Mathematician:Emil Artin

Mathematician

Austrian-American mathematician mainly working in abstract algebra and topology.

Nationality

Austrian-American

History

• Born: 3 March 1898, Vienna, Austria
• Died: 20 Dec 1962, Hamburg, Germany

Theorems and Definitions

Theorems

• Artin Reciprocity Law
• Artin's Theorem on Alternative Algebras

• Artin-Rees Lemma (also known as Artin-Rees Theorem) (with David Rees)
• Artin-Schreier Theorem (with Otto Schreier)
• Artin-Wedderburn Theorem (with Joseph Wedderburn)
• Artin-Zorn Theorem (with Max August Zorn)

Definitions

• Artin Billiard
• Artin's Constant
• Artin Group
• Artinian Module
• Artinian Ring
• Local Artin Symbol

• Ankeny-Artin-Chowla Congruence (with Nesmith Cornett Ankeny and Sarvadaman Chowla)
• Artin-Hasse Exponential (with Helmut Hasse)
• Artin-Schreier Extension (with Otto Schreier)
• Artin-Schreier Polynomial (with Otto Schreier)
• Artin-Schreier Theory (with Otto Schreier)
• Fox-Artin Arc (with Ralph Hartzler Fox)

Conjectures

• Artin's Conjecture:
  • Artin's Conjecture on Primitive Roots
  • Artin Conjecture on L-Functions

Results named for Emil Artin can be found here.

Definitions of concepts named for Emil Artin can be found here.

Publications

• 1923: Über eine neue Art von L-Reihen
• 1924: Ein Mechanisches System mit Quasi-Ergodischen Bahnen
• 1927: Beweis des Allgemeinen Reziprozitätsgesetzes
• 1927: Über die Zerlegung definiter Funcktionen in Quadrate
• 1930: Idealklassen in Oberkörpern und allgemeines Reziprozitätsgesetzes
• 1942: Galois Theory (with Arthur N. Milgram)
• 1944: Galois Theory, 2nd ed. (with Arthur N. Milgram)
• 1947: The theory of braids
• 1948: Rings with Minimum Condition (with C.J. Nesbitt and R.M. Thrall)
• 1951: The class-number of real quadratic number fields (Bull. Amer. Math. Soc. Vol. 57: pp. 524 – 525) (with Nesmith Cornett Ankeny and Sarvadaman Chowla)
• 1953: Bourbaki: Éléments de mathématique (Review) (Bull. Amer. Math. Soc. Vol. 59: pp. 474 – 479)
• 1957: Geometric Algebra
• 1961: Class field theory (with John Torrence Tate)

Notable Quotes

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 all have experienced on some rare occasions the feeling of elation in realizing that we have enabled our listeners to see at a moment's glance the whole architecture and all its ramifications. How can this be achieved? Clinging stubbornly to the logical sequence inhibits visualization of the whole, and yet this logical structure must predominate or chaos would result.

-- 1953: Bourbaki: Éléments de mathématique (Review) (Bull. Amer. Math. Soc. Vol. 59: pp. 474 – 479)

-- Quoted in the foreword to 1971: Allan Clark: Elements of Abstract Algebra.

Sources

• John J. O'Connor and Edmund F. Robertson: "Emil Artin": MacTutor History of Mathematics archive

• 1971: Allan Clark: Elements of Abstract Algebra ... (next): Foreword