no. 2
Leonard Dickson's History of the Theory of Numbers: An historical study with mathematical implications
[History of the theory of numbers de Leonard Dickson : étude historique avec des prolongements mathématiques]
Revue d'histoire des mathématiques, Tome 5 (1999) no. 2, pp. 159-179.

En 1911, le mathématicien Leonard Dickson s'est lancé dans une étude historique de la théorie des nombres, qui a culminé avec la publication de son History of the Theory of Numbers en trois volumes. Notre étude examine la genèse de ce travail, l'approche historiographique qui la sous-tend et les contributions mathématiques qui en découlent.

In 1911, the research mathematician Leonard Dickson embarked on a historical study of the theory of numbers which culminated in the publication of his three-volume History of the Theory of Numbers. This paper discusses the genesis of this work, the historiographic style revealed therein, and the mathematical contributions which arose out of it.

@article{RHM_1999__5_2_159_0,
     author = {Fenster, Della D.},
     title = {Leonard {Dickson's} {\protect\emph{History} of the {Theory} of {Numbers}:} {An} historical study with mathematical implications},
     journal = {Revue d'histoire des math\'ematiques},
     pages = {159--179},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {5},
     number = {2},
     year = {1999},
     zbl = {0958.01013},
     language = {en},
     url = {http://www.numdam.org/item/RHM_1999__5_2_159_0/}
}
TY  - JOUR
AU  - Fenster, Della D.
TI  - Leonard Dickson's History of the Theory of Numbers: An historical study with mathematical implications
JO  - Revue d'histoire des mathématiques
PY  - 1999
SP  - 159
EP  - 179
VL  - 5
IS  - 2
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/RHM_1999__5_2_159_0/
LA  - en
ID  - RHM_1999__5_2_159_0
ER  - 
%0 Journal Article
%A Fenster, Della D.
%T Leonard Dickson's History of the Theory of Numbers: An historical study with mathematical implications
%J Revue d'histoire des mathématiques
%D 1999
%P 159-179
%V 5
%N 2
%I Société mathématique de France
%U http://www.numdam.org/item/RHM_1999__5_2_159_0/
%G en
%F RHM_1999__5_2_159_0
Fenster, Della D. Leonard Dickson's History of the Theory of Numbers: An historical study with mathematical implications. Revue d'histoire des mathématiques, Tome 5 (1999) no. 2, pp. 159-179. http://www.numdam.org/item/RHM_1999__5_2_159_0/

[1] Albers (Donald J.) & Alexanderson (Gerald L.) [1991] A Conversation with Ivan Niven, College Mathematics Journal, 22 (1991), pp.370-402.

[2] Albers (Donald J.) & Alexanderson (Gerald L.) [1993] A Conversation with Richard K.Guy, College Mathematics Journal, 24 (1993), pp.123-148.

[3] Albert (A. Adrian) [1955] Leonard Eugene Dickson 1874-1954, Bulletin of the American Mathematical Society, 37 (1931), pp.331-345. | MR | Zbl

[4] Archibald (Raymond Clare) [1938a] A Semicentennial History of the American Mathematical Society 1888-1938, New York: American Mathematical Society, 1938. | Zbl

[5] Archibald (Raymond Clare) [1938b] (ed.) Semicentennial Addresses of the American Mathematical Society 1888-1938, New York: American Mathematical Society, 1938. | JFM | Zbl

[6] Bell (Eric Temple) [1938] Fifty Years of Algebra in America, 1888-1938, in Archibald (Raymond C.), ed., Semicentennial Addresses of the American Mathematical Society 1888-1938, New York: American Mathematical Society, 1938, pp.1-34. | JFM | Zbl

[7] Birkhoff (George David) [1938] Fifty Years of American Mathematics, in Archibald (Raymond C.), ed., Semicentennial Addresses of the American Mathematical Society 1888-1938, New York: American Mathematical Society, 1938, pp.270-315. | JFM | Zbl

[8] Carmichael (Robert D.) [1919] Review of History of the Theory of Numbers, vol 1.: Divisibility and Primality, by Leonard Eugene Dickson, American Mathematical Monthly, 26 (1919), pp.396-403. | JFM | MR

[9] Carmichael (Robert D.) [1921] Review of History of the Theory of Numbers, vol 2.: Diophantine Analysis, by Leonard Eugene Dickson, American Mathematical Monthly, 28 (1921), pp.72-78. | JFM | MR | Zbl

[10] Dickson (Leonard Eugene) [Collected Works] The Collected Mathematical Papers of Leonard Eugene Dickson, ed. by A. Adrian Albert, 6 vols., New York: Chelsea Publishing Co., 1975, 1983. | MR | Zbl

[11] Dickson (Leonard Eugene) [1897] The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group, Annals of Mathematics, 11 (1897), pp.65-143; Collected Works 2, pp.651-729. | JFM | Zbl

[12] Dickson (Leonard Eugene) [1911] Leonard Dickson to R.S. Woodward, 11 February, 1911, Carnegie Institution Archives, Washington, D.C., Dickson Papers.

