Abstract
During the closing quarter of the nineteenth century, a self-sustaining community of mathematical researchers emerged in the United States due largely to the combined influences of three mathematicians — two foreign and one American. In 1876, the English mathematician, James Joseph Sylvester, arrived at Baltimore’s Johns Hopkins University to set up the first real graduate-level program in mathematics in the United States. After Sylvester’s return to England in 1883, would-be American mathematical researchers turned to Europe — and particularly to Germany and Felix Klein — for their training. By the final decade of the century, however, changes in American higher education, such as the increasingly widespread adoption of the research ethic at the university level, provided educational opportunities, jobs, and incentives for research mathematicians as well as for researchers in the other academic disciplines. At the forefront of these developments, the University of Chicago opened in 1892 with research, graduate teaching, and undergraduate instruction among its articulated institutional goals. In mathematics, Eliakim Hastings Moore and his colleagues, Oskar Bolza and Heinrich Maschke, worked successfully not only toward these aims but also toward the building of a national mathematical organization complete with professional society, publication outlets, and regular forums for active mathematical interchange. As David Rowe and I have argued elsewhere, this groundwork was firmly in place by 1900.1
The original research for this article was funded by National Science Foundation Scholars Award #SES-8509795.
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References
Karen Hunger Parshall and David E. Rowe: The Emergence of the American Mathematical Research Community 1876–1900: James Joseph Sylvester, Felix Klein, and Eliakim Hastings Moore. Providence: American Mathematical Society (forthcoming).
The Edinburgh University Calendar 1900–1901. Edinburgh: James Thin, 1900, p. 90.
A. Logan Turner: History of the University of Edinburgh 1883–1933. Edinburgh: Oliver and Boyd, 1933, pp. 210–211.
Many of the biographical details which follow may be found in the following limited accounts: H. S. Taylor: Joseph Henry Maclagen [sic] Wedderburn, Obituary Notices of Fellows of the Royal Society: 1948–1949, vol. 6, pp. 619–625; H. W. Turnbull: Joseph Henry Maclagan Wedderburn, M.A., D.Sc., F.R.S., Year Book of the Royal Society of Edinburgh 1948 and 1949, Edinburgh: Oliver and Boyd, 1950, 51-52; and Dictionary of Scientific Biography, V. “Wedderburn, Joseph Henry Maclagan„, by Henry Nathan. According to officials at the bank which settled Wedderburn’s estate (the Bank of Princeton), the papers remaining at his death were subsequently destroyed, thereby limiting historical study of Wedderburn’s life and work almost exclusively to published sources. Because of the superficiality and unreliabilty of much of this published information, I attempt here both to correct published factual errors and to integrate Wedderburn’s work into the description of his troubled life through an examination of new archival and published sources. For a detailed genealogy of the Wedderburn family, see Alexander Wedderburn: The Wedderburn Book: A History of the Wedderburns in the Counties of Berwick and Forfar, Designed of Wedderburn, Kingennie, Easter, Powrie, Blackness, Balindean, and Gosford; And Their Younger Branches; Together With Some Account of Other Families of the Name 1296–1896, 2 vols., Printed for Private Circulation, 1898.
Alexander J. Warden: Angus or Forfarshire: The Land and People, Descriptive and Historical, 5 vols. Dundee: Charles Alexander & Co., 1884, 4:43.
This house still (as of 1983) stands and continues to serve as a private residence and doctor’s office.
In his article, Taylor gives the year of Wedderburn’s matriculation at the Edinburgh Unviersity as 1898, but the matriculation books held there show that he entered on October 17, 1899 at the age of seventeen. See “Matriculation 1899–1900„, Department of Special Collections, Edinburgh University (hereinafter denoted Special Collections Edinburgh).
The Edinburgh University Calendar 1900–1901, pp. 149–150.
“Class Lists 1898–1901 — Natural Philosophy„, Special Collections Edinburgh.
The Edinburgh University Calendar 1902–1903. Edinburgh: James Thin, 1902, pp. 196–197. Wedderburn is listed as holding the assistantship in 1901, but Taylor gives the date as 1902–1903.
See Michael J. Crowe: A History of Vector Analysis: The Evolution of the Idea of a Vector Space. Notre Dame: University of Notre Dame Press, 1967, p. 120. There, he noted that “[s]imilarly one would expect that Tait in his mathematical physics courses at Edinburgh would have used quaternions wherever possible. This he did not do. One of Tait’s students wrote in a biographical sketch of Tait: ‘Tait, as far as I know, never lectured on the subject [quaternions] at the University of Edinburgh.’„
See Joseph H. M. Wedderburn: On the General Scalar Function of a Vector, Proceedings of the Royal Society of Edinburgh 24 (1903), 409–412; On the Application of Quaternions in the Theory of Differential Equations, Transactions of the Royal Society of Edinburgh 40 (1903), 709–721; Note on the Linear Matrix Equation, Proceedings of the Edinburgh Mathematical Society 22 (1903–1904), 49–53.
