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.
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.
In 1899 and at the extraordinarily young age of 25, Dickson was appointed associate professor at the University of Texas.
Dickson married Susan McLeod Davis in 1902; they had two children, Campbell and Eleanor.
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.
His December 1918 presidential address, titled "Mathematics in War Perspective", criticized American mathematics for falling short of those of Britain, France, and Germany: 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.
The Collected Mathematical Papers of Leonard Eugene Dickson fill six large volumes.
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.
Dickson had already published 43 research papers in the preceding five years; all but seven on finite linear groups.
Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Joseph Wedderburn and Cartan.
[7] 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.