BOOK REVIEW
Training for the Tripos
Kathryn Olesko
Masters of Theory: Cambridge and the Rise of Mathematical Physics.
Andrew Warwick.
xiv + 572 pp. University of Chicago
Press, 2003. $89 cloth, $29 paper.
By the end of the 19th century, such well-known British physicists
as William Thomson, James Clerk Maxwell, J. J. Thomson, W. H. Bragg
and James Jeans had trained for and survived the Cambridge
University Mathematical Tripos, an analytical written examination
for the bachelor's degree, lasting several days and demanding an
exacting virtuoso performance in the mathematical techniques of a
classical physics based on principles rooted in Newtonian mechanics.
Masters of Theory, Andrew Warwick's long-awaited study
of this test, is a major contribution to the historical scholarship
on science teaching and learning and on mathematical physics. The
central element of Warwick's imaginative and richly documented story
is the emergence of a training style that required students to
prepare for the examination outside the classroom with special
tutors known as "coaches," the most well-known of whom was
Edward Routh. That the Tripos had such a profound effect on the
intellectual orientation and research style of so many physicists is
all the more remarkable when one considers that it was the
apotheosis of Cambridge undergraduate education, in which
research was scarcely the goal of instruction.
Based on the author's doctoral dissertation, Masters of
Theory is a part of the growing literature on science pedagogy
that has drawn its theoretical inspiration from Michel Foucault,
Thomas Kuhn, Jerome Ravetz and others, who early on made provocative
statements about scientific training but lacked sufficient data from
empirical studies to substantiate them. Warwick provides an
extremely important case study.
A part of the liberal undergraduate education at Cambridge, where
men were for the most part trained for the liberal professions
rather than for scholarship, the Mathematical Tripos had its origins
in the 18th century in the university's Senate House Examination, an
oral disputation originally conducted to test a student's knowledge
broadly. Merely passing was not the point. In 1747 university
officials began to publish the rank order of grades on the
examination, listing the highest scorers (known as
"wranglers") at the top and the low-scoring hoi polloi at
the bottom; only those with the highest ranking could compete for
scholarships. By the 1760s, though, the examination had changed
markedly: The emphasis on mathematics had increased, written answers
were required for honors status, and the competition had
intensified. When an examination for classical studies (the
Classical Tripos) was founded in 1824, the Senate House Examination
became known as the Mathematical Tripos.
Through Warwick's masterful treatment, the Tripos becomes a
revealing artifact of Victorian culture. Just as Frederic Lawrence
Holmes's studies of laboratory notebooks have done, Masters of
Theory diverts attention from a scientist's published papers to
knowledge as it is being made, demonstrating once again how
published scientific literature masks the route to discovery and
novelty. But unlike the notebooks Holmes analyzed (intensely private
records, which seemed to have no contact with life outside the
laboratory), Warwick's Tripos examinations were public events
saturated with palpable stress, surrounded by elaborate ritual (both
before and after the exam) and imbued with social significance
(especially status)—elements that make them richer sources of
cultural history than laboratory notebooks could ever be. Warwick's
own historical virtuosity is especially evident in chapters devoted
to these cultural dimensions of the Tripos: its linkages to the
history of body and gender during the Victorian era, its cultivation
of a system of morals and values that defined the Victorian
gentleman, and its dependency on forms of sociability in instruction
that underscored the central role of face-to-face encounters and
human bonding in small-group learning under special tutors. These
chapters in particular should provoke historians to reexamine their
own assumptions about the historical meaning of technical knowledge
in context, just as they will challenge educators and textbook
publishers to rethink the rush toward online instruction.
Yet although copies of the Tripos examinations themselves are
abundantly available, the answers—the real evidence for
knowledge-in-the-making—are less so. Warwick successfully
reconstructs the content and more so the experience of working
through those answers by triangulating from sources that touch on
the learning experience: diaries, correspondence, autobiographies
and textbooks. Likewise, although Warwick has only two sets of
coaching notes (Stephen Parkinson's from the 1850s and Robert Webb's
from the 1890s), his wide-ranging knowledge of Cambridge culture
permits him to extrapolate general observations about the coaching
and training experience as a whole from his sources. (Interestingly,
coaching declined in the 1880s.)
Masters of Theory ends with four chapters describing how
Cambridge practitioners reacted to new developments, including
Maxwell's Treatise on Electricity and Magnetism (1873) and
Albert Einstein's general theory of relativity (1916). Of note is
Warwick's sustained and convincing argument that Maxwell's Treatise
was not a response to study of electrical metrology by the British
Association for the Advancement of Science, but rather the outcome
of unresolved pedagogical issues after electromagnetic theory was
reintroduced into the Tripos in 1868. These final chapters, laced
with the intellectual ruminations of Cambridge-trained mathematical
physicists wrestling with new theories, demonstrate how difficult it
was to transcend the intellectually conservative mindset shaped by
the pedagogical regime of the Tripos.
Warwick strongly and repeatedly emphasizes that the broader
international significance of his work is found in the material
culture of the "pen, ink and paper" that constituted the
tools of the Cambridge mathematical physicist, who worked at his
desk, not in a laboratory. He also suggests that examinations were
central to the development of mathematical physics elsewhere. For
instance, at one point he interprets the Prussian system of state
teaching examinations as being shaped in the Cambridge mold, and he
draws strained conclusions. The Cambridge Tripos—which tested
students for analytical virtuosity—was for undergraduates, was
not in service of the professions and was strongly tied to a local
culture. By contrast the Prussian state examinations—which
were designed to assess only competency—were