University of Chicago
Where was Joseph Wedderburn educated from 1904 to 1905?
Joseph Wedderburn Joseph Henry Maclagan Wedderburn FRSE FRS ( 2 February 1882 – 9 October 1948 ) was a Scottish mathematician , who taught at Princeton University for most of his career . A significant algebraist , he proved that a finite division algebra is a field , and part of the Artin–Wedderburn theorem on simple algebras . He also worked on group theory and matrix algebra . His younger brother was the lawyer Ernest Wedderburn . Life . Joseph Wedderburn was the tenth of fourteen children of Alexander Wedderburn of Pearsie , a physician , and Anne Ogilvie . He was educated at Forfar Academy then in 1895 his parents sent Joseph and his younger brother Ernest to live in Edinburgh with their paternal uncle , J R Maclagan Wedderburn , allowing them to attend George Watsons College . This house was at 3 Glencairn Crescent in the West End of the city . In 1898 Joseph entered the University of Edinburgh . In 1903 , he published his first three papers , worked as an assistant in the Physical Laboratory of the University , obtained an MA degree with First Class Honours in mathematics , and was elected a Fellow of the Royal Society of Edinburgh , upon the proposal of George Chrystal , James Gordon MacGregor , Cargill Gilston Knott and William Peddie . Aged only 21 he remains one of the youngest Fellows ever . He then studied briefly at the University of Leipzig and the University of Berlin , where he met the algebraists Frobenius and Schur . A Carnegie Scholarship allowed him to spend the 1904–1905 academic year at the University of Chicago where he worked with Oswald 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 the University of Edinburgh as an assistant to George Chrystal , who supervised his D.Sc , awarded in 1908 for a thesis titled On Hypercomplex Numbers . He gained a PhD in algebra from the University of Edinburgh in 1908 . From 1906 to 1908 , Wedderburn edited the Proceedings of the Edinburgh Mathematical Society . In 1909 , he returned to the United States to become a Preceptor in Mathematics at Princeton University ; his colleagues included Luther P . Eisenhart , Oswald Veblen , Gilbert Ames Bliss , and George Birkhoff . Upon the outbreak of the First 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 the Seaforth Highlanders in France , as Lieutenant ( 1914 ) , then as Captain of the 10th Battalion ( 1915–18 ) . While a Captain in the Fourth Field Survey Battalion of the Royal Engineers in France , he devised sound-ranging equipment to locate enemy artillery . He returned to Princeton after the war , becoming Associate Professor in 1921 and editing the Annals of Mathematics until 1928 . While at Princeton , he supervised only three PhDs , one of them being Nathan 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 . His Nachlass was destroyed , as per his instructions . Wedderburn received the MacDougall-Brisbane Gold Medal and Prize from the Royal Society of Edinburgh in 1921 , and was elected to the Royal Society of London in 1933 . Work . 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 noncommutative finite division ring could not exist . The proofs all made clever use of the interplay between the additive group of a finite division algebra A , and the multiplicative group A* = A- { 0 } . Parshall ( 1983 ) notes that the first of these three proofs had a gap not noticed at the time . Meanwhile , Wedderburns Chicago colleague Dickson also found a proof of this result but , believing Wedderburns first proof to be correct , Dickson acknowledged Wedderburns priority . But Dickson also noted that Wedderburn constructed his second and third proofs only after having seen Dicksons proof . Parshall concludes that Dickson should be credited with the first correct proof . A corollary to this theorem yields the complete structure of all finite projective geometry . In their paper on Non-Desarguesian and non-Pascalian geometries in the 1907 Transactions of the American Mathematical Society , Wedderburn and Veblen showed that in these geometries , Pascals theorem is a consequence of Desargues theorem . They also constructed finite projective geometries which are neither Desarguesian nor Pascalian ( the terminology is Hilberts ) . Wedderburns best-known paper was his sole-authored On hypercomplex numbers , published in the 1907 Proceedings of the London Mathematical Society , and for which he was awarded the D.Sc . the following year . This paper gives a complete classification of simple and semisimple algebras . He then showed that every semisimple algebra finite-dimensional can be constructed as a direct sum of simple algebras and that every simple algebra is isomorphic to a matrix algebra for some division ring . The Artin–Wedderburn theorem generalises this result , with the ascending chain condition . His best known book is his Lectures on Matrices ( 1934 ) , which Jacobson praised as follows : About Wedderburns teaching :