J. Sutherland Black and C. G. Knott: Professor George Chrystal, M.A., LL.D., Proceedings of the Royal Society of Edinburgh 32 (1911–1912), 477–503 on p. 492.
Joseph H. M. Wedderburn: On the Isoclinal Lines of a Differential Equation of the Joint Order, Proceedings of the Royal Society of Edinburgh 24 (1903), 400–408; and George Chrystal: On the p-Discriminant of a Differential Equation of the First Order, and on Certain Points in the General Theory of Envelopes Connected Therewith, Transactions of the Royal Society of Edinburgh 38 (1896).
Although Wedderburn’s papers do not seem to survive (see note 4 above), three bound volumes of the reprints he collected during the first decade of the century were salvaged from his estate by his student, Nathan Jacobson. These provide some important clues to Wedderburn’s early career. In particular, he preserved two papers on which he had written the notation “Berlin 3/5/04„. They were Friedrich Engel’s Die höheren Differentialquotienten, Leipziger Berichte 54 (1902), 17–51, and Gerhard Kowalewski’s Über projektive Transformationsgruppen, Leipziger Berichte 55 (1903), 97–105. For the complete list of reprints contained in these volumes, see Karen Hunger Parshall: Joseph H. M. Wedderburn and the Structure Theory of Algebras, Archive for History of Exact Sciences 32 (1985), 223–349 on pp. 337–343. I am indebted to Professor Jacobson for making these volumes available to me and for several illuminating conversations about Wedderburn.
In particular, Wedderburn saved Burnside’s On the Continuous Groups That Is Defined by Any Given Group of Finite Order, Proceedings of the London Mathematical Society 29 (1898), 207–224, and On the Continuous Group That Is Defined by Any Given Group of Finite Order (Second Paper), Proceedings of the London Mathematical Society 29 (1898), 546–565. These two papers directly linked Burnside’s work to the Continental, Lie-theoretic tradition and to Frobenius’ work on group characters. See Thomas Hawkins: Hypercomplex Numbers, Lie Groups, and the Creation of Group Representation Theory, Archive for History of Exact Sciences 8 (1972), 243–287.
William Burnside: Theory of Groups of Finite Order, 2d ed. Cambridge: University Press, 1911; reprint ed., New York: Dover Publications, Inc., 1955, p. viii.
Leonard Eugene Dickson: Linear Groups with an Exposition of the Galois Field Theory. New York: Dover Publications, Inc., 1955; reprint ed., Leipzig: B. G. Teubner, 1901.
For more on E. H. Moore and the early Chicago Mathematics Department, see Karen Hunger Parshall: Eliakim Hastings Moore and the Founding of a Mathematical Community in America: 1892–1902, Annals of Science 41 (1984), 313–333, reprinted in A Century of Mathematics in America — Part II, Peter Duren, et al., ed. Providence: American Mathematical Society, 1989, 155–175; and Parshall and Rowe, Chapters 6–8.
Saul Epsteen and Joseph H. M. Wedderburn: On the Structure of Hypercomplex Number Systems, Transactions of the American Mathematical Society 6 (1905), 172–178.
Department of Mathematics, “Logbook of the Mathematical Club of the University of Chicago„, Chicago, 1903–1954, p. 8. (Handwritten.)
Joseph H. M. Wedderburn: A Theorem on Finite Algebras, Transactions of the American Mathematical Society 6 (1905), 349–352.
Oswald Veblen and Joseph H. M. Wedderburn: Non-Desarguesian and Non-Pascalian Geometries, Transactions of the American Mathematical Society 8 (1907), 379–388.
Joseph H. M. Wedderburn: On Hypercomplex Numbers, Proceedings of the London Mathematical Society 6 (1907), 77–118.
A few letters written by Wedderburn may be found in Box 15 of the Oswald Veblen Papers, Manuscript Division, Library of Congress. The particular letter in which Wedderburn gives this information is dated “108 Middle D. U of C June 11, 1905„.
Joseph H. M. Wedderburn: On a Theorem in Hypercomplex Numbers, Proceedings of the Royal Society of Edinburgh 26 (1906), 48–50; and Note on Hypercomplex Numbers, Proceedings of the Edinburgh Mathematical Society 25 (1906–1907), 2–4.
