Leonard Eugene Dickson

Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, History of the Theory of Numbers. The L. E. Dickson instructorships at the University of Chicago Department of Mathematics are named after him.

Life Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry.

Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago instead. In 1896, when he was only 22 years of age, he was awarded Chicago's first doctorate in mathematics, for a dissertation titled The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group, supervised by E. H. Moore.

Dickson then went to Leipzig and Paris to study under Sophus Lie and Camille Jordan, respectively. On returning to the US, he became an instructor at the University of California. In 1899 and at the extraordinarily young age of 25, Dickson was appointed associate professor at the University of Texas. Chicago countered by offering him a position in 1900, and he spent the balance of his career there. At Chicago, he supervised 53 Ph.D. theses; his most accomplished student was probably A. A. Albert. He was a visiting professor at the University of California in 1914, 1918, and 1922. In 1939, he returned to Texas to retire.

Dickson married Susan McLeod Davis in 1902; they had two children, Campbell and Eleanor.

Dickson was elected to the National Academy of Sciences in 1913, and was also a member of the American Philosophical Society, the American Academy of Arts and Sciences, the London Mathematical Society, the French Academy of Sciences and the Union of Czech Mathematicians and Physicists. Dickson was the first recipient of a prize created in 1924 by The American Association for the Advancement of Science, for his work on the arithmetics of algebras. Harvard (1936) and Princeton (1941) awarded him honorary doctorates.

Dickson presided over the American Mathematical Society in 1917–1918. His December 1918 presidential address, titled "Mathematics in War Perspective", criticized American mathematics for falling short of those of Britain, France, and Germany:

"Let it not again become possible that thousands of young men shall be so seriously handicapped in their Army and Navy work by lack of adequate preparation in mathematics."

In 1928, he was also the first recipient of the Cole Prize for algebra, awarded annually by the AMS, for his book Algebren und ihre Zahlentheorie.

It appears that Dickson was a hard man:

"A hard-bitten character, Dickson tended to speak his mind bluntly; he was always sparing in his praise for the work of others. ... he indulged his serious passions for bridge and billiards and reportedly did not like to lose at either game."

"He delivered terse and unpolished lectures and spoke sternly to his students. ... Given Dickson's intolerance for student weaknesses in mathematics, however, his comments could be harsh, even though not intended to be personal. He did not aim to make students feel good about themselves."

"Dickson had a sudden death trial for his prospective doctoral students: he assigned a preliminary problem which was shorter than a dissertation problem, and if the student could solve it in three months, Dickson would agree to oversee the graduate student's work. If not the student had to look elsewhere for an advisor."

Dickson's search for a counterexample to Wedderburn's theorem led him to investigate nonassociative algebras, and in a series of papers he found all possible three and four-dimensional (nonassociative) division algebras over a field.

In 1919 Dickson constructed Cayley numbers by a doubling process starting with quaternions . His method was extended to a doubling of to produce , and of to produce by A. A. Albert in 1922, and the procedure is known now as the Cayley–Dickson construction of composition algebras.

The number theorist Dickson proved many interesting results in number theory, using results of Vinogradov to deduce the ideal Waring theorem in his investigations of additive number theory. He proved the Waring's problem for under the further condition of

independently of Subbayya Sivasankaranarayana Pillai who proved it for ahead of him.

The three-volume History of the Theory of Numbers (1919–23) is still much consulted today, covering divisibility and primality, Diophantine analysis, and quadratic and higher forms. The work contains little interpretation and makes no attempt to contextualize the results being described, yet it contains essentially every significant number theoretic idea from the dawn of mathematics up to the 1920s except for quadratic reciprocity and higher reciprocity laws. A planned fourth volume on these topics was never written. A. A. Albert remarked that this three volume work "would be a life's work by itself for a more ordinary man."