Emil Artin (nonfiction)

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Emil Artin.

Emil Artin (German: [ˈaɐ̯tiːn]; March 3, 1898 – December 20, 1962) was an Austrian mathematician. One of the leading mathematicians of the twentieth century, he is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. Artin also contributed to the pure theories of rings, groups and fields.

As a boy, Artin formed a lifelong friendship with a young neighbor, Arthur Baer, who became an astronomer, teaching for many years at Cambridge University. Astronomy was an interest the two boys shared already at this time. They each had telescopes. They also rigged a telegraph between their houses, over which once Baer excitedly reported to his friend an astronomical discovery he thought he had made—perhaps a supernova, he thought—and told Artin where in the sky to look. Artin tapped back the terse reply “A-N-D-R-O-M-E-D-A N-E-B-E-L” (Andromeda nebula).

By June 1919, he had moved to Leipzig and matriculated at the University there as a "Class 2 Auditor" ("Hörer zweiter Ordnung").

From 1919 to June 1921, Artin pursued mostly mathematical studies at Leipzig. His principal teacher and dissertation advisor was Gustav Herglotz. Additionally, Artin took courses in chemistry and various fields of physics, including mechanics, atomic theory, quantum theory, Maxwellian theory, radioactivity, and astrophysics. In June, 1921 he was awarded the Doctor of Philosophy degree, based on his “excellent” dissertation, “Quadratische Körper im Gebiete der höheren Kongruenzen“ ("On the Arithmetic of Quadratic Function Fields over Finite Fields"), and the oral examination which—his diploma affirms—he had passed three days earlier “with extraordinary success.”

In the fall of 1921, Artin moved to Göttingen, considered the "Mecca" of mathematics at the time, where he pursued one year of post-doctoral studies in mathematics and mathematical physics with Richard Courant and David Hilbert. While at Göttingen, he worked closely with Emmy Noether and Helmut Hasse.

Courant arranged for Artin to receive a stipend for the summer of 1922 in Göttingen, which occasioned his declining a position offered him at the University of Kiel. The following October, however, he accepted an equivalent position at Hamburg, where in 1923, he completed the Habilitation thesis (required of aspirants to a professorship in Germany), and on July 24 advanced to the rank of Privatdozent.

On April 1, 1925, Artin was promoted to Associate Professor (außerordentlicher Professor). In this year also, Artin applied for and was granted German citizenship. He was promoted to full Professor (ordentlicher Professor) on October 15, 1926.

Early in 1926, the University of Münster offered Artin a professorial position; however, Hamburg matched the offer financially, and (as noted above) promoted him to full professor, making him (along with his young colleague Helmut Hasse) one of the two youngest professors of mathematics in Germany.

It was in this period that he acquired his lifelong nickname, “Ma,” short for mathematics, which he came to prefer to his given name, and which virtually everyone who knew him well used. Although the nickname might seem to imply a narrow intellectual focus, quite the reverse was true of Artin. Even his teaching at the University of Hamburg went beyond the strict boundaries of mathematics to include mechanics and relativity theory. He kept up on a serious level with advances in astronomy, chemistry and biology (he owned and used a fine microscope), and the circle of his friends in Hamburg attests to the catholicity of his interests. It included the painter Heinrich Stegemann, and the author and organ-builder Hans Henny Jahn. Stegemann was a particularly close friend, and made portraits of Artin, Natascha and the two children born in Hamburg. Music continued to play a central role in his life; he acquired a Neupert double manual harpsichord, and a clavichord made by the Hamburg builder Walter Ebeloe, as well as a silver flute made in Hamburg by G. Urban. Chamber music gatherings became a regular event at the Artin apartment as they had been at the Courants in Göttingen.

On August 15, 1929, Artin married Natalia Naumovna Jasny (Natascha), a young Russian émigré who had been a student in several of his classes.

In January 1933, Natascha gave birth to their first child, Karin. A year and a half later, in the summer of 1934, son Michael was born. The political climate at Hamburg was not so poisonous as that at Göttingen, where by 1935 the mathematics department had been purged of Jewish and dissident professors. Still, Artin's situation became increasingly precarious, not only because Natascha was half Jewish, but also because Artin made no secret of his distaste for the Hitler regime. At one point, Wilhelm Blaschke, by then a Nazi Party member, but nonetheless solicitous of the Artins’ well-being, warned Artin discreetly to close his classroom door so his frankly anti-Nazi comments could not be heard by passersby in the hallway.

On July 15, 1937, because of Natascha’s status as “Mischling ersten Grades,” Artin had lost his post at the University—technically, compelled into early retirement—on the grounds of paragraph 6 of the Act to Restore the Professional Civil Service (Gesetz zur Wiederherstellung des Berufsbeamtentums) of April 7, 1933. Ironically, he had applied only some months earlier, on February 8, 1937, for a leave of absence from the University in order to accept a position offered him at Stanford. On March 15, 1937, the response had come back denying his application for leave on the grounds that his services to the University were indispensable (“Da die Tätigkeit des Professors Dr. Artin an der Universität Hamburg nicht entbehrt werden kann. . .”).

By July, when he was summarily “retired,” (“in Ruhestand versetzt”) the position at Stanford had been filled. However, through the efforts of Richard Courant (by then in New York), and Solomon Lefschetz at Princeton, a position was found for him at Notre Dame University in South Bend, Indiana.

It was early November, 1937 by the time they arrived in South Bend, where Artin joined the faculty at Notre Dame, and taught for the rest of that academic year. He was offered a permanent position the following year 170 miles to the south at Indiana University, in Bloomington. Shortly after the family resettled there, a second son, Thomas, was born on November 12, 1938.

On the orders of a Hamburg doctor whom he had consulted about a chronic cough, Artin had given up smoking years before. He had vowed not to smoke so long as Adolf Hitler remained in power. On May 8, 1945, at the news of Germany’s surrender and the fall of the Third Reich, in lieu of a champagne toast, Artin indulged in what was intended to be the smoking of a single, celebratory cigarette. He returned to heavy smoking for the rest of his life.

If Göttingen had been the “Mecca” of mathematics in the 1920s and early ‘30s, Princeton, following the decimation of German mathematics under the Nazis, had become the center of the mathematical world in the 1940s.

Whenever he was asked whether mathematics was a science, Artin would reply unhesitatingly, “No. An art.” His elegant elaboration of this idea is often cited, and worth repeating here: “We all believe that mathematics is an art. The author of a book, the lecturer in a classroom tries to convey the structural beauty of mathematics to his readers, to his listeners. In this attempt, he must always fail. Mathematics is logical to be sure, each conclusion is drawn from previously derived statements. Yet the whole of it, the real piece of art, is not linear; worse than that, its perception should be instantaneous. We have all experienced on some rare occasion the feeling of elation in realizing that we have enabled our listeners to see at a glance the whole architecture and all its ramifications.”

In September 1955, Artin accepted an invitation to visit Japan. From his letters, it is clear he was treated like royalty by the Japanese mathematical community, and was charmed by the country. He was interested in learning about the diverse threads of Buddhism, and visiting its holy sites.

By 1958 Artin's marriage to Natascha had seriously deteriorated. Artin was offered a professorship at Hamburg, and at the conclusion of Princeton's spring semester, 1958, he moved permanently to Germany. Artin and Natascha were divorced in 1959.

In Hamburg, Artin had taken an apartment, but soon gave it over to his mother whom he had brought from Vienna to live near him in Hamburg. He in turn moved into the apartment of the mathematician Hel Braun in the same neighborhood; though they never married, their relationship was equivalent to marriage. On January 4, 1961, he was granted German citizenship. In June, 1962, on the occasion of the 300th anniversary of the death of Blaise Pascal, the University of Clermont-Ferrand conferred an honorary doctorate on him. On December 20 of the same year, Artin died at home in Hamburg, aged 64, of a heart attack.

Artin was one of the leading algebraists of the century, with an influence larger than might be guessed from the one volume of his Collected Papers edited by Serge Lang and John Tate. He worked in algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as well as those of Emmy Noether. Artin solved Hilbert's seventeenth problem in 1927.

Artin was also an important expositor of Galois theory, and of the group cohomology approach to class ring theory (with John Tate), to mention two theories where his formulations became standard. In 1957, Artin wrote a book on geometric algebra, an insightful development of the classical groups in a Kleinian context. He also developed the theory of braids[11] as a branch of algebraic topology.

He left two conjectures, both known as Artin's conjecture. The first concerns Artin L-functions for a linear representation of a Galois group; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies. These are unproven; in 1967, Hooley published a conditional proof for the second conjecture, assuming certain cases of the Generalized Riemann hypothesis.

Artin advised over thirty doctoral students, including Bernard Dwork, Serge Lang, K. G. Ramanathan, John Tate, Harold N. Shapiro, Hans Zassenhaus, and Max Zorn.

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