Salomon Chaim Bochner papers

Salomon Chaim Bochner, a mathematician, historian, and teacher of international fame, was born on 20 August 1899 in the small town of Podgorzu, Austria-Hungary, now in Poland. His early schooling included grammar school and attendance at the Academia w Krakowie. Reputedly, he had already mastered the calculus by age 13, and completed his first original research in his fifteenth year. In 1915 he moved to Berlin to attend the Konigstadtisch Oberrealschule until he was conscripted into the Austro-Hungarian army in May 1917.

In the army Bochner received medical training at a military school near Vienna, and eventually obtained the rank of corporal in the medical corps. He was stationed at Feldpost # 3, a military hospital, until November of 1918. Soon thereafter he matriculated at the University of Berlin where he studied mathematics for three years. He received the D.Phil. on 8 April 1921, his examiners being Max Planck, Ehrhardt Schmidt, Issai Schur and Alois Riehl.

Directly after receiving his degree, Bochner was employed as a volunteer in the Cuten and Syman Banking House in Berlin, but left at the end of the year to "do other things." Exactly what he did for most of the next three years is unknown. In 1925, however, he was awarded an International Education Board Fellowship, which brought him to Copenhagen to study with Harald Bohr and to Oxford and Cambridge to work with G.H. Hardy and J.E. Littlewood. In 1927 Bochner accepted a position as a Lecturer in the Mathematics Department of the University of Munich. His colleagues there included several well-known mathematicians, among them C. Caratheodory, O. Perron, H. Tietre, and H. Hartogs.

Bochner made his debut as a young scholar in the 1920s in an incident involving the Danish mathematician, Harald Bohr, the brother of the well-known physicist, Niels Bohr. Inspired on the one hand by the analytic number theory of Bernhard Riemann and on the other by the celestial mechanics of Lagrange and the later astronomers, Bohl and Esclangon, Bohr had developed a general theory of a phenomenon which he named "almost periodicity" and which was described in brief announcements published in 1923. On reading such exciting news, Bochner lacked the patience to wait for the publication of the detailed proofs and simply worked it out himself. Upon learning of the young man's work a month later, Bohr invited Bochner to visit him in Copenhagen. They soon discovered that Bochner had achieved Bohr's result by means of a highly original and parallel approach, entirely different from that of Bohr. Moreover, the Bochner approach was the one that would stand the test of time, being the basis for future generalizations of Bohr's theory.

Notoriety at such an early age led Bochner onto his life-long study of harmonic analysis, starting in 1932 with the now classical treatise, "Lectures on the Fourier Integral." This work laid out the seeds of what was later to be called the theory of distributions and set forth his most famous theorem, actually known as the "Bochner Theorem." In the later development of abstract Fourier analysis, the Bochner theorem became the cornerstone of the theory of distributions.

As a Jew, Bochner evidently decided that the growing tide of Nazism in Germany left him with no other choice than to seek a new life elsewhere. Accordingly, after a six-month stay in Cambridge, England, he joined the Princeton University faculty in 1933, and served as an assistant, associate, and full professor of mathematics until 1968. During that period Bochner held other professional positions. He was a temporary member of the Institute for Advanced Study of Princeton University. He spent one year as a visiting professor at Harvard University and another at the University of California, Berkeley. He was a consultant at the Los Alamos Project and for the Air Research and Development Command. In 1968 Bochner retired from Princeton University and accepted Rice University's offer of the Edgar Odell Lovett Chair in Mathematics. He subsequently became the chairman of the Mathematics Department.

Although Bochner was most devoted to his work and study, he nonetheless led a very active personal life that involved much correspondence and travel. In November 1937 he married Naomi Weinberg of Brooklyn, New York. They went on a three-month honeymoon trip the following year to Holland, France, and Great Britain. One daughter, Deborah, was born to them. His father, Joseph Bochner, became ill in 1935 and died soon thereafter. Upon his father's death, his mother, Ruda Bochner, moved to London to live with his sister, Fannie Rabinowicz. He maintained close ties with his family throughout his life.

During those early years at Princeton, Bochner was extremely preoccupied with pure mathematical theory and proved to be a provocative and prolific writer. His research was original and pioneering. He was a forerunner in the theory of the so-called Schwartz distributions in that he introduced generalized Fourier transforms for functions that do not grow faster at infinity than a power of "x." Also, he was the first to introduce, in 1936, the much-studied process of spherical summability of multiple Fourier series; and by a nonobvious construction, he showed that Riemann's classical localization property in one dimension does not have the "expected" analog in two dimensions.

In the field of several complex variables, Bochner's achievements were very significant and spanned a broad horizon, especially in their interaction with other areas of mathematics. In 1938 he proved that the envelope of holomorphy of a tube is again a tube, the basis of the envelope tube being the convex closure of the basis of the original tube. In 1943 he used the "Bochner-Martinelli kernel" to prove Hartog's key theorem that, for a bounded domain with a connected boundary, a holomorphic function on the boundary has a continuation into the entire interior of the domain. The "Bochner-Montgomery Theorem," published in 1946, maintains that, on a compact complex manifold, the Lie group of holomorphic automorphism is a complex Lie group. Bochner created, for real and complex manifolds, the topic of "curvature and Betti numbers," a title under which he published a book with Kentaro Yano in 1953. Finally, the crowning honor in this field came in 1967 with the fifth printing of "Several Complex Variables," originally published in 1947.