[13] Dickson (Leonard Eugene) [1919, 1920, 1923a] History of the Theory of Numbers, 3 vols., New York: Chelsea Publishing Company, 1919, 1920, 1923. | Zbl

[14] Dickson (Leonard Eugene) [1921a] A New Method in Diophantine Analysis, Bulletin of the American Mathematical Society, 27 (1921), pp.353-365; Collected Works 4, pp.619-631. | JFM

[15] Dickson (Leonard Eugene) [1921b] Arithmetic of Quaternions, Proceedings of the London Mathematical Society, 20 (1921), pp.225-232; Collected Works 3, pp.397-404. | JFM

[16] Dickson (Leonard Eugene) [1921c] Fallacies and Misconceptions in Diophantine Analysis, Bulletin of the American Mathematical Society, 27 (1921), pp.312-319; Collected Works 4, pp.611-618. | JFM

[17] Dickson (Leonard Eugene) [1921d] Some Relations Between the Theory of Numbers and Other Branches of Mathematics, in Villat (Henri), ed., Conférence générale, Comptes rendus du Congrès international des mathématiciens, Strasbourg, Toulouse, 1921, pp.41-56; reprint Nendeln/Liechtenstein: Kraus Reprint Limited, 1967; Collected Works 2, pp.579-594. | JFM

[18] Dickson (Leonard Eugene) [1923b] Algebras and Their Arithmetics, Chicago: University of Chicago Press, 1923. | JFM | Zbl

[19] Dickson (Leonard Eugene) [1924] Algebras and their Arithmetics, Bulletin of the American Mathematical Society, 30 (1930), pp.247-257; Collected Works 5, pp.591-602. | JFM | MR

[20] Dickson (Leonard Eugene) [1928] Outline of the Theory to Date of the Arithmetics of Algebras, in Fields (J.C.), ed., Proceedings of the International Mathematical Congress held in Toronto, August 11-16, 1924, vol. 1, pp.95-102, Toronto: The University of Toronto Press, 1928; Collected Works 3, pp.469-476. | JFM

[21] Dickson (Leonard Eugene) [1929] Introduction to the Theory of Numbers, Chicago: University of Chicago Press, 1929. | JFM | Zbl

[22] Dickson (Leonard Eugene) [1930] Studies in the Theory of Numbers, Chicago: University of Chicago Press (The University of Chicago Science Series), 1930. | JFM

[23] Dickson (Leonard Eugene) [1936] The Waring Problem and its Generalizations, Bulletin of the American Mathematical Society, 42 (1936), pp.833-842. | JFM | MR | Zbl

[24] Dickson (Leonard Eugene) [1939] Modern Elementary Theory of Numbers, Chicago: University of Chicago Press, 1939. | Zbl

[25] Duren (Peter) [1989] A Century of Mathematics in America-Part III, Providence: American Mathematical Society, 1989. | MR | Zbl

[26] Fenster (Della Dumbaugh) [1997] Role Modeling in Mathematics: The Case of Leonard Eugene Dickson (1874-1954), Historia Mathematica, 24 (1997), pp.7-24. | MR | Zbl

[27] Fenster (Della Dumbaugh) [1998] Leonard Eugene Dickson and his work in the Arithmetic of Algebras, Archive for History of Exact Sciences, 52 (1998), pp.119-159. | MR | Zbl

[28] Fenster (Della Dumbaugh) [1999] Why Dickson Left Quadratic Reciprocity Out of His History of the Theory of Numbers, American Mathematical Monthly, 106 (1999), pp.618-627. | MR | Zbl

[29] Fenster (Della Dumbaugh) [forthcoming] American Initiatives Toward Internationalization, forthcoming.

