Whitehead's Cambridge Training

"I have lived three distinct lives in this single span," said Whitehead to Lucien Price on December 15, 1939; "one from childhood to the first world war; one from 1914 to my residence in America in 1924; and a third here since 1924." (D 131) Whitehead's philosophical writings all belong to the second and the third stage of his life. However, it would be a mistake to think that these writings can be understood while ignoring the first stage. Each stage of Whitehead's life integrated the previous one.
In this paper I will focus on an early episode of the first stage of Whitehead's life, his Cambridge training, which, according to me, is of utmost importance to understand Whitehead's later philosophy of mathematics as well as his later relativistic theory of gravity. Actually, the scope of this paper is more restricted, for it only deals in detail with one aspect of Whitehead's Cambridge training, the impact of coach Edward Routh and intercollegiate lecturer William Davidson Niven on Whitehead.
Biographical details with regard to Whitehead's Cambridge training can be found in Chapters V and VI of the first volume of Victor Lowe's Whitehead biography (1985). It is not the aim of this paper to repeat all of these details here. Instead of giving a chronological account of the facts constituting the 1880-1884 period of Whitehead's biography, this paper extensively quotes Andrew Warwick's Masters of Theory: Cambridge and the Rise of Mathematical Physics (2003) to clarify Lowe's statements that Edward Routh was "the man from whom Whitehead got most of his mathematical training" (97) and that W. D. Niven was the man who "gave Whitehead the most valuable part of his eductation in mathematical physics" (94).
In other words, the aim of this paper consists in clarifying, by means of Warwick's book, and better than Lowe himself has done, what Lowe meant when he wrote: "Routh and Niven gave him most." (99) The conclusion of this paper is that Whitehead learned from Routh and Niven that the analogical application of common mathematical techniques across mathematical physics is the appropriate method, not only to solve a variety of problems in mathematical physics as an undergraduate and graduate student, but also as a researcher after graduation. Moreover, this paper highlights some elements to justify the belief that this conclusion is important, and that Routh and Niven's analogical application of common mathematical structures in problem-solving and research can help us to better understand both the particularity of Whitehead's philosophy of mathematics, and the path of discovery that led to Whitehead's relativistic theory of gravity.