**Dickson** is known for his contributions to number theory and group theory.

- His parents were Lucy Tracy and Campbell Dickson, who worked as a banker.
- Leonard attended both primary and secondary school in his home town of Cleburne.
- 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.
- Dickson received a Ph.D. from the University of Chicago in 1896 for a dissertation entitled The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group.
- Dickson then spent some time with Lie at Leipzig and later with Jordan in Paris.
- 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.
- Dickson's mathematical output was vast and his list of published works contains 275 items.
- However we should note that before publishing the book, Dickson had already published 43 research papers in the preceding five years which, with the exception of seven, were all on finite linear groups.
- Dickson published 17 books in addition to Linear groups with an exposition of the Galois field theory.
- Dickson published Modern Elementary Theory of Numbers in 1939.
- The final area of Dickson's research which we should look at is his work on algebras.
- Eliakim Moore and Dickson had done much work on fields but it was the arrival of Wedderburn in Chicago in 1904 when work began there on finite division algebras.
- Dickson, who at first looked for a counterexample, was led to find a (rather obscure) proof himself which he showed to Wedderburn.
- Then Wedderburn devised two further elegant proofs using ideas from Dickson's proof.
- Dickson's search for a counterexample led him to consider non-associative algebras and in a series of papers he determined all three and four-dimensional (non-associative) division algebras over a field.
- Given Dickson's intolerance for student weaknesses in mathematics, however, his comments could be harsh, even though not intended to be personal.
- Dickson was awarded many honours.
- Dickson was the first recipient of the prize, being awarded $1,000 in 1924 for his work on the arithmetics of algebras.
- Dickson was much involved with the American Mathematical Society, becoming its president in 1917-1918 having earlier, in 1913, been its Colloquium Lecturer.
- As a final comment on honours given to Dickson, we note that Princeton (1941) and Harvard (1936) were among the universities that awarded him an honorary degrees.
- We mentioned at the beginning of this article that Dickson always considered himself a Texan, so it was natural that he should return 'home' after he retired.

Born 22 January 1874, Independence, Iowa, USA. Died 17 January 1954, Harlingen, Texas, USA.

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Group Theory, Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive