Co-founder of modern abstract algebra
Emil Artin 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.
Along with Emmy Noether, he is considered the founder of modern abstract algebra.
He is Michael Artin‘s father.
University education
In October 1916, Artin matriculated at the University of Vienna, having focused by now on mathematics. He also took courses in astrophysics and Latin.
Studies at Vienna were interrupted when Artin was drafted in June 1918 into the Austrian army (his Army photo ID is dated July 1, 1918). He was stationed northwest of Venice at Primolano, on the Italian front in the foothills of the Dolomites. To his great relief, Artin managed to avoid combat by volunteering for service as a translator—his ignorance of Italian notwithstanding. He did know French, of course, and some Latin, was generally a quick study, and was motivated by a highly rational fear in a theater of that war that had often proven a meat-grinder.
Artin survived both war and vermin on the Italian front, and returned late in 1918 to the University of Vienna, where he remained through Easter of the following year.
By June 1919, he had moved to Leipzig and matriculated at the university there as a « Class 2 Auditor ». Late the same year, Artin undertook the formality of standing for a qualifying examination by an academic board of the Oberrealschule in Leipzig, which he passed with the grade of « gut » (good), receiving for the second time the Reifezeugnis (diploma attesting the equivalence of satisfactory completion of 6 years at a Realschule). How this Leipzig Reifezeugnis differed technically from the one he had been granted at Reichenberg is unclear from the document, but it apparently qualified him for regular matriculation as a student at the university, which normally required the Abitur.
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.
In the fall of 1921, Artin moved to the University of 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.
Aside from consistently good school grades in singing, the first documentary evidence of Artin’s deep and lifelong engagement with music comes from the year in Göttingen, where he was regularly invited to join in the chamber music sessions hosted by Richard Courant. He played all the keyboard instruments, and was an especially accomplished flautist, although it is not known exactly by what instruction he had achieved proficiency on these instruments. He became especially devoted to the music of Johann Sebastian Bach.
Career
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. In this year also, Artin applied for and was granted German citizenship. He was promoted to full 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.
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.
On July 15, 1937 because of his wife Natascha’s status as « Mischling ersten Grades » (half Jewish) 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 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.
By July, when he was summarily « retired », the position at Stanford University had been filled. However, through the efforts of Richard Courant (by then at New York University), and Solomon Lefschetz at Princeton University, a position was found for him at the University of Notre Dame 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.
After moving to Bloomington, Artin quickly acquired a piano, and soon after that a Hammond Organ, a recently invented electronic instrument that simulated the sound of a pipe organ. He wanted this instrument in order primarily to play the works of J. S. Bach, and because the pedal set that came with the production model had a range of only two octaves (not quite wide enough for all the Bach pieces), he set about extending its range.
As German citizens, Artin and Natascha were technically classified as enemy aliens for the duration of the war. On April 12, 1945, with the end of the war in Europe only weeks away, they applied for naturalization as American citizens. American citizenship was granted them on February 7, 1946.
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, Natascha made the mistake of reminding him of this vow, and in lieu of a champagne toast, he indulged in what was intended to be the smoking of a single, celebratory cigarette. Unfortunately, the single cigarette led to a second, and another after that. Artin returned to heavy smoking for the rest of his life.
Artin and his family moved to princeton in the fall of 1946.
During the Princeton years, Artin built a 6-inch (15 cm) reflecting telescope to plans he found in the magazine Sky and Telescope, which he subscribed to. He spent weeks in the basement attempting to grind the mirror to specifications, without success, and his continued failure to get it right led to increasing frustration. Then, in California to give a talk, he made a side trip to the Mt. Wilson Observatory, where he discussed his project with the astronomers. Whether it was their technical advice, or Natascha’s intuitive suggestion that it might be too cold in the basement, and that he should try the procedure upstairs in the warmth of his study (which he did), he completed the grinding of the mirror in a matter of days. With this telescope, he surveyed the night skies over Princeton.
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.
The following year, Artin took a leave of absence to return to Germany for the first time since emigration, nearly twenty years earlier. He spent the fall semester at Göttingen, and the next at Hamburg. For the Christmas holidays, he travelled to his birthplace, Vienna, to visit his mother, Vienna being a city he had not seen in decades.
Artin’s marriage to Natascha had by this time seriously frayed. Though nominally still husband and wife, resident in the same house, they were for all intents and purposes living separate lives. Artin was offered a professorship at Hamburg, and at the conclusion of Princeton’s spring semester, 1958, he moved permanently to Germany. His decision to leave Princeton University and the United States was complicated, based on multiple factors, prominent among them Princeton’s (then operative) mandatory retirement age of 65. Artin had no wish to retire from teaching and direct involvement with students. Hamburg’s offer was open-ended.
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.
The University of Hamburg honored his memory on April 26, 2005, by naming one of its newly renovated lecture halls The Emil Artin Lecture Hall.
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 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.
