Leonard E. Dickson

Leonard Eugene Dickson (born January 22, 1874 in Independence , Iowa , † January 17, 1954 in Harlingen , Texas ) was an American mathematician who mainly worked in the field of number theory and algebra .

life and work

Dickson grew up in Cleburne , Texas, where his father was a banker and merchant. He studied mathematics with William Halsted at the University of Texas at Austin , where he graduated in 1894 (MS). At first he worked like his teacher on geometry, but switched to group theory during his doctorate in 1896 at the University of Chicago (the first in mathematics at this university), where he studied with Heinrich Maschke , Oskar Bolza and Eliakim Hastings Moore . He then visited the leading European group theorists Sophus Lie in Leipzig and Camille Jordan in Paris. In 1899 he became a professor in Austin and from 1900, at Moore's effort, in Chicago, where he received a full professorship in 1910 and remained until his retirement in 1939, apart from several visiting professorships at the University of California, Berkeley .

In 1901 his dissertation resulted in a book on finite groups, in particular as matrix groups (general linear group) in finite fields of any prime number power characteristic ( Galois field ), in which he wrote many results by Camille Jordan, Émile Mathieu and others. a. continued and simplified.

He also made contributions to additive number theory, for example in the Waring problem (where an exact formula for g (k) follows from the work of him, SS Pillai and others). His History of the Theory of Numbers is considered a standard work, where many results of number theory can be traced back exactly in their history.

During his time in Chicago, the Scottish mathematician Wedderburn stayed , who proved that all finite division algebras are commutative. Here he worked closely with Dickson, who independently found evidence for this theorem. Dickson made the theory of algebras another focus of his work, and the book The Algebras and Their Number Theory greatly influenced the work of the algebraic school of Emmy Noether and Helmut Hasse in Germany, where important results were achieved in the 1920s and 1930s.

Dickson was the first to receive the Cole Prize for Algebra (1928 for his book Algebras and Their Number Theory ). He was instrumental in the rise of algebra in the USA and created a large school, but he also made high demands on his students. In 1920 he gave a plenary lecture at the International Congress of Mathematicians in Strasbourg ( Some Relations between the Theory of Numbers and Other Branches of Mathematics ) and also in Toronto in 1925 ( Outline of the theory to date of the arithmetics of algebras ). In 1913 he was elected to the National Academy of Sciences , 1915 to the American Academy of Arts and Sciences, and 1920 to the American Philosophical Society . He was also a corresponding member of the Académie des sciences in Paris.

He had been married since 1902 and had three children.

Dickson instructor

A Dickson instructor, or LE Dickson instructor, is a position at the University of Chicago for mathematicians who have recently completed, or are about to complete, a PhD in mathematics or a related subject. The appointment usually lasts for a few years and is associated with a teaching obligation.

literature

• Collected mathematical papers (Adrian Albert ed.), 6 vols., New York 1975–1983
• History of the theory of numbers , Washington DC: Carnegie Institution, 3 volumes, 1919, 1920, 1923, Reprint Dover, Volume 1 , Divisibility and Primality, Volume 2 , Diophantine Analysis, Volume 3 , Quadratic and Higher Forms.

• Linear groups with an exposition of Galois Field Theory , Teubner, Leipzig 1901
• with H. Blichfeldt , GA Miller : Theory and applications of finite groups , 1938
• Algebras and their number theory , (English Algebras and their arithmetics 1923, 1938) Zurich, Leipzig 1927
• Algebraic invariants , 1914
• Linear algebras , 1914
• Elementary theory of equations , New York 1914
• Modern algebraic theories , 1926
• Karen Parshall : A study in group theory: Leonard Eugene Dickson's Linear groups, Mathematical Intelligencer Vol. 13, 1991, pp. 7-11.
• dies .: In pursuit of the finite division algebra theorem and beyond: Joseph Wedderburn, Leonard Dickson and Oswald Veblen , Archiv Internat. History Sciences Vol. 33, 1983, pp. 274-299.
• Adrian Albert : Leonard Dickson , Bulletin American Mathematical Society 1955, p. 331
• Della Fenster: Leonard Dickson - an american legacy in mathematics , Mathematical Intelligencer Vol. 21, 1999, No. 4, p. 54
• Della Fenster: Why Dickson left quadratic reciprocity out of his history of the theory of numbers , American Mathematical Monthly, Vol. 106, 1999, pp. 618-627

Web links

• John J. O'Connor, Edmund F. Robertson :  Leonard E. Dickson. In: MacTutor History of Mathematics archive .
• Dickson: The known systems of simple groups and their inter-isomorphisms , ICM Paris 1900

Dickson's books Elementary Theory of Equations, Linear groups - with an exposure of Galois field theory, and Algebraic Invariants are online in the Historical Mathematics Monographs at Cornell University . Volume 1 of his "History of the theory of numbers" is available online in the California Digital Library of the University of California , as are the works "College algebra", "Elementary theory of equations", "First course in the theory of equations" and "Linear groups - with an exposure of Galois field theory".

Footnotes and sources

1. ↑ More precisely, elementary number theory, Diophantine equations, quadratic and higher-order forms. It was another band u. a. planned about reciprocity laws, but never appeared.
2. ↑ Division for denominators not equal to zero can be clearly carried out, free of zero dividers Examples of division algebras over the real numbers R are the complex numbers C (only commutative), the quaternions (associative) and the octonions (non-associative).
3. ↑ As Karen Parshall showed, Dickson was actually the first to prove this theorem, since Wedderburn's first proof was flawed and the later ones were based on Dickson's work.
4. ^ Member History: Leonard E. Dickson. American Philosophical Society, accessed July 15, 2018 .