Alfred Theodor Brauer

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Alfred Theodor Brauer

Alfred Theodor Brauer (born April 9, 1894 in Charlottenburg , † December 23, 1985 in Chapel Hill , North Carolina ) was a German-American mathematician of Jewish origin. By participating in the war in World War I initially damaged, he succeeded only in the year 1928 , with a doctorate summa cum laude complete. Because of his problems, he founded the mathematical-physical study group with other war participants from his institute to enable new students to study more easily. In teaching and research, he was primarily concerned with number theory and classical algebra in relation to the theory of matrices, initially in Germany and since the late 1930s - when emigration was inevitable for survival as a Jew - in the United States. Already during his time as assistant to Issai Schur in Germany, but also in the further course in the United States, he always tried to have a presentable library for his institute. The recognition of his performance becomes clear in his appreciation.

Life

youth

Brauer was born into a Jewish family as the son of the wholesale merchant and trade judge Max Brauer and his wife Lilly Brauer. He was the eldest of three siblings, including Richard Dagobert Brauer - his better-known younger brother.

At Easter 1912 he passed the final examination at the Kaiser Friedrich School in Charlottenburg. After a year of practical work in a commercial position, he decided to study mathematics, physics and philosophy.

Studies and time as a soldier

He began his studies in Heidelberg in the summer semester of 1913 and studied the next two semesters in Berlin . At the outbreak of the First World War, Alfred Brauer - like many Germans with a national sentiment - volunteered. He was assigned to machine gun companies and spent four years in the theaters of war in the West, East and the Balkans. When he attacked Stojnik in Serbia, he suffered an injury and was awarded the Iron Cross, second class. At the end of the war he was a sergeant in platoon leader position.

Alfred Brauer returned from captivity in 1919 and, depressed by the defeat and severely handicapped by health problems resulting from the fighting, resumed his studies in Berlin. He completed his studies in February 1928 with a doctorate. phil. summa cum laude from Issai Schur and Erhard Schmidt on the topic of Diophantine equations with a finite number of solutions . His brother, born in 1901, who could begin his studies unhindered in 1919, also completed his studies summa cum laude with a doctorate in July 1925. Both brothers were excellent students of Issai Schur.

In 1928 he became an assistant at Schur and mainly supported him in his lectures and seminars. Furthermore, he was responsible for the maintenance and expansion of the library in the Mathematical Institute (at that time still Mathematical Seminar). When Hans Rohrbach was employed by Erhard Schmidt in 1929, a friendship developed between him and Brauer.

National Socialism

Alfred Brauer completed his habilitation in 1932 and then worked as a private lecturer. From 1933 he had to suffer increasing anti-Semitic reprisals. As a participant in the war, like Issai Schur , he was initially allowed to continue teaching. However, National Socialist students - mostly non-faculty - interfered with his lectures again and again. In 1935, the Nuremberg Laws made it impossible to continue teaching . Finally, in 1938, he completely lost the right to publish in German mathematical journals.

Despite the circumstances of the time, Brauer married Hilde Wolf from Stadthagen in 1934 as he was the child of a wholesale merchant. Since Brauer was still in office at the time, they found an apartment in Charlottenburg. However, the Nuremberg Laws made it impossible for him and his wife to continue living in Germany in 1935. However, he was reluctant to emigrate for a long time because he saw himself as a German and Germany was his home. He even turned down an invitation from Hermann Weyl to the USA on behalf of threatened Jewish German scientists. In the summer of 1939 - only two and a half months before the outbreak of war - Hans Rohrbach succeeded in persuading Alfred Brauer to emigrate.

His mother died in 1943, badly battered, but still in her apartment. Sister and brother-in-law attended the funeral, but were soon deported to an extermination camp. Your children were already safe abroad.

emigration

On arrival in New York, his family first met Paul Erdős and other family members. From there it went straight to Princeton in New Jersey , where Brauer got an assistant position to Hermann Weyl, like his brother had held in 1934/35.

