Background

Emil Artin was born on March 3, 1898 in Vienna, Austria and was the son of the art dealer Emil Artin and the opera singer Emma Laura-Artin. He grew up in Reichenberg, Bohemia (now Liberec, Czechoslovakia).

Education

Artin passed his school certificate examination in Reichenberg, Bohemia in 1916. After one semester at the University of Vienna he was called to military service. In January 1919 he resumed his studies at the University of Leipzig, where he worked primarily with Gustav Herglotz, and in June 1921 he was awarded the Ph.D. His thesis concerned applying the methods of the theory of quadratic number fields to quadratic extensions of a field of rational functions of one variable taken over a finite prime field of constants.

Career

After receiving his doctorate Emil Artin attended the University of Göttingen for one year (1921-22) and then went to the University of Hamburg, where he was appointed lecturer in 1923, extraordinary professor in 1925, and ordinary professor in 1926. He lectured on mathematics, mechanics, and the theory of relativity.

In 1937 he emigrated to the United States and taught at various universities there. He was at Notre Dame for the academic year 1937-38, he spent eight years at Bloomington at Indiana University from 1938 to 1946, and then he was twelve years at Princeton from 1946 to 1958. He returned to the University of Hamburg in 1958, and taught there until his death.

In 1921, in his thesis, Artin applied the arithmetical and analytical theory of quadratic number fields over the field of rational numbers to study the quadratic extensions of the field of rational functions of one variable over finite constant fields. For the zeta function of these fields he formulated the analogue of the Riemann hypothesis about the zeros of the classical zeta function. In 1934 Helmut Hasse proved this hypothesis of Artin’s for function fields of genus 1, and in 1948 André Weil proved the analogue of the Riemann hypothesis for the general case.

In 1923 Artin began the investigations that occupied him for the rest of his life. Artin assumed, and in 1923 proved for special cases, the identity of his L-series formed of simple character and the functions L (s, X) for Abelian groups, if at the same time X were regarded as a certain ideal class character. The proof of this assumption led him to the general law of reciprocity, a phrase he coined. Artin proved this in 1927, using a method developed by Nikolai Chebotaryov (1924). This law includes all previously known laws of reciprocity, going back to Gauss’s. It has become the main theorem of class field theory.

With the aid of the theorem, Artin traced Hilbert’s assumption, according to which each ideal of a field becomes a principal ideal of its absolute class field, to a theory on groups that had been proved in 1930 by Philip Furtwaengler.

In 1923 Artin derived a functional equation for his L-series that was completed in 1947 by Richard Brauer. Since then it has been found that the Artin L-series define functions that are meromorphic in the whole plane. Artin’s conjecture - that these are integral if X is not the main character still remains unproved.

Artin had a major role in the further development of the class field theory, and he stated his results in Class Field Theory, written with John T. Tate (1961).

In 1926 Artin achieved a major advance in abstract algebra (as it was then called) in collaboration with Otto Schreier. They succeeded in treating real algebra in an abstract manner by defining a field as real - today we say formal-real - if in it - 1 is not representable as a sum of square numbers. They defined a field as real-closed if the field itself was real but none of the algebraic extensions were. They then demonstrated that a real-closed field could be ordered in one exact manner and that in it typical laws of algebra, as it had been known until then, were valid.

With the help of the theory of formal-real fields, Artin in 1927 solved the Hilbert problem of definite functions. This problem, expressed by Hilbert in 1900 in his Paris lecture “Mathematical Problems,” is related to the solution of geometrical constructions with ruler and measuring standard, an instrument that permits the marking off of a single defined distance.

In his work on hypercomplex numbers in 1927, Artin expanded the theory of algebras of associative rings, established in 1908 by J. H. Maclagan Wedderburn, in which the double-chain law for right ideals is assumed; in 1944 he postulated rings with minimum conditions for right ideals (Artin rings). In 1927 he further presented a new foundation for, and extension of, the arithmetic of semisimple algebras over the field of rational numbers.

Artin’s scientific achievements are only partially set forth in his papers and textbooks and in the drafts of his lectures, which often contained new insights. They are also to be seen in his influence on many mathematicians of his period, especially his Ph.D. candidates (eleven in Hamburg, two in Bloomington, eighteen in Princeton). His assistance is acknowledged in several works of other mathematicians. His influence on the work of Nicholas Bourbaki is obvious.

He died on December 20, 1962 at the age of 64 in Hamburg, West Germany.

Achievements

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  Artin contributed to the study of nodes in three-dimensional space with his theory of braids in 1925. His definition of a braid as a tissue made up of fibers comes from topology, but the method of treatment belongs to group theory.
  
  Artin was honoured by the award of the American Mathematical Society's Cole Prize. Also, in 1932 he received the Alfred Ackermann–Teubner Memorial Award for the Promotion of Mathematical Sciences recognized work in mathematical analysis. In 1962, on the three-hundredth anniversary of the death of Blaise Pascal, the University of Clermont-Ferrand, France, conferred an honorary doctorate upon Artin.

Works

More photos

• book

  • The Gamma Function

    (This brief monograph on the gamma function was designed b...)

  • Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2)

    (In the nineteenth century, French mathematician Evariste ...)

  • Rings with Minimum Condition

    (Dealing with algebraic ring theory, this book was written...)

  • Geometric Algebra

    (This concise classic presents advanced undergraduates and...)

  • Algebraic Numbers and Algebraic Functions

    (Famous Norwegian mathematician Niels Henrik Abel advised ...)

  • A Freshman Honors Course in Calculus and Analytic Geometry

    (Emil Artin was on born March 3, 1898, in Vienna, Austria ...)

  • Elements of Algebraic Geometry

    (Excerpt from Elements of Algebraic Geometry Basis Conditi...)

  • Algebra with Galois Theory
  • A Freshman Honors Course In Calculus And Analytic Geometry Taught At Princeton University
  • Class Field Theory
  • Modern Higher Algebra: Galois Theory
  • The Collected Papers of Emil Artin
  • Collected Papers
  • Collected Papers
  • Algebra Geometrica
  • Theory of algebraic numbers: Notes by Gerhard Wurges from lectures held at the Mathematisches Institut, Gottingen, Germany

Views

All his life Emil would have a love of music which essentially equalled his love of mathematics.

Membership

Artin was a member of the American Mathematical Society.

Interests

• Artin`s avocations were astronomy and biology; he was also a connoisseur of old music and played the flute, the harpsichord, and the clavichord.

Connections

In 1929 Artin married Natalie Jasny. Eight years later they and their two children emigrated to the United States, where their third child was born. He was divorced in 1959.

Father:

Emil Artin

Mother:

Emma Laura-Artin

Wife:

Natalie Jasny

collaborator:

Otto Schreier

In 1926 Artin achieved a major advance in abstract algebra (as it was then called) in collaboration with Otto Schreier.

References

• Emil Artin and Helmut Hasse: The Correspondence 1923-1958 This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.
• Dictionary of Scientific Biography
• The Collected Papers of Emil Artin