Andrew Warwick, the author of Masters of Theory: Cambridge and the Rise of Mathematical Physics, is a senior lecturer in the history of sciences at the Imperial College in London. Warwick started the research project presented in Masters of Theory in the mid-1980s during his doctoral study period at the Department of History and Philosophy of Science at Cambridge University. He is a student of Simon Schaffer, the co-author of Leviathan and the Air Pump: Hobbes, Boyle, and the Experimental Life.
In Masters of Theory Warwick argued that “The cultural history of mathematical physics is not an alternative to its technical history but an explanation of how the latter was made possible.” He explored the specifics of the paper-and-pencil method of learning, teaching and testing mathematical knowledge and the role of the newly-introduced Mathematical Tripos examinations along with their effect on the way students studied and conducted their own research later in their academic careers. He also studied the intricacies of reception and teaching of new theories and the important part that tacit knowledge played in the transmission of new ideas in mathematical physics. The author used numerous primary sources such as students’ exam papers, private written accounts that illustrated the social and academic experiences of Cambridge undergraduates and numerous archival sources that gave the reader an insight about the presentation of mathematics and physics that Cambridge students were exposed to in the 19th century.
In order to demonstrate the role of culture and academic tradition in the history of mathematical physics, Warwick revealed that the personas of teachers, their pedagogical strategies, the concrete concepts they presented and the ways the knowledge of these concepts were tested were equally important for understanding the academic culture that prevailed in the 19th century Cambridge science community. The author supported his argument by providing the shift from oral mathematics examinations to written ones. The former style of examination focused on testing the rhetoric skills of the students. The problems were designed in a way that would allow students to solve them without recording the details of their answer on paper. The switch between oral and written examination practices was gradual. The availability of paper and pencils during the examination allowed the administration to offer more difficult problems that could not be solved mentally. Detailed formal solutions became a requirement. If the knowledge were to be assessed in a different way, it is natural that the way of learning the material needed to change as well. Warwick referred to numerous reports of students who felt that private coaching was absolutely necessary for the successful completion of written exams. As a result, private tutoring was on the rise during the mid-19th century. The author effectively demonstrated that tutors not only offered a different pedagogical approach that allowed for more one-on-one instruction time, but also introduced new topics, such as Continental analysis, that were not traditionally taught at that time.
Warwick argued against the “distinction between theoretical and experimental works.” He stated that in order to deepen the understanding of theoretical and experimental practices a symmetric account of the two needs to be constructed. Moreover, it should be based on numerous similarities in theoretical and experimental works. Both works take nearly an equal amount of time and meet equal amounts of opposition while travelling to new sites and practitioners. To illustrate this point Warwick offered the reception of the first edition of Isaac Newton’s Principia Mathematica as an example. Newton’s contemporaries inside and outside of Cambridge found the text impenetrable. They were waiting for the second edition and hoped that the explanation of “many obscurities” would be provided there. Newton did not always state the mathematical methods for solving problems in dynamics in an explicit manner. These methods were, rather, implied. The scientific community members who planned to read and understand Newton’s ideas needed to possess the ‘tacit’ knowledge regarding the methods that Newton was using.
In Masters of Theory, emphasized the important role of pedagogical methods that were used to teach mathematics and physics in the 19th century. Warwick traced the origins of the research methodology that was later employed by Cambridge graduates to the ways in which they were taught mathematics in their undergraduate years. He demonstrated that changing pedagogical practices and assessment methods had an immense influence on the reception and interpretation of new research ideas that were faced by Cambridge graduates later in their careers. The author emphasized the personal aspect of learning, teaching and research experiences of students, coaches and scientists more than the authors of previous books.
Although Warwick’s book provided a thorough account of Cambridge pedagogical practices and their aftermath, the over-abundance of details sometimes obscures the main points that the author tries to convey. The numerous examples, although relevant, were mostly too lengthy and caused a disconnection with the main narrative.