# Leonard Eugene Dickson

**Leonard Eugene Dickson**(22 January 1874 ,Independence, Iowa –17 January 1954 ,Harlingen, Texas ) (often called**L. E. Dickson**) was an Americanmathematician . He was one of the first American researchers inabstract algebra , in particular the theory of finite fields andclassical group s, and is also remembered for a three-volume history ofnumber theory .**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 , whereGeorge 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 andHarvard 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 byE. H. Moore .Dickson then went to

Leipzig andParis to study underSophus Lie andCamille Jordan , respectively. On returning to the USA, he became an instructor at theUniversity 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 probablyA. A. Albert . He was a visiting professor at theUniversity 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.

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 , theLondon Mathematical Society , theFrench 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." (Parshall 1999)

:"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." (Fenster 1997)

:"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." (Fenster 1997)

**Work**Dickson had a major impact on American mathematics, especially

abstract algebra . His enormous mathematical output consists of 18 books and more than 250 papers. The "Collected Mathematical Papers of Leonard Eugene Dickson" fill six large volumes.**The algebraist**In 1901, Dickson published his first book "Linear groups with an exposition of the Galois field theory", a revision and expansion of his Ph.D. thesis. Teubner in Leipzig published the book, as there was no well-established American scientific publisher at the time. Dickson had already published 43 research papers in the preceding five years; all but seven on

finite linear group s. Parshall (1991) described the book as follows::"Dickson presented a unified, complete, and general theory of the

classical linear group s—not merely over theprime field GF("p") as Jordan had done—but over the generalfinite 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 offinite field s in the mathematical literature."An appendix in this book lists the non-abelian simple groups then known having order less than 1 billion. He listed 53 of the 56 having order less than 1 million. The remaining 3 were found in 1960, 1965, and 1967.

Dickson worked on

finite field s and extended the theory oflinear associative algebra s initiated byJoseph Wedderburn andCartan .In 1905,

Joseph Wedderburn , then at Chicago on a Carnegie Fellowship, published a paper that included three claimed proofs of a theorem stating that all finitedivision algebra s werecommutative . The proofs all made clever use of the interplay between theadditive group of a finitedivision algebra "A", and themultiplicative group "A"* = "A" − {0}. Parshall (1983) notes that the first of these three proofs had a gap not noticed at the time. Dickson also found a proof of this result but, believing Wedderburn's first proof to be correct, Dickson acknowledged Wedderburn's priority. But Dickson also noted that Wedderburn constructed his second and third proofs only after having seen Dickson's proof. Parshall concludes that Dickson should be credited with the first correct proof.Dickson's search for a counterexample to Wedderburn's theorem led him to investigate

nonassociative algebra s, and in a series of papers he found all possible three and four-dimensional (nonassociative)division algebra s over a field.**The number theorist**Dickson proved many interesting results in

number theory , using results ofVinogradov to deduce the ideal Waring theorem in his investigations ofadditive number theory .The 3-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. A planned fourth volume 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."**ee also***

Dickson's lemma

*Dickson invariant .

*Dickson polynomial **Bibliography**Primary:

*1901. "Linear Groups With an Exposition of the Galois Field Theory"

*1914. "Linear Algebras"

*1914. "Algebraic Invariants"

*1914. "Elementary Theory of Equations"

*1919-23. "History of the Theory of Numbers" 3 vols.

*1922. "First Course in the Theory of Equations"

* 1923. "Algebras and their arithmetics"

* 1926. "Modern algebraic theories"

*1923, 1928. "Algebraic Numbers". Report with others for U. S. National Research Council.

*1929. "Introduction to the Theory of Numbers"

*1930. "Studies in the Theory of Numbers"

*1935. (withG. A. Bliss ) "Biographical Memoir of Eliakim Hastings Moore 1862–1932."

*1935. "Researches on Waring's problem"

*1938. (with H. F. Blichfeldt and G. A. Miller) "Theory and Applications of Finite Groups"

*1938. "Algebras And Their Arithmetics"

*1939. "Modern Elementary Theory of Numbers"

*1939. "New First Course in the Theory of Equations"

*"On Invariants and the Theory of Numbers"

*"Plane Trigonometry With Practical Applications"Secondary:

*Fenster, D. D., 1997, "Role modeling in mathematics: the case of Leonard Eugene Dickson (1874–1954)," "Historia Mathematica 24": 7–24.