[30] Fenster (Della Dumbaugh) & Parshall (Karen Hunger) [1994] A Profile of the American Mathematical Research Community: 1891-1906, in Knobloch (Eberhard) and Rowe (David E.), eds., The History of Modern Mathematics, vol. 3, Boston: Academic Press, 1994, pp.179-227. | MR | Zbl

[31] Gauss (Carl Friedrich) [1966] Disquisitiones arithmeticae, trans. by Arthur A. Clarke, New Haven: Yale University Press, 1966. | MR | Zbl

[32] Grattan-Guinness (Ivor) [1990] Does History of Science Treat of the History of Science: The Case of Mathematics, History of Science, 28 (1990), pp.149-173. | MR

[33] Gray (Jeremy) [1998] The Foundations of Geometry and the History of Geometry, The Mathematical Intelligencer, 20 (1998), pp.54-59. | MR | Zbl

[34] Hardy (Godfrey H.) [1940] A Mathematician's Apology, Cambridge: Cambridge University Press, 1940. | JFM | MR | Zbl

[35] Hurwitz (Adolf) [1896] Über die Zahlentheorie der Quaternionen, Göttinger Nachrichten, (1896), pp.311-340. | EuDML | JFM

[36] Knobloch (Eberhard) and Rowe (David), eds. [1994] The History of Modern Mathematics, vol. 3, Boston: Academic Press, 1994. | MR | Zbl

[37] Lehmer (Derrick N.) [1920] Dickson's History of the Theory of Numbers, Bulletin of the American Mathematical Society, 26 (1919-1920), pp.125-132. | JFM

[38] Lehto (Olli) [1998] Mathematics Without Borders: A History of the International Mathematical Union, New York: Springer-Verlag, 1998. | MR | Zbl

[39] Mac Lane (Saunders) [1992] Interview by author, 5-6 March, Charlottesville, Virginia, Tape Recording.

[40] Merzbach (Uta C.) [1989] The Study of the History of Mathematics in America: A Centennial Sketch, in Duren (Peter), ed., A Century of Mathematics in America, Part III, Providence: American Mathematical Society, 1989, pp.639-666. | MR | Zbl

[41] Minkowski (Hermann) [1896] Ueber Eigenschaften von ganzen Zahlen, die durch räumliche Anschauung erschlossen sind, in Moore (E.H.), Bolza (Oskar), Maschke (Heinrich) & White (Henry S.), eds., Mathematical Papers Read at the International Mathematics Congress Held in Connection with the World's Columbian Exposition: Chicago, 1893, New York: Macmillan & Co., 1896, pp.201-207. | JFM

[42] Moore (Eliakim H.), Bolza (Oskar), Maschke (Heinrich) & White (Henry S.), eds. [1896] Mathematical Papers Read at the International Mathematics Congress Held in Connection with the World's Columbian Exposition: Chicago, 1893, New York: Macmillan & Co., 1896.

[43] Parshall (Karen Hunger) [1991] A Study in Group Theory: Leonard Eugene Dickson's Linear Groups, The Mathematical Intelligencer, 13 (1991), pp.7-11. | MR | Zbl

[44] Parshall (Karen Hunger) [1996] How We Got Where We Are: An International Overview of Mathematics in National Contexts (1875-1900), Notices of the American Mathematical Society, 43 (1996), pp.287-296. | MR | Zbl

[45] Parshall (Karen Hunger) & Rowe (David E.) [1994] The Emergence of an American Mathematical Research Community: J.J. Sylvester, Felix Klein, and E.H. Moore, Providence: American Mathematical Society; London: London Mathematical Society, 1994. | MR | Zbl

[46] Reingold (Nathan) & Reingold (Ida) [1981] Science in America: A Documentary History, 1900-1939, Chicago: University of Chicago Press, 1981.

[47] University Of Chicago [1931] Announcements: The University of Chicago, vol. 31, number 19, May 15, 1931, Doctors of Philosophy June, 1893-April, 1931, Chicago: University of Chicago Press, 1931.

[48] University Of Chicago [1938] Register of Doctors of Philosophy 1938-1939, vol. 38, number 14, May 25, 1938.

[49] University Of Chicago [1941] Records of the University of Chicago Convocation Programs, Convocations 191-207, 1938-1941.

[50] University Of Texas [1899] The University of Texas, vol. 1, no. 3, August, 1899

[51] University Of Texas [1914] “Who's Who at Texas?” The Alcalde, January 1914, pp.266-268.

[52] Villat (Henri), ed. [1921] Comptes rendus du Congrès international des mathématiciens, Strasbourg, Toulouse, 1921; reprint Nendeln/Liechtenstein: Kraus Reprint Limited, 1967. | JFM