In probability theory, Bochner constructed, analyzed, and introduced in 1946 the Fourier transform of a rather general type of stochastic process, randomizing not point functions, but additive set functions, and obtaining not only differential space but other homogeneous processes. In this area of study Bochner's "Harmonic Analysis and the Theory of Probability" became a standard work. Finally, a belated honor arrived in 1977, when it became generally known that Zorn's lemma of 1933 had been fully published and applied by Bochner in 1926.

In the period from 1950 to 1965, Bochner published at least eighty mathematical articles, most being elaborations of the enormous body of his earlier ideas. Afterwards, however, he turned almost exclusively to the history and philosophy of science. In his later years, Bochner wrote books and articles on the role of the concepts of space, infinity, real numbers, functions, and continuity in major junctures and upheavals in the rise of Western mathematics, such as the decline of Greek mathematics in its own phase, the sudden emergence of analysis in the late Renaissance, and a subtle but very tangible change of style in mathematics in the transition from the eighteenth to the nineteenth century. His "The Role of Mathematics in the Rise of Science," perhaps his most famous book, was published in 1966 and soon thereafter translated into many languages. Indeed, a very large proportion of the working papers in this collection deal with the history of science.

Salomon Bochner died in Houston, Texas on 2 May 1982, eleven years after the death of his beloved wife, Naomi. His life began at the turn of the century and his work influenced and sowed seeds of ideas in his students and colleagues that will continue to be important long after his death and beyond the turn of the next century.

Biological Chronology

• 1899: Born on 20 August in Podgorzu, Kracow, Austria-Hungary.
• 1906: Began Grammar School, Kracow.
• 1913: Graduated from Grammar School. Entered the Academia Handlowa w Krakowie, Kracow.
• 1914: Graduated from the Akademia Handlowa w Krakowie on 10 December.
• 1915: In February began to attend the Konigstadtische Oberrealschule in Berlin, Prussia.
• 1917: Left the Konigstadtisch Oberrealschule on 25 April. Entered the Austro-Hungarian army in May. On June 11 began to attend a school for medical training near Vienna, Austria-Hungary, eventually obtaining the rank of corporal in the medical corps.
• 1918: Left Feldpost # 3, a military hospital, on 14 March to travel to Berlin on a leave of absence valid until 12 October. Discharged honorably from the Austro-Hungarian army in November. Matriculated at the University of Berlin.
• 1921: Received D.Phil. degree from the University of Berlin on 8 April. Joined the German Mathematical Society.
• 1922: On April 1 began employment as a volunteer in the Cuten and Syman Banking House in Berlin. On 31 December left Cuten and Syman to do other things.
• 1925: Became International Education Board Fellow and studied with Harald Bohr in Copenhagen and with G.H. Hardy and J. E. Littlewood at Oxford and Cambridge.
• 1927: Accepted position as a Lecturer, University of Munich.
• 1933: Joined the American Mathematical Society. Became an Associate at Princeton University in October.
• 1934: Spent three months in Great Britain, from July to September, securing an immigration visa to the United States. Promoted to Assistant Professor, Princeton University.
• 1935: Visited Germany for two months, from July to September, to pay his respects to his father, who was incurably ill.
• 1936: Visited mother in Great Britain for three months, from July to September.
• 1937: Married Naomi Weinberg in November.
• 1938: Made three-month honeymoon trip in July to Holland, France, and Great Britain.
• 1939: Promoted to Associate Professor, Princeton University.
• 1945: Gained membership in the Institute for Advanced Study, Princeton University.
• 1946: Promoted to Professor, Princeton University. Served as a Visiting Lecturer, Harvard University.
• 1950: Elected to the National Academy of Sciences.
• 1951: Served as a Consultant, Los Alamos Project, Princeton University.
• 1952: Served as a Consultant for the Air Research and Development Command. Worked as a Visiting Professor, University of California, Berkeley.
• 1957: Elected Vice President of the American Mathematical Society.
• 1958: Chosen as a Delegate to the International Congress of Mathematicians.
• 1959: Awarded Henry Burchard Fine Chair of Mathematics, Princeton University.
• 1968: Retired from Princeton in June with the title of Professor Emeritus. In September accepted the Edgar Odell Lovett Chair in Mathematics, Rice University.
• 1969: Honored with Symposium in Honor of Salomon Bochner, Princeton University. Made Chairman of Mathematics Department of Rice University in May.
• 1971: Delivered the Keynote Speech, American Association for the Advancement of Science Symposium: The Role of Mathematics in the Development of Science. Naomi died of a ruptured esophagus in Santa Monica, California on 4 April.
• 1973: Served as an editor of the Dictionary of the History of Ideas.
• 1979: Awarded the Leroy P. Steele Prize of the American Mathematical Society on 25 January.
• 1982: Salomon Bochner died in Houston, Texas, on 2 May.