His brother Richard, who had taught in Königsberg until the spring of 1933, had to go abroad when the National Socialists came to power because he had not served in World War I like his brother Alfred. He was gratefully received in the United States. Richard initially went to Lexington , Kentucky for a year . After this engagement he became assistant to Hermann Weyl, with whom he published in 1935 in the American Journal of Mathematics . In the fall of 1935 he got his first permanent position as an assistant professor at the University of Toronto . From then on, he stayed in the USA, teaching and researching at various universities, most recently until his retirement from Harvard University .

In addition to his brother, John von Neumann and Oswald Veblen supported him in his search for a job. So he was quickly integrated economically and socially into the United States; Nevertheless, it was difficult for him to settle in a foreign country - the language of which was largely unknown to him. The fate of the Jews in Germany also hit him hard, so that he never wanted to return to his homeland, especially since all attempts to bring his sister and brother-in-law to America, who had been deported towards the end of the war, failed.

From 1939, Brauer published again: in English in American mathematical journals. His assistantship lasted until 1942, where he had been a lecturer at New York University since 1940. During this time he built a considerable library at Princeton.

In 1942 a decision was made that had a major impact on his life. He received a call to the University of North Carolina at Chapel Hill, initially as an instructor. In the same year he became an assistant professor and a year later an associate professor . He held this position from 1943 to 1947. In 1944 he and his wife received naturalization , citizenship of the United States. They had their second child Carolyn in 1945.

Brauer's helpful manner and ability was praised in the commemorative speech given by Hans Rohrbach, on the occasion of his appointment as a member of the North Carolina Academy of Science in 1946. In 1947 he was appointed Full Professor of Mathematics . In this position he taught and researched until 1959. Then he was awarded the Kenan Professorship , another award that should show the honor by the University of North Carolina. He took this position until his retirement , but then remained Kenan Professor emeritus .

Alfred Theodor Brauer died on December 23, 1985 in Chapel Hill, North Carolina, USA, at the age of 91.

return

It was not until December 1960 that Alfred and Hilde Brauer returned to Germany to take part in the 150th anniversary of the University of Berlin, where Alfred Brauer gave a lecture on the work of Issai Schur. He was later honored for this excellent presentation.

plant

Alfred Brauer's scientific interest extended to classical algebra and number theory. Under the guidance of his teacher Issai Schur, Alfred, like his brother, excelled in this area. Through specialization, Alfred turned mainly to matrix theory. He received the first impetus for research in this area by holding a corresponding lecture.

Number theory

In number theory, Brauer was primarily concerned with questions of a multiplicative nature.

Among other things, works of this appeared because of their great importance in the meeting reports of the Prussian Academy of Sciences . Then it was questions of additive number theory that he turned to

Classical algebra

Here he worked

  • about the position of zeros of certain polynomials
  • about the irreducibility of certain polynomials
  • Investigation of irreducibility criteria by George Polya and Issai Schur together with Richard Brauer

His main interest, however, was the investigation of the properties of characteristic roots of matrices, their position, their limits, their calculation, their distance, etc. a. It is to him that we owe the discovery of the Cassini ovals , which contain eigenvalues. Furthermore, statements about eigenvectors result. It is also worth mentioning the merit of having published the collected essays on Issai Schur.

Mathematical-physical study group

Alfred Brauer took care of his fellow students who, like him, returned from captivity. With other war participants in the fields of mathematics and physics, he founded the Mathematical-Physical Working Group , or MAPHA for short, in 1919.

He wanted to help students with the initial difficulties of their studies. This included, among other things

  • Advice to freshmen about the subjects to be taken during the course
  • Working circles for basic lectures, led by older students, in which questions about the lecture material were discussed
  • Arranging textbooks at preferential prices, as well as loans and financial aid
  • Establishing social contacts through house concerts, excursions, hikes, Christmas parties, etc. a.

Although certainly a spiritus rector , Alfred Brauer left the management to the non-Jewish students and always kept himself in the background. The organization was banned in 1933.