*Parshall, K. H., 1983, "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn,Leonard Dickson , andOswald Veblen ," "Archives of International History of Science 33": 274–99.

*--------, 1991, "A study in group theory: Leonard Eugene Dickson's Linear groups," "Mathematical Intelligencer 13": 7–11.

*--------, 1999, "Leonard Eugene Dickson" in "American National Biography, vol. 6". Oxford Univ. Press: 578–79.**Texts available on the Internet**[

*http://www.archive.org/details/firstcourseinthe00dickuoft First course in the theory of equations (1922)*] [*http://www.archive.org/index.php Internet archive*]**External links***

*

*Wikimedia Foundation.
2010.*

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**Leonard Eugene Dickson**— (* 22. Januar 1874 in Independence, Iowa, USA; † 17. Januar 1954 in Harlington, Texas, USA) war ein US amerikanischer Mathematiker, der vor allem auf dem Gebiet der Zahlentheorie und der Algebra arbeitete. Inhaltsverzeichnis 1 Leben und Werk 2 … Deutsch Wikipedia**Leonard Eugene Dickson**— Pour les articles homonymes, voir Dickson. Leonard Eugene Dickson (22 janvier 1874 à Independence (Iowa) 17 janvier 1954 à Harlingen (Texas)) est un mathématicien américain, spécialiste en théorie des nombres et en algèbre.… … Wikipédia en Français**Leonard E. Dickson**— Leonard Eugene Dickson (* 22. Januar 1874 in Independence, Iowa, USA; † 17. Januar 1954 in Harlingen, Texas, USA) war ein US amerikanischer Mathematiker, der vor allem auf dem Gebiet der Zahlentheorie und der Algebra arbeitete. Inhaltsverzeichnis … Deutsch Wikipedia**Dickson, Leonard Eugene**— ▪ American mathematician born Jan. 22, 1874, Independence, Iowa, U.S. died Jan. 17, 1954, Harlingen, Texas American mathematician who made important contributions to the theory of numbers and the theory of groups. Appointed associate… … Universalium**Leonard Dickson**— Leonard Eugene Dickson (* 22. Januar 1874 in Independence, Iowa, USA; † 17. Januar 1954 in Harlington, Texas, USA) war ein US amerikanischer Mathematiker, der vor allem auf dem Gebiet der Zahlentheorie und der Algebra arbeitete.… … Deutsch Wikipedia**Dickson (surname)**— Dickson or, as is common in England, Dixon, is a patronymic surname, traditionally Scottish and thought to have originated upon the birth of the son of Richard Keith, son of Hervey de Keith, Earl Marischal of Scotland, and Margaret, daughter of… … Wikipedia**Dickson**— Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Patronyme Classement par ordre alphabétique du prénom Chris Dickson (1961 ), marin néozélandais. Ed Dickson (1987 ), joueur américain de football… … Wikipédia en Français**Dickson invariant**— In mathematics, the Dickson invariant, named after Leonard Eugene Dickson, may mean: The Dickson invariant of an element of the orthogonal group in characteristic 2 A modular invariant of a group studied by Dickson This disambiguation page lists… … Wikipedia**DICKSON (L. E.)**— DICKSON LEONARD EUGENE (1874 1954) Mathématicien américain, né à Independence dans l’Iowa et mort à Harlingen, dans le Texas. Dickson fit ses premières études à l’université du Texas, avant de les poursuivre à Chicago, à Leipzig et à Paris. Il… … Encyclopédie Universelle**Dickson**— [dɪksn], Leonard Eugene, amerikanischer Mathematiker, * Independence (Iowa) 22. 1. 1874, ✝ Harlingen (Texas) 17. 1. 1954; lehrte 1900 39 in Chicago und arbeitete v. a. über Algebra und Zahlentheorie. Seine monumentale »History of the theory of… … Universal-Lexikon