View source for Biography:Leonard Eugene Dickson

{{short description|American mathematician}}
{{Infobox scientist
| name              = Leonard Eugene Dickson
| image             = <!--(filename only)-->
| image_size        = 
| caption           = 
| birth_date        = {{Birth date|1874|01|22}}
| birth_place       = Independence, Iowa, US
| death_date        = {{Death date and age|1954|01|17|1874|01|22}}
| death_place       = Harlingen, Texas, US
| fields            = [[Mathematics]]
| workplaces        = [[Organization:University of Chicago|University of Chicago]]
| alma_mater        = University of Chicago (Ph.D., 1896)
| thesis_title = The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group
| thesis_url   = 
| thesis_year  = 1896
| doctoral_advisor  = [[Biography:E. H. Moore|E. H. Moore]]
| doctoral_students = {{plainlist|1=
*[[Biography:Abraham Adrian Albert|Abraham Adrian Albert]]
*Frances Baker
*Olive Hazlett
*[[Biography:Mabel Gweneth Humphreys|Mabel Gweneth Humphreys]]
*[[Biography:Ralph Duncan James|Ralph James]]
*Burton W. Jones
*Claiborne Latimer
*Mayme Logsdon
*Cyrus MacDuffee
*[[Biography:Ivan M. Niven|Ivan M. Niven]]
*[[Biography:Alexander Oppenheim|Alexander Oppenheim]]
*[[Biography:Gordon Pall|Gordon Pall]]
*[[Biography:Mina Rees|Mina Rees]]
*Arnold Ross
*Marion Elizabeth Stark
*[[Biography:John Williamson (mathematician)|John Williamson]]
}}
| known_for         = [[Cayley–Dickson construction]]<br>[[Dickson's conjecture]]<br>[[Dickson's lemma]]<br>Dickson invariant<br>[[Dickson polynomial]]<br>[[Modular invariant theory]]
| awards            = Newcomb Cleveland Prize {{small|(1923)}}<br>Cole Prize in Algebra <small>(1928)</small>
}}
'''Leonard Eugene Dickson''' (January 22, 1874&nbsp;– January 17, 1954) was an American [[Biography:Mathematician|mathematician]]. He was one of the first American researchers in [[Abstract algebra|abstract algebra]], in particular the theory of finite [[Field (mathematics)|fields]] and [[Classical group|classical group]]s, and is also remembered for a three-volume history of [[Number theory|number theory]], ''[[History of the Theory of Numbers]]''. The L. E. Dickson instructorships at the [[Organization:University of Chicago|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 [[Organization:University of Texas at Austin|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|geometry]].<ref name=AAA>A. A. Albert (1955) [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/dickson-leonard.pdf Leonard Eugene Dickson 1874–1954] from National Academy of Sciences</ref>

Both the [[Organization:University of Chicago|University of Chicago]] and [[Organization:Harvard University|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 [[Biography:E. H. Moore|E. H. Moore]].

Dickson then went to Leipzig and [[Place:Paris|Paris]] to study under [[Biography:Sophus Lie|Sophus Lie]] and [[Biography:Camille Jordan|Camille Jordan]], respectively. On returning to the US, he became an instructor at the [[Organization:University of California|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 [[Organization:University of California|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."<ref>Karen Parshall (1999) "Leonard Eugene Dickson" in ''American National Biography'', volume 6, [[Organization:Oxford University Press|Oxford University Press]], pp 578–79</ref>

:"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."<ref name=DDF>{{cite journal | last1 = Fenster | first1 = D. D. | year = 1997 | title = Role modeling in mathematics: the case of Leonard Eugene Dickson (1874–1954) | journal = Historia Mathematica | volume = 24 | pages = 7–24 | doi=10.1006/hmat.1997.2120| doi-access = free }}</ref>

:"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."<ref name=DDF/>

==Work==
Dickson had a major impact on American mathematics, especially [[Abstract algebra|abstract algebra]]. His 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 groups. Parshall (1991) described the book as follows:

:"Dickson presented a unified, complete, and general theory of the classical linear groups—not merely over the prime field GF(''p'') as [[Biography:Camille Jordan|Jordan]] had done—but over the general [[Finite field|finite field]] GF(''p<sup>n</sup>''), 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 field|finite 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 three were found in 1960, 1965, and 1967.

Dickson worked on [[Finite field|finite field]]s and extended the theory of linear associative algebras initiated by [[Biography:Joseph Wedderburn|Joseph Wedderburn]] and [[Biography:Élie Cartan|Cartan]].

He started the study of modular invariants of a group.

In 1905, Wedderburn, then at Chicago on a Carnegie Fellowship, published a paper that included three claimed proofs of a theorem stating that all finite [[Division algebra|division algebra]]s were commutative, now known as [[Wedderburn's little theorem|Wedderburn's theorem]]. The proofs all made clever use of the interplay between the [[Ring (mathematics)|additive group]] of a finite [[Division algebra|division algebra]] ''A'', and the [[Multiplicative group|multiplicative group]] ''A''*&nbsp;=&nbsp;''A''&nbsp;−&nbsp;{0}. [[Biography:Karen Parshall|Karen Parshall]] noted 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. She concluded that Dickson should be credited with the first correct proof.<ref>{{cite journal | last1 = Parshall | first1 = Karen |  year = 1983 | title = In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn, Leonard Dickson, and Oswald Veblen | journal = Archives of International History of Science | volume = 33 | pages = 274–99 }}</ref>

Dickson's search for a counterexample to Wedderburn's theorem led him to investigate [[Algebra over a field#Non-associative algebras|nonassociative algebras]], and in a series of papers he found all possible three and four-dimensional (nonassociative) [[Division algebra|division algebra]]s over a field.

In 1919 Dickson constructed Cayley numbers by a doubling process starting with [[Quaternion|quaternion]]s <math>\mathbb{H}</math>.<ref>{{Citation | last1=Dickson | first1=L. E. | title=On Quaternions and Their Generalization and the History of the Eight Square Theorem | jstor=1967865  | series=2nd | year=1919 | journal=[[Annals of Mathematics]] | issn=0003-486X | volume=20 | issue=3 | pages=155–171 | doi=10.2307/1967865}}</ref> His method was extended to a doubling of <math>\mathbb{R}</math> to produce <math>\mathbb{C}</math>, and of <math>\mathbb{C}</math> to produce <math>\mathbb{H}</math> by A. A. Albert in 1922, and the procedure is known now as the [[Cayley–Dickson construction]] of [[Composition algebra|composition algebra]]s.

==The number theorist==
Dickson proved many interesting results in [[Number theory|number theory]], using results of Vinogradov to deduce the ideal [[Waring's problem|Waring theorem]] in his investigations of [[Additive number theory|additive number theory]]. He proved the [[Waring's problem]] for <math>k\ge 7</math> under the further condition of
:<math>(3^k + 1)/(2^k - 1)\le [1.5^k] + 1</math>

independently of Subbayya Sivasankaranarayana Pillai who proved it for <math>k\ge 6</math> ahead of him.<ref>{{cite book|title=Number Theory|url=https://books.google.com/books?id=BkBSfFjT1BgC&pg=PA95|access-date=15 July 2013|year=2003|publisher=Universities Press|isbn=978-81-7371-454-2|pages=95–}}</ref>

The three-volume ''[[History of the Theory of Numbers]]'' (1919–23) is still much consulted today, covering divisibility and primality, Diophantine analysis, and [[Quadratic form|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."

==Bibliography==
*{{Citation | last1=Dickson | first1=Leonard Eugene |  editor1-last=Magnus | editor1-first=Wilhelm | editor1-link=Wilhelm Magnus | title=Linear groups: With an exposition of the Galois field theory | orig-year=1901 | url=https://archive.org/details/lineargroupswith00dickuoft | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | series=Dover Phoenix editions | isbn=978-0-486-49548-4 | mr=0104735 | year=1958}}<ref>{{cite journal|author=Miller, G. A.|title=Review: ''Linear Groups with an Exposition of the Galois Field Theory'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1902|volume=9|issue=2|pages=165–172|url=https://www.ams.org/journals/bull/1902-09-03/S0002-9904-1902-00970-1/S0002-9904-1902-00970-1.pdf|doi=10.1090/s0002-9904-1902-00970-1|doi-access=free}}</ref><ref>Karen Parshall (1991) "A study in group theory: Leonard Eugene Dickson's Linear groups", Mathematical Intelligencer 13: 7–11</ref> ({{cite book|title=online hathitrust|series=B.G. Teubner's Sammlung von lehrbüchern auf dem gebiete der mathematischen wissenschaften mit einschluss ihrer anwendungen. Bd. VI |year=1901 |publisher=B. G. Teubner |url=http://catalog.hathitrust.org/Record/000421365}})
*{{Citation | last1=Dickson | first1=Leonard Eugene |   title=Introduction to the theory of algebraic equations | orig-year=1903 | url=https://archive.org/details/introductiontoth00dickuoft | publisher={{wipe|John Wiley & Sons}} | location=New York | year=1903}}<ref>{{cite journal|author=Miller, G. A.|title=Review: ''Introduction to the Theory of Algebraic Equations'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1904|volume=10|issue=8|pages=411–412|url=https://www.ams.org/journals/bull/1904-10-08/S0002-9904-1904-01143-X/S0002-9904-1904-01143-X.pdf|doi=10.1090/s0002-9904-1904-01143-x}}</ref> ({{cite book|title=online hathitrust|year=1903 |publisher=J. Wiley & Sons |url=http://catalog.hathitrust.org/Record/000422480}})
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=Linear algebras | orig-year=1914 | url=https://archive.org/details/cu31924001557515 | publisher=Naub press | series=Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No. 16 | isbn=978-1-178-36805-5 | mr=0118745 | year=2010}}<ref>{{cite journal|author=Graustein, William Caspar|title=Review: ''Linear Algebra'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1915|volume=21|issue=10|pages=511–522|url=https://www.ams.org/journals/bull/1915-21-10/S0002-9904-1915-02690-X/S0002-9904-1915-02690-X.pdf|doi=10.1090/s0002-9904-1915-02690-x|doi-access=free}}</ref>
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=Algebraic invariants | orig-year=1914 | url=http://projecteuclid.org/euclid.chmm/1263317248 | publisher=Cornell University Library | isbn=978-1-4297-0042-9 | year=2010}}<ref>{{cite journal|author=Carmichael, R. D.|title=Review: ''Algebraic Invariants'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1916|volume=22|issue=4|pages=197–199|url=https://www.ams.org/journals/bull/1916-22-04/S0002-9904-1916-02758-3/S0002-9904-1916-02758-3.pdf|doi=10.1090/s0002-9904-1916-02758-3|doi-access=free}}</ref>
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=On invariants and the theory of numbers | orig-year=1914 | url=https://archive.org/details/madisoncolloquiu00amer | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | series=Dover Phoenix editions | isbn=978-0-486-43828-3 | mr=0201389 | year=2004}}<ref>{{cite journal|author=Glenn, Oliver Edmunds|title=Review: ''Part I: On Invariants and the Theory of Numbers'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1915|volume=21|issue=9|pages=464–470|url=https://www.ams.org/journals/bull/1915-21-09/S0002-9904-1915-02689-3/S0002-9904-1915-02689-3.pdf|doi=10.1090/s0002-9904-1915-02689-3|doi-access=free}}</ref>
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=Elementary theory of equations | orig-year=1914 | url=https://archive.org/details/elementarytheory00dickuoft | publisher=Cornell University Library | isbn=978-1-112-27988-1 | year=2009}}
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=History of the theory of numbers. Vol. I: Divisibility and primality. | orig-year=1919 | url=https://archive.org/details/historyoftheoryo01dick | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | isbn=978-0-486-44232-7 | mr=0245499 | year=2005}}<ref>{{cite journal|author=Lehmer, D. N.|title=Review: ''History of the Theory of Numbers'', by L. E. Dickson. Volume I|journal=Bull. Amer. Math. Soc.|year=1919|volume=26|issue=3|pages=125–132|url=https://www.ams.org/journals/bull/1919-26-03/S0002-9904-1919-03280-7/S0002-9904-1919-03280-7.pdf|doi=10.1090/s0002-9904-1919-03280-7|doi-access=free}}</ref>
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=History of the theory of numbers. Vol. II: Diophantine analysis | orig-year=1920 | url=https://archive.org/details/historyoftheoryo02dickuoft | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | isbn=978-0-486-44233-4 | mr=0245500 | year=2005}}<ref name="ReviewHistoryNumbersvols2and3">{{cite journal|author=Vandiver, H. S.|title=Review; ''History of the Theory of Numbers'', by L. E. Dickson. Volume II, ''Diophantine Analysis''. Volume III, ''Quadratic and Higher Forms'', (with a chapter on the class number by George Hoffman Cresse)|journal=Bull. Amer. Math. Soc.|year=1924|volume=30|issue=1|pages=65–70|url=https://www.ams.org/journals/bull/1924-30-01/S0002-9904-1924-03852-X/S0002-9904-1924-03852-X.pdf|doi=10.1090/S0002-9904-1924-03852-X|doi-access=free}}</ref>
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=History of the theory of numbers. Vol. III: Quadratic and higher forms | orig-year=1923 | url=https://archive.org/details/historyoftheoryo03dickuoft | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | isbn=978-0-486-44234-1 | mr=0245501 | year=2005}}
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=First course in the theory of equations | orig-year=1922 | url=https://archive.org/details/firstcourseinthe00dickuoft | publisher=University of Michigan Library | year=2009}}
*{{Citation | last1=Dickson | first1=Leonard Eugene |  title=Algebras and their arithmetics | orig-year=1923 | url=https://archive.org/details/117770259 | publisher=[[Social:Dover Publications|Dover Publications]] | location=New York | isbn=978-0-486-60616-3 | mr=0111764 | year=1960}}<ref>{{cite journal|author=Hazlett, O. C.|title=Review: ''Algebras and their Arithmetics'', by L. E. Dickson and ''Corpi Numerici e Algebre'', by Gaetano Scorza|journal=Bull. Amer. Math. Soc.|year=1924|volume=30|issue=5|pages=263–270|url=https://www.ams.org/journals/bull/1924-30-05/S0002-9904-1924-03899-3/S0002-9904-1924-03899-3.pdf | doi = 10.1090/S0002-9904-1924-03899-3}}</ref>
* 1926. ''Modern algebraic theories''<ref>{{cite journal|author=Bell, E. T.|title=Review: ''Modern Algebraic Theories'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1926|volume=32|issue=6|pages=707–710|url=https://www.ams.org/journals/bull/1926-32-06/S0002-9904-1926-04303-2/S0002-9904-1926-04303-2.pdf|doi=10.1090/s0002-9904-1926-04303-2|doi-access=free}}</ref>
*1923, 1928. ''Algebraic Numbers''. Report with others for U. S. National Research Council.
*1929. ''Introduction to the Theory of Numbers''<ref>{{cite journal|author=Bell, E. T.|title=Review: ''Introduction to the Theory of Numbers'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1930|volume=36|issue=7|pages=455–459|url=https://www.ams.org/journals/bull/1930-36-07/S0002-9904-1930-04968-X/S0002-9904-1930-04968-X.pdf|doi=10.1090/s0002-9904-1930-04968-x|doi-access=free}}</ref>
*1930. ''Studies in the Theory of Numbers''<ref>{{cite journal|author=Uspensky, J. V.|title=Review: ''Studies in the Theory of Numbers'', by L. E. Dickson|journal=Bull. Amer. Math. Soc.|year=1932|volume=38|issue=7|pages=463–465|url=https://www.ams.org/journals/bull/1932-38-07/S0002-9904-1932-05419-2/S0002-9904-1932-05419-2.pdf|doi=10.1090/s0002-9904-1932-05419-2|doi-access=free}}</ref>
*1935. (with G. A. Bliss) "Biographical Memoir of Eliakim Hastings Moore 1862–1932."
*1935. ''Researches on Waring's problem''
*1938. (with [[Biography:Hans Frederick Blichfeldt|Hans Frederick Blichfeldt]] and [[Biography:George Abram Miller|George Abram Miller]]) ''Theory and Applications of Finite Groups''
*1938. ''Algebras And Their Arithmetics'' (1st edn. in 1923)
*1939. ''Modern Elementary Theory of Numbers''
*1939. ''New First Course in the Theory of Equations''
*''Plane Trigonometry With Practical Applications''
*{{Citation | last1=Dickson | first1=Leonard Eugene |  editor1-last=Albert | editor1-first=A. Adrian | title=The collected mathematical papers of Leonard Eugene Dickson | url=https://www.ams.org/bookstore-getitem/item=CHEL-273 | publisher=AMS Chelsea Publishing | location=New York | isbn=978-0-8284-0273-6 | mr = 0749229 | year=1975 | volume=I-VI}} {{MR|0441665}}

==Notes==
{{Reflist}}

==External links==
* {{MacTutor Biography|id=Dickson}}
* {{mathgenealogy|name=Leonard Eugene Dickson|id=5695}}
* {{Gutenberg author |id=34169| name=Leonard Eugene Dickson}}
* {{Internet Archive author |sname=Leonard Eugene Dickson}}

{{AMS Presidents}}


{{DEFAULTSORT:Dickson, Leonard Eugene}}
[[Category:Algebraists]]
[[Category:Number theorists]]

{{Sourceattribution|Leonard Eugene Dickson}}