Artin (name)

Emil Artin (1898-1962) was a prominent mathematician of the 20th century, known for his significant contributions to abstract algebra, number theory, and algebraic topology.

Artin was born in Vienna, Austria (then Austria-Hungary). He studied at the University of Vienna and received his doctorate in 1921. He taught at the University of Hamburg from 1923 to 1937. Due to his wife's Jewish heritage, he faced increasing persecution under the Nazi regime and emigrated to the United States in 1937. He taught at Indiana University and later at Princeton University until his death.

Artin's work is characterized by its elegance, clarity, and insightful approach to fundamental mathematical concepts. Some of his key contributions include:

• Artin reciprocity law: A central result in algebraic number theory that describes the relationship between ideal class groups and Galois groups of abelian extensions of number fields.

• Artin's primitive root conjecture: A conjecture stating that for any integer a which is neither a perfect square nor -1, there are infinitely many primes p for which a is a primitive root modulo p. This conjecture remains unproven.

• Artin's representation theory: He developed important results in the representation theory of finite groups, including the Artin induction theorem.

• Artin-Wedderburn theorem: A fundamental theorem in ring theory that classifies semisimple rings.

• Algebraic theory of braids: Introduced the concept of the braid group and developed its algebraic theory.

Artin's influence extends beyond his specific mathematical results. His clear and rigorous approach to teaching and exposition has had a lasting impact on mathematics education. He is remembered as one of the great mathematicians of the 20th century.