Leonard Eugene Dickson

Born: 22 Jan 1874 in Independence, Iowa, USA
Died: 17 Jan 1954 in Harlingen, Texas, USA

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L E Dickson is known for his contributions to number theory and group theory.
Dickson's family moved to Texas while he was a young child and he attended both primary and secondary school in his home town of Cleburne. He entered the University of Texas and quickly came under the influence of Halsted who encouraged him to study mathematics.

Dickson studied widely within mathematics but specialised in Halsted's own subjects of euclidean and non-euclidean geometry. Dickson received his B.S. in 1893 and his M.S. in 1894, again under Halsted's supervision.

Dickson applied for doctoral fellowships at both Harvard and Chicago. He accepted an offer from Harvard but, on receiving a later offer from Chicago, changed his mind. At Chicago he was supervised by Eliakim Moore, but others there influenced him, for example Bolza and Maschke. Dickson received a Ph.D. from the University of Chicago in 1896.

Dickson then spent some time with Lie at Leipzig and later with Jordan in Paris. On returning to the USA he became an instructor at the University of California in Berkeley.

He was appointed to the University of Texas at Austin in 1899. However Eliakim Moore and his colleagues in Chicago were keen that Dickson should return there and they offered him a permanent post on the faculty. He accepted immediately and served as professor at the University of Chicago from 1900 to 1939.

Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan. He proved many interesting results in number theory, using results of Vinogradov to deduce the ideal Waring theorem in his investigations of additive number theory.

In 1901 his famous book Linear groups with an exposition of the Galois field theory was published. This was a revised and expanded version of his 1896 doctoral thesis. In the proposal for his book, sent to Klein, Dickson wrote:-

The book here announced proposes to treat of linear congruence groups, or more generally, of linear groups in a Galois field, a subject enriched by the labors of Galois, Betti, Mathieu [Emile Mathieu], Jordan and many recent writers.
In his letter to Klein, Dickson also talks of introducing marked simplifications and presenting parts of the theory without the difficult calculations given in the published papers.

Parshall in [6] describing the book writes:-

Dickson presented a unified, complete, and general theory of the classical linear groups - not merely over the prime field GF(p) as Jordan had done - but over the general finite field GF(p^n), and he did this against the backdrop of a well- developed theory of these underlying fields. ... his book represented the first systematic treatment of finite fields in the mathematical literature.
Dickson published 17 books in addition to Linear groups with an exposition of the Galois field theory . The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today.

Dickson was awarded many honours. The American Association for the Advancement of Science decided to set up a prize for the most major contribution to the advancement of science. Dickson was the first recipient of the prize. He was also the first recipient of the Cole Prize for algebra awarded by the American Mathematical Society in 1928 for his book Algebren und ihre Zahlentheorie published in Zurich and Leipzig in 1927.

In fact Dickson was much involved with the American Mathematical Society, becoming its president in 1917-1918 and having earlier, in 1913, been its Colloquium Lecturer. Princeton and Harvard were among the universities that awarded him an honorary degrees.

References (7 books/articles)

References elsewhere in this archive:

L E Dickson was the President of the American Mathematical Society in 1917 - 1918. You can see a history of the AMS and a list of AMS presidents.
He was the American Mathematical Society Colloquium Lecturer in 1913. You can see a history of the AMS Colloquium and a list of the lecturers.
He was the Cole Prize winner in 1928. You can see a history of the AMS Cole Prize and a list of the winners.

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JOC/EFR October 1997