Arthur Cayley's appointment to the Sadleirian Professorship in 1863 may be taken to mark the start of a new, recognisably modern period in the study of mathematics at Cambridge. The appointment is significant not just because Cayley was the first mathematician with a truly international reputation to work at Cambridge since the days of Newton; the Sadleirian Chair was itself a new position, created to replace nine University lectureships in mathematics that had become moribund. In his inaugural lecture Cayley defined his task in these terms: he was to explain and teach the principles of pure mathematics and to apply himself to the advancement of that science.

Cambridge could hardly have found a better person for the job. Cayley, then 42, was a dazzling mathematician: energetic, prolific, eager to promote the subject, congenial to talk to, knowledgeable in nearly all branches of the subject and original in many. He also belonged to the first generation of English mathematicians for over 100 years who were not insular in their outlook. It was only within Cayley's day that British mathematics connected to European mainstream developments, whatever may have been its earlier claims to innovation. Cayley in particular wrote extensive survey articles, describing the state of the art in various branches of the subject. This is an invaluable service for any nation that is cut off from the research tradition. In every respect, Cayley was the man for the job. And yet he did not create a school of mathematics.