He 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 (bracketed with George Chrystal) in 1875.

[3] He lectured at Cambridge for the following ten years, before being appointed professor of mathematics at the Royal Naval College in Greenwich.

This work was of sufficient distinction to merit his election as a fellow of the Royal Society in 1893, though it is little remembered today.

This was not a widely studied subject in Britain in the late 19th century, and it took some years for his research in this area to gain widespread recognition.

[4] Burnside is also remembered for the formulation of Burnside's problem that concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it, and also for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Augustin Cauchy.