Joseph Wedderburn | |
|---|---|
 Joseph Henry Maclagan Wedderburn (1882–1948) | |
| Born | (1882-02-02)2 February 1882 Forfar, Angus, Scotland |
| Died | 9 October 1948(1948-10-09) (aged 66) |
| Nationality | British |
| Citizenship | American |
| Alma mater | University of Edinburgh |
| Known for | Wedderburn-Etherington number Artin–Wedderburn theorem |
| Awards | MacDougall-Brisbane Gold Medal, Fellow of the Royal Society[1] |
| Scientific career | |
| Fields | Mathematician |
| Institutions | Princeton University |
| Doctoral advisor | George Chrystal |
| Doctoral students | Merrill Flood Nathan Jacobson Ernst Snapper |
Joseph Henry Maclagan WedderburnFRSEFRS (2 February 1882 – 9 October 1948) was a Scottish mathematician, who taught atPrinceton University for most of his career. A significantalgebraist, he proved that a finitedivision algebra is afield (Wedderburn's little theorem), and part of theArtin–Wedderburn theorem onsimple algebras. He also worked ongroup theory andmatrix algebra.[2][3]
His younger brother was the lawyerErnest Wedderburn.
Joseph Wedderburn was the tenth of fourteen children of Alexander Wedderburn of Pearsie, a physician, and Anne Ogilvie. He was educated atForfar Academy then in 1895 his parents sent Joseph and his younger brotherErnest to live inEdinburgh with their paternal uncle, J. R. Maclagan Wedderburn, allowing them to attendGeorge Watson's College. This house was at 3 Glencairn Crescent in the West End of the city.[4]
In 1898 Joseph entered theUniversity of Edinburgh. In 1903, he published his first three papers, worked as an assistant in the Physical Laboratory of the University, obtained anMA degree withfirst class honours in mathematics, and was elected a Fellow of theRoyal Society of Edinburgh, upon the proposal ofGeorge Chrystal,James Gordon MacGregor,Cargill Gilston Knott andWilliam Peddie. Aged 21 on election he remains one of the youngest Fellows ever.[5]
He then studied briefly at theUniversity of Leipzig and theUniversity of Berlin, where he met the algebraistsFrobenius andSchur. ACarnegie Scholarship allowed him to spend the 1904–1905 academic year at theUniversity of Chicago where he worked withOswald Veblen,E. H. Moore, and most importantly,Leonard Dickson, who was to become the most important American algebraist of his day.
Returning to Scotland in 1905, Wedderburn worked for four years at theUniversity of Edinburgh as an assistant toGeorge Chrystal, who supervised hisD.Sc, awarded in 1908 for a thesis titledOn Hypercomplex Numbers. He gained a PhD in algebra from the University of Edinburgh in 1908.[6] From 1906 to 1908, Wedderburn edited theProceedings of the Edinburgh Mathematical Society. In 1909, he returned to the United States to become a Preceptor in Mathematics atPrinceton University; his colleagues includedLuther P. Eisenhart,Oswald Veblen,Gilbert Ames Bliss, andGeorge Birkhoff.
Upon the outbreak of theFirst World War, Wedderburn enlisted in the British Army as a private. He was the first person at Princeton to volunteer for that war, and had the longest war service of anyone on the staff. He served with theSeaforth Highlanders in France, asLieutenant (1914), then asCaptain of the 10th Battalion (1915–18). While a Captain in the Fourth Field Survey Battalion of theRoyal Engineers in France, he devisedsound-ranging equipment to locate enemy artillery.
He returned to Princeton after the war, becoming Associate Professor in 1921 and editing theAnnals of Mathematics until 1928. While at Princeton, he supervised only three PhDs, one of them beingNathan Jacobson. In his later years, Wedderburn became an increasingly solitary figure and may even have suffered from depression. His isolation after his 1945 early retirement was such that his death from a heart attack was not noticed for several days. HisNachlass was destroyed, as per his instructions.
Wedderburn received theMacDougall-Brisbane Gold Medal and Prize from theRoyal Society of Edinburgh in 1921, and was elected to theRoyal Society of London in 1933.[1]
In all, Wedderburn published about 40 books and papers, making important advances in the theory of rings, algebras and matrix theory.
In 1905, Wedderburn published a paper that included three claimed proofs of a theorem stating that a noncommutativefinitedivision ring could not exist. The proofs all made clever use of the interplay between theadditive group of a finitedivision algebraA, and themultiplicative groupA* =A-{0}. Parshall (1983) notes that the first of these three proofs had a gap not noticed at the time. Meanwhile, Wedderburn's Chicago colleague 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.
This theorem yields insights into the structure offiniteprojective geometries. In their paper on "Non-Desarguesian and non-Pascalian geometries" in the 1907Transactions of the American Mathematical Society, Wedderburn andVeblen showed that in these geometries,Pascal's theorem is a consequence ofDesargues' theorem. They also constructed finite projective geometries which are neither "Desarguesian" nor "Pascalian" (the terminology isHilbert's).
Wedderburn's best-known paper was his sole-authored "On hypercomplex numbers," published in the 1907Proceedings of the London Mathematical Society, and for which he was awarded the D.Sc. the following year. This paper gives a complete classification ofsimple andsemisimple algebras. He then showed that every finite-dimensionalsemisimple algebra can be constructed as a direct sum ofsimple algebras and that everysimple algebra isisomorphic to amatrix algebra for somedivision ring. TheArtin–Wedderburn theorem generalises these results to algebras with the descending chain condition.
His best known book is hisLectures on Matrices (1934),[7] which Jacobson praised as follows:
That this was the result of a number of years of painstaking labour is evidenced by the bibliography of 661 items (in the revised printing) covering the period 1853 to 1936. The work is, however, not a compilation of the literature, but a synthesis that is Wedderburn's own. It contains a number of original contributions to the subject.
— Nathan Jacobson, quoted in Taylor 1949
About Wedderburn's teaching:
He was apparently a very shy man and much preferred looking at the blackboard to looking at the students. He had thegalley proofs from his book "Lectures on Matrices" pasted to cardboard for durability, and his "lecturing" consisted of reading this out loud while simultaneously copying it onto the blackboard.
— Hooke, 1984