Visiting professorships

His reputation as a talented university lecturer went far beyond his home university. He was offered presentations at specialist conferences. He taught at the University of Colorado in Colorado Springs in 1962, and in 1967 in the summer school. The same position, but as a permanent visiting professor , he received following his teaching activity in Chapel Hill for the academic years from 1965 to 1975 at Wake Forest University in Winston-Salem .

student

20 students of Brauer's are known. The most important of these are

Appreciation

Awards

Alfred T. Brauer Library

It goes without saying that Brauer devoted himself intensively to the library of the mathematics department of his university. He devoted an immeasurable amount of time and effort to expanding it. The result is one of the most beautiful and comprehensive libraries that there are at universities. It was named in his honor of the Alfred T. Brauer Library , which, in addition to complete mathematics, also includes theoretical physics, statistics and computer science.

In the same way, he also expanded the library in the Department of Mathematics at Wake Forest University in Winston-Salem, which honored him with the establishment of an Alfred T. Brauer Instructorship in 1976.

Alfred T. Brauer Gift Trust Fund

At the age of 90 in 1984, the Mathematics Department of the University of North Carolina established the Alfred T. Brauer Gift Trust Fund . This fund includes an Alfred T. Brauer Prize to be awarded annually to an outstanding younger student in the fields of number theory and algebra - the two areas in which Brauer has excelled.

Alfred T. Brauer Lectures

The Alfred T. Brauer Lectures were also set up for Brauer's 90th birthday. For this purpose, an excellent mathematician is to be invited every year to commemorate Brauer's teaching and research in two lectures.

At the first of these events in April 1985 (Brewer's month of birth), to which Daniel Gorenstein from Rutgers University in New Brunswick was invited, Alfred Brauer himself was able to be present.

obituary

Hans Rohrbach, a long-time good acquaintance and friend, wrote the following words in memory of Alfred Brauer:

Alfred Theodor Brauer died on December 23, 1985 in Chapel Hill, North Carolina, USA, at the age of 91. He was not only a great mathematician, who was greatly valued and revered as a researcher and teacher wherever he worked. He was also a person with a special stamp: of selfless modesty and sincere generosity, of deepest sense of family and deepest affection for friends. In short, he had an aura that captured everyone who met him. In the scientific field, it was his seldom deep love for mathematics - as a science, as a subject, as art - that took everyone, whether colleagues or students, into his great enthusiasm. "

- Annual German. Math Association. 90 (3) (1988), pp. 145-154.

Fonts (selection)

A complete listing of Brauer's writings can be found at the end of Hans Rohrbach's memorial.

  • About some special Diophantine equations. In: Math. Z. 25 (1926) pp. 499-504.
  • About the irreducibility of some special classes of polynomials. In: Jahresber. d. German Math Association. 35 (1926) pp. 99-112. (with R. Brauer and H. Hopf)
  • Via sequences of potency residues. In: Sitz.Ber. Prussia. Akad. Wiss. Phys.-math. Class. 1928, pp. 9-16.
  • On the extension of Fermat's little theorem. In: Math. Z. 42 (1937) pp. 255-262.

literature

  • A. Brauer: Commemorative speech for Issai Schur. Collected treatises, Berlin 1973.
  • RH Hudson, TL Markham: Alfred T Brauer as a mathematician and teacher. In: Linear Algebra. Appl. 59: 1-17 (1984).
  • H. Rohrbach: Alfred Brauer in memory. In: Jahresber. German. Math Association. 90 (3) (1988), pp. 145-154.

Web links

Individual evidence

  1. a b s. Annual report of the DMV Volume 90 Issue 3 Page 145
  2. a b s. Annual report of the DMV. Volume 90 Issue 3 p. 148.
  3. s. Annual report of the DMV Volume 90 Issue 3 p. 146.
  4. ^ Annual report of the DMV. Volume 90, Issue 3, pp. 151-154.