Arthur Cayley, Mathematician Laureate of the Victorian Age, and: James Joseph Sylvester, Jewish Mathematician in a Victorian World (review)

The careers of the two most eminent mathematicians in nineteenth-century England, Arthur Cayley and J. J. Sylvester, were so fully intertwined that some have considered their stories inseparable, worthy of a joint biography. In 2006, however, two distinct biographies appeared, one by Tony Crilly and one by Karen Parshall. Each of these works represents many years of effort, and each is comprehensive. Reading both tomes is a treat, both for the individual biographies that they develop, and for the insights of each of the subjects from the point of view of the other. As a mathematician with an interest in the concept of higher dimensions in late-Victorian England, I looked forward to reading histories that would set the stage for developments in this area. I did find many clues to the society that was satirized in my favorite book, "Flatland" (1884), by Edwin Abbott Abbott, even though I missed a more complete treatment of some of the stories about these two figures as they related to my primary interest. That is almost inevitable, in that the range of subjects each of these mathematicians studied was vast by modern standards, and their output was so voluminous that no biography can treat them all. Nonetheless, I looked for some dramatic threads that would guide an approach to these interlaced stories, and several emerged.

For Sylvester, a great deal of the story is his search for a perfect academic position. As Second Wrangler and Smith's Prizeman at Cambridge in 1837, his mathematical credentials were well established in spite of his ineligibility to receive a degree since he could not subscribe to the Articles of the Anglican faith. He made futile searches in various parts of England and even in the US for positions that would let him teach and develop his mathematics, finding none for most of his career and ending up practicing law for a time. It would be easy to blame this on his Jewish identity except that Arthur Cayley, First Wrangler and Smith's Prizeman in 1842, was similarly unsuccessful in obtaining a desirable academic position, even though he had no difficulty qualifying for a Cambridge degree. He, too, practiced law.

Their problems stemmed from the system of examinations that dominated undergraduate mathematics education at Cambridge. The tutors who specialized in preparing students for the Tripos examinations discouraged their students from following any other courses of mathematics. Neither Cayley nor Sylvester wanted a job of such limited scope. Sylvester's extroverted personality led him to try teaching in some other institutions, where instructors were expected to impart some applied knowledge, but that repeatedly did not work out.

Cayley did finally get his professorship at Cambridge, a position which suited him. But it was Sylvester who found his dream job, not at Cambridge but at the Johns Hopkins University in the US. (It is no accident that the Johns Hopkins Press published both of these biographies.) With the support of the president of the university, Sylvester flourished in an atmosphere of convivial and intense research, in collaboration with active and successful graduate students, and with responsibility for the new American Journal of Mathematics. While he later got what he thought he always wanted—an Oxford University professorship—this was by no means as happy and fulfilling as the job he left in the US.

This brief academic career survey ignores much of the research careers of these dominant figures in nineteenth-century mathematics, and there are some dramatic lines that we can identify there as well. Although many mathematicians shared ideas constantly through correspondence, delivered sometimes several times a day, there was no opportunity for collaboration that could lead to co-authorship. Inevitably a certain amount of effort was...