Background
William Burnside was born on July 2, 1852, in London, England.
1904
William Burnside was awarded the Royal Medal, also known as The Queen's Medal and The King's Medal (depending on the gender of the monarch at the time of the award), for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences."
1899
William Burnside was awarded the De Morgan Medal, which is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society.
1904
William Burnside was awarded the Royal Medal, also known as The Queen's Medal and The King's Medal (depending on the gender of the monarch at the time of the award), for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences."
Royal Society, London, England, United Kingdom
William Burnside was elected a fellow of the Royal Society in 1893.
Pembroke College, Trumpington Street, Cambridge, England, United Kingdom
Burnside attended Pembroke College at the University of Cambridge, where he was the Second Wrangler in 1875.
St. John's College, St. John's Street, Cambridge, England, United Kingdom
Burnside attended St. John's College at the University of Cambridge.
William Burnside, British mathematician.
William Burnside was born on July 2, 1852, in London, England.
Burnside went to school at Christ's Hospital until 1871 and attended St. John's and Pembroke Colleges at the University of Cambridge, where he was the Second Wrangler in 1875. He received an honorary doctorate (D.Sc.) from the University of Dublin in June 1901.
After the graduation from the St. John's and Pembroke Colleges at the University of Cambridge, Burnside lectured at Cambridge for the following ten years, before being appointed a professor of mathematics at the Royal Naval College in Greenwich. While this was a little outside the main centers of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career.
With the hope of stirring up interest in group theory in England, Burnside published his Theory of Groups in 1897. It was the first treatise on groups in English and also the first to develop the theory from the modern standpoint of abstract groups vis a vis permutation groups, although this approach had already been pioneered by H. Weber in his Lehrbuch der Algebra (1896). One topic Burnside excluded from his book was that of linear groups, because it did not seem that any result could be obtained most directly by considering linear transformations. This opinion soon became outdated, however, with G. Frobenius’ development of the theory of group representations and characters (1896-1899), and Burnside was one of the first to recognize the importance of Frobenius’ ideas and to contribute to their development, simplification, and application.
Using group characters, Burnside was able to prove, for example, that every transitive group of prime degree is either solvable or doubly transitive (1901) and that every group of order pnqb (p and q prime) is solvable (1904). The latter result greatly extended results of Sylow (b = 0, 1872), Frobenius (b = 1, 1895), and Jordan (b — 2, 1898). It was also Burnside who discovered that groups of odd order admit no nontrivial real irreducible representations, and he was led by its consequences to suspect that every group of odd order is solvable. W. Feit and J. G. Thompson finally established this in 1962 with a proof that involves, among other things, frequent applications of Burnside’s discovery.
Because he was convinced of the important role that representation theory was destined to play in the future advancement of group theory, Burnside devoted considerable space to its systematic presentation in the second edition of Theory of Groups (1911). This edition was widely read and is now considered a classic.
William Burnside was elected a fellow of the Royal Society in 1893.