Minutes of Senatus, vol. 13, pp. 383–384, Special Collections Edinburgh. (Hand-written and dated 31 Jan. 1903 to 13 Jan. 1906.) I would like to thank the Edinburgh University for permission to quote from its archives.
Minutes of Senatus, vol. 14, p. 203, Special Collections Edinburgh. (Handwritten and dated 3 Feb. 1906 to 10 Oct. 1908.)
Wedderburn’s doctoral dissertation may be found at Edinburgh University alphabetized under the letter “M.„ (Wedderburn maintained the hyphenated family name of Maclagan-Wedderburn until sometime after his return to the United States in 1909. By 1913, he had permanently dropped the hyphen.) The version of the paper On Hypercomplex Numbers which he gave there differed somewhat from the final version. The four other papers submitted for the degree were: the articles jointly authored with Epsteen and Veblen (see notes 20 and 23, respectively), A Theorem on Finite Algebras (see note 22), and On a Theorem in Hypercomplex Numbers (see note 26).
On Hypercomplex Numbers, p. 99.
See Theodor Molien: Ueber Systeme höherer complexer Zahlen, Mathematische Annalen 41 (1893), 83–156, and Elie Cartan: Sur les Groupes bilinéaires et les Systemes de Nombres complexes, Annales de la Faculte des Sciences de Toulouse 12B (1898), B1–B99.
Woodrow Wilson: The Preceptorial System at Princeton, Educational Review 39 (1910), 385–390 on p. 387.
For the history of the Princeton Mathematics Department, see William Aspray: The Emergence of Princeton as a World Center for Mathematical Research, 1896–1939, pp. 346–366 in History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher, ed. Minneapolis: University of Minnesota Press, 1988.
See the dedication page of the Annals of Mathematics, 2d ser., 48 (1947).
Joseph H. M. Wedderburn: On Long Waves, American Journal of Mathematics 36 (1914), 211–230.
See The Edinburgh University Calendar 1909–1910. Edinburgh: James Thin, 1909, pp. 745–747.
Joseph H. M. Wedderburn, Faculty Files, Princeton University Archives. This differs from the published accounts of Wedderburn’s life, which record him as having enlisted as a Private. Given his rank of Second Lieutenant in the Officer Training Corps at Edinburgh, the entering rank of Lieutenant seems more likely. The official British records of Wedderburn’s service were destroyed during the Second World War according to the War Office.
Taylor, p. 621.
Proceedings of the Royal Society of Edinburgh 41 (1920–1921), 218.
Joseph H. M. Wedderburn: Algebras Which Do Not Possess a Finite Basis, Transactions of the American Mathematical Society 26 (1924), 395–426.
Joseph H. M. Wedderburn: The Absolute Value of the Product of Two Matrices, Bulletin of the American Mathematical Society 31 (1925), 304–308; Note on Matrices in a Given Field, Annals of Mathematics 27 (1926), 245–248; and Lectures on Matrices, American Mathematical Society Colloquium Publications. New York: American Mathematical Society, 1934.
For the personal aspects of Wedderburn’s life in Princeton and at the University in the 1930’s and 1940’s, I am indebted to the following people who knew Wedderburn and who willingly shared their recollections of him with me: his colleagues, Professors Solomon Bochner and Albert Tucker; his doctoral students, Professors Merrill Flood, Nathan Jacobson, and Ernst Snapper; post-graduate fellows who worked under him, Professors J. L. Dorroh and Neil McCoy; the Princeton undergraduate, Professor Howard Osborn; and the department secretary of forty years, Mrs. Agnes F. Henry.
In the Veblen Papers, there remains an exchange of letters between Veblen, Wedderburn, and Dickson concerning the revisions of this article which attest to Veblen’s complete and lasting friendship for Wedderburn. See note 25 above.
Joseph H. M. Wedderburn: Non-Commutative Domains of Integrity, Journal fur die reine und angewandte Mathematik 167 (1931), 129–141; and Leonard E. Dickson: Algebras and Their Arithmetics. Chicago: University of Chicago Press, 1923.
For a history of mathematics at the Institute for Advanced Study, see Armand Borel: The School of Mathematics at the Institute for Advanced Study, pp. 119–147 in A Century of American Mathematics — Part III, Peter Duren et al., ed. Providence: American Mathematical Society, 1989.
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Parshall, K.H. (1992). New Light on the Life and Work of Joseph Henry Maclagan Wedderburn (1882 – 1948). In: Demidov, S.S., Rowe, D., Folkerts, M., Scriba, C.J. (eds) Amphora. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8599-7_24
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