royal Aircraft Establishment in Farnborough—he and Renée had survived the war happier than many. They were married, Renée had a well-paying, interesting position as a fashion designer, and Abby could finally think seriously again about the future. He looked forward to his release from government service, and longed to return to pure mathematics. But first there was a period of transition.

    When the facts and figures—and especially the photographs—of the devastation wrought upon...

  8. CHAPTER SIX The University of Toronto: 1951–1957
    (pp. 185-242)

    In moving from London to Toronto, Robinson did not miss a beat, mathematically. Sailing first class from Liverpool on a Cunard liner, theFranconia,the Robinsons headed for the New World in August of 1951. Although Renée was seasick most of the time, Abby worked at his usual steady pace, writing three pages a day.² By the time they reached North America in early September, he had finished a twenty-five-page manuscript.

    Robinson’s latest effort was designed to cast new light upon dimensional analysis:

    It is shown that the main proposition of dimensional analysis, the so-called “π-theorem,” can be deduced in...

  9. CHAPTER SEVEN The Hebrew University: Jerusalem 1957–1962
    (pp. 243-304)

    The Israel of 1957 was not the Palestine that Robinson had known as a boy in the 1930s. The crucial moment for Eretz-Israel had come in November of 1947, when the United Nations adopted its historic resolution in favor of establishing a Jewish State in Palestine. Only a few months later, on May 14, 1948, the British gave up control and withdrew from the country.²

    Meanwhile, without the British, full-scale conflict erupted between Jews and Arabs. The War of Independence that began on May 15 found the new country in a seemingly defenseless position, threatened by five hostile armies converging...

  10. CHAPTER EIGHT UCLA and Nonstandard Analysis: 1962–1967
    (pp. 305-402)

    The possibility of bringing Abraham Robinson to the Los Angeles campus of the University of California arose during the visit he made to southern California in the spring of 1961, when he was working briefly at Berkeley while on leave from the Hebrew University. Although he was invited by the Mathematics Department, the Philosophy Department was just then considering ways to replace Rudolf Carnap (who was about to retire), with the hope of luring Alfred Tarski from Berkeley. Robinson, having expressed his interest in UCLA, offered an attractive alternative, one that would also serve to continue the department's strong reputation...

  11. CHAPTER NINE Robinson Joins the Ivy League: Yale University 1967–1974
    (pp. 403-489)

    New Haven was a town “whose one distinction, apart from Yale, was its reputation as the birthplace of vulcanized rubber, sulfur matches and the hamburger.”² Yale, by contrast, was one of America's oldest and most outstanding universities, an oasis of learning. Architecturally, it reflected a mishmash of styles running from American colonial and collegiate gothic to sleek alabaster walls of the Beinecke Rare Book Library. The heart of the university was the historic old campus:

    The feel of that old part of the campus was Victorian. . . . Grand, dark brownstone dormitories surrounded it, elm trees shaded the grass,...

  12. EPILOGUE. Abraham Robinson: The Man and His Mathematics
    (pp. 491-494)

    Abraham Robinson published more articles during the seven years he was at Yale than he did during any other period of his career. Yale, of course, placed a premium on research, offered reduced teaching loads and attractive leaves for concentrated study and writing. This, coupled with the constant stimulation of the brightest graduate students, prominent colleagues, and the constant stream of visitors to a renowned academic center like New Haven, all help to account for this extraordinary burst of productivity.

    But there is another ingredient as well—Robinson had matured as a mathematician, and his efforts peaked during the time...