Emil Artin (German: [ˈaɐ̯tiːn]; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was 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. He also contributed to the pure theories of rings, groups and fields.

Early life and education

Parents

Emil Artin was born in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin,^{[citation needed]} Austrian-born of mixed Austrian and Armenian descent. Several documents, including Emil's birth certificate,^{[citation needed]} list the father's occupation as “opera singer” though others list it as “art dealer.” It seems at least plausible that he and Emma had met as colleagues in the theater. They were married in St. Stephen's Parish on July 24, 1895.

Career

Professorship at Hamburg

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 the summer of 1925, Artin attended the Congress of the Wandervogel youth movement at Wilhelmshausen near Kassel with the intention of gathering a congenial group to undertake a trek through Iceland later that summer. Iceland (before the transforming presence of American and British forces stationed there during World War II) was still a primitive country in 1925, with a thinly scattered population and little transportation infrastructure. Artin succeeded in finding six young men to join him in this adventure. In the second half of August, 1925, the group set out by steamer from Hamburg, first to Norway, where they boarded a second steamer that took them to Iceland, stopping at several of the small east fjord ports before arriving at their destination, Húsavík in the north of the island. Here the Wandervogel group disembarked, their initial goal, trekking down the Laxá River to Lake Mývatn. They made a circuit of the large, irregular lake, staying in farm houses, barns, and occasionally a tent as they went. When they slept in barns, it was often on piles of wet straw or hay. On those lucky occasions when they slept in beds, it could be nearly as damp on account of the rain trickling through the sod roofs. The tent leaked as well.

Artin kept a meticulous journal of this trip, making daily entries in a neat, minuscule hand. He and several of the young men had brought cameras, so that the trek is documented also by nearly 200 small photographs.^[6] Artin's journal attests to his overarching interest in the geology of this mid-Atlantic island, situated over the boundary of two tectonic plates whose shifting relation makes it geologically hyperactive.

In keeping with the Wandervogel ethos, Artin and his companions carried music with them wherever they visited. The young men had packed guitars and violins, and Artin played the harmoniums common in the isolated farmsteads where they found lodging. The group regularly entertained their Icelandic hosts, not in full exchange for board and lodging, to be sure, but for goodwill certainly, and sometimes for a little extra on their plates, or a modestly discounted tariff.

From Lake Mývatn, Artin and his companions headed west towards Akureyri, passing the large waterfall Goðafoss on the way. From Akureyri, they trekked west down the Öxnadalur (Ox Valley) intending to rent pack horses and cross the high and barren interior by foot to Reykjavík. By the time they reached the lower end of Skagafjörður, however, they were persuaded by a local farmer from whom they had hoped to rent the horses that a cross-country trek was by then impracticable; with the approach of winter, highland routes were already snow-bound and impassable. Instead of turning south, then, they turned north to Siglufjörður, where they boarded another steamer that took them around the western peninsula and down the coast to Reykjavík. From Reykjavík, they returned via Norway to Hamburg. By Artin's calculation the distance they had covered on foot through Iceland totaled 450 kilometers.

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, his wife Natascha, and their two Hamburg-born children. 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. One of their shared interests was photography, and when Artin bought a Leica for their joint use (a Leica A, the first commercial model of this legendary camera), Natascha began chronicling the life of the family, as well as the city of Hamburg. For the next decade, she made a series of artful and expressive portraits of Artin that remain by far the best images of him taken at any age. Artin, in turn, took many fine and evocative portraits of Natascha. Lacking access to a professional darkroom, their films and prints had to be developed in a makeshift darkroom set up each time (and then dismantled again) in the small bathroom of whatever apartment they were occupying. The makeshift darkroom notwithstanding, the high artistic level of the resulting photographic prints is attested to by the exhibit of Natascha's photographs mounted in 2001 by the Museum für Kunst und Gewerbe Hamburg, and its accompanying catalogue, “Hamburg—Wie Ich Es Sah.”

In 1930, Artin was offered a professorship at ETH (Eidgenössische Technische Hochschule) in Zürich, to replace Hermann Weyl, who had moved to Göttingen. He chose to remain at Hamburg, however. Two years later, in 1932, for contributions leading to the advancement of mathematics, Artin was honored—jointly with Emmy Noether—with the Ackermann–Teubner Memorial Award, which carried a grant of 500 marks.

Influence and work

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. He also developed the theory of braids^[9] as a branch of algebraic topology.

In 1955 Artin was teaching foundations of geometry at New York University. He used his notes to publish Geometric Algebra in 1957, where he extended the material to include symplectic geometry.

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.

Conjectures

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.

Supervision of research

Artin advised over thirty doctoral students, including Bernard Dwork, Serge Lang, K. G. Ramanathan, John Tate, Harold N. Shapiro, Hans Zassenhaus and Max Zorn. A more complete list of his students can be found at the Mathematics Genealogy Project website (see "External Links," below).