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{{Use mdy dates|date=November 2011}}
{{Infobox scientist
| name              = Leonard Eugene Dickson
| image            = <!--(filename only)-->
| image_size        =
| caption          =
| birth_date        = {{Birth date|1874|01|22}}
| birth_place      = [[Independence, Iowa]]
| death_date        = {{Death date and age|1954|01|17|1874|01|22}}
| death_place      = [[Harlingen, Texas]]
| nationality      = [[USA|American]]
| fields            = [[Mathematics]]
| workplaces        = [[University of Chicago]]
| alma_mater        = University of Chicago
| doctoral_advisor  = [[E. H. Moore]]
| doctoral_students = [[Abraham Adrian Albert]]<br>[[Olive Hazlett]]<br>[[Ralph Duncan James|Ralph James]]<br>[[Burton W. Jones]]<br>[[Claiborne Latimer]]<br>[[Cyrus MacDuffee]]<br>[[Ivan M. Niven]]<br>[[Alexander Oppenheim]]<br>[[Mina Rees]]<br>[[Arnold Ross]]<br>[[John Williamson (mathematician)|John Williamson]]
| known_for        = [[Cayley–Dickson construction]]<br>[[Cayley–Dickson sedenions]]<br>[[Dickson's conjecture]]<br>[[Dickson's lemma]]<br>[[Dickson invariant (disambiguation)|Dickson invariant]]<br>[[Dickson polynomial]]
| awards            =
}}
'''Leonard Eugene Dickson''' (January 22, 1874&nbsp;– January 17, 1954) was an [[United States|American]] [[mathematician]]. He was one of the first American researchers in [[abstract algebra]], in particular the theory of finite [[Field (mathematics)|fields]] and [[classical group]]s, and is also remembered for a three-volume history of [[number theory]], ''[[History of the Theory of Numbers]]''.


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Dickson considered himself a Texan by virtue of having grown up in [[Cleburne, Texas|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. 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]].
 
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Both the [[University of Chicago]] and [[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 [[E. H. Moore]].
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Dickson then went to [[Leipzig]] and [[Paris]] to study under [[Sophus Lie]] and [[Camille Jordan]], respectively. On returning to the USA, he became an instructor at the [[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 [[University of California]] in 1914, 1918, and 1922. In 1939, he returned to Texas to retire.
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Dickson married Susan McLeod Davis in 1902; they had two children, Campbell and Eleanor.
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Dickson was elected to the [[United States National Academy of Sciences|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.
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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:
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:"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."
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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''.
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It appears that Dickson was a hard man:
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:"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)
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:"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)
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:"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)
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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.
 
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==The algebraist==
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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 the [[prime field]] GF(''p'') as [[Camille Jordan|Jordan]] had done—but over the general [[finite field]] GF(''p<sup>n</sup>''), and he did this against the backdrop of a well-developed theory of these underlying [[field (algebra)|field]]s. ... his book represented the first systematic treatment of [[finite field]]s in the mathematical literature."
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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.
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Dickson worked on [[finite field]]s and extended the theory of [[linear associative algebra]]s initiated by [[Joseph Wedderburn]] and [[Élie Cartan|Cartan]].
  <li>[http://www.weixiyang.com/bbs/forum.php?mod=viewthread&tid=1697112 http://www.weixiyang.com/bbs/forum.php?mod=viewthread&tid=1697112]</li>
 
 
He started the study of [[modular invariants of a group]].
  <li>[http://bbs.ewche.com/forum.php?mod=viewthread&tid=409262&fromuid=83428 http://bbs.ewche.com/forum.php?mod=viewthread&tid=409262&fromuid=83428]</li>
 
 
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]]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]] ''A'', and the [[multiplicative group]] ''A''*&nbsp;=&nbsp;''A''&nbsp;−&nbsp;{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.
  <li>[https://fratpoet.com/activity/p/32212/ https://fratpoet.com/activity/p/32212/]</li>
 
 
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]]s over a [[field (algebra)|field]].
</ul>
 
==The number theorist==
Dickson proved many interesting results in [[number theory]], using results of [[Ivan Matveyevich Vinogradov|Vinogradov]] to deduce the ideal [[Waring's problem|Waring theorem]] in his investigations of [[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=http://books.google.com/books?id=BkBSfFjT1BgC&pg=PA95|accessdate=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 | author1-link=Leonard Eugene Dickson | editor1-last=Magnus | editor1-first=Wilhelm | editor1-link=Wilhelm Magnus | title=Linear groups: With an exposition of the Galois field theory | origyear=1901 | url=http://www.archive.org/details/lineargroupswith00dickuoft | publisher=[[Dover Publications]] | location=New York | series=Dover Phoenix editions | isbn=978-0-486-49548-4 | mr=0104735 | year=1958}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson |  title=Introduction to the theory of algebraic equations | origyear=1903 | url=http://archive.org/details/introductiontoth00dickuoft | publisher=[[John Wiley & Sons]] | location=New York | year=1903}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=Linear algebras | origyear=1914 | url=http://www.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}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=Algebraic invariants | origyear=1914 | url=http://projecteuclid.org/euclid.chmm/1263317248 | publisher=Cornell University Library | isbn=978-1-4297-0042-9 | year=2010}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=On invariants and the theory of numbers | origyear=1914 | url=http://www.archive.org/details/madisoncolloquiu00amer | publisher=[[Dover Publications]] | location=New York | series=Dover Phoenix editions | isbn=978-0-486-43828-3 | mr=0201389 | year=2004}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=Elementary theory of equations | origyear=1914 | url=http://www.archive.org/details/elementarytheory00dickuoft | publisher=Cornell University Library | isbn=978-1-112-27988-1 | year=2009}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=History of the theory of numbers. Vol. I: Divisibility and primality. | origyear=1919 | url=http://www.archive.org/details/historyoftheoryo01dick | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-44232-7 | mr=0245499 | year=2005}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=History of the theory of numbers. Vol. II: Diophantine analysis | origyear=1920 | url=http://www.archive.org/details/historyoftheoryo02dickuoft | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-44233-4 | mr=0245500 | year=2005}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=History of the theory of numbers. Vol. III: Quadratic and higher forms | origyear=1923 | url=http://www.archive.org/details/historyoftheoryo03dickuoft | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-44234-1 | mr=0245501 | year=2005}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=First course in the  theory of equations | origyear=1922 | url=http://www.archive.org/details/firstcourseinthe00dickuoft | publisher=University of Michigan Library | year=2009}}
*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=Algebras and their arithmetics | origyear=1923 | url=http://www.archive.org/details/117770259 | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-60616-3 | mr=0111764 | year=1960}}
* 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. (with [[G. 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'' (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 | author1-link=Leonard Eugene Dickson | editor1-last=Albert | editor1-first=A. Adrian | title=The collected mathematical papers of Leonard Eugene Dickson | url=http://www.ams.org/bookstore-getitem/item=CHEL-273 | publisher=AMS Chelsea Publishing | location=New York | isbn=978-0-8284-0273-6 | mr=0441665 | mr = 0749229 | year=1975 | volume=I-VI}}
 
==References==
{{Reflist}}
*Fenster, D. D., 1997, "Role modeling in mathematics: the case of Leonard Eugene Dickson (1874–1954)," ''Historia Mathematica 24'': 7–24.
*[[Karen Parshall]], 1983, "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn, [[Leonard Dickson]], and [[Oswald 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.
* {{MacTutor Biography|id=Dickson}}
* {{mathgenealogy|name=Leonard Eugene Dickson|id=5695}}
 
==External links==
{{Sister project links| wikt=no | commons=no | b=no | n=no | q=Leonard Eugene Dickson | s=Author:Leonard Eugene Dickson | v=no | voy=no | species=no | d=q891058}}
 
* {{gutenberg author}}
* [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/dickson-leonard.pdf Leonard Eugene Dickson 1874–1954], A Biographical Memoir by [[A. A. Albert]]
 
{{Authority control|VIAF=109626945}}
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Dickson, Leonard Eugene
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH    = January 22, 1874
| PLACE OF BIRTH    = [[Independence, Iowa]]
| DATE OF DEATH    = January 17, 1954
| PLACE OF DEATH    = [[Harlingen, Texas]]
}}
{{DEFAULTSORT:Dickson, Leonard Eugene}}
[[Category:1874 births]]
[[Category:1954 deaths]]
[[Category:20th-century mathematicians]]
[[Category:American mathematicians]]
[[Category:Algebraists]]
[[Category:Number theorists]]
[[Category:University of Texas at Austin alumni]]
[[Category:University of Chicago alumni]]
[[Category:University of Texas at Austin faculty]]
[[Category:University of Chicago faculty]]
[[Category:Historians of mathematics]]
[[Category:Presidents of the American Mathematical Society]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:ICM 1900 Plenary and Invited Speakers]]

Latest revision as of 13:51, 5 May 2014

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From site visits and lectures to panel discussions with health educators, AIDS activists, general practitioners, and a priest, I have come back having a newfound excitement for the real and positive impact of youth's access to sexuality education, information, and medical services. The 3 of the countries visited throughout the study tour have one major thing in common positive, inclusive, nationally funded, sexuality education initiatives have come about relatively recently. The Dutch, French, and German people did something radical.

Additionally, it revealed the dangers of having a partisan state when it comes to dealing with such volatile events and the resultant constitutional impasse that could worsen the impact. (History repeated itself in Gujarat 10 years later after Godhra and the question still remains as to why AB Vajpayee never sacked Narendra Modi and declared President rule when it was apparent that the state machinery had didn't protect citizens from the mob and also the attacks were directed against the minority Muslim community. Why point fingers only against Rao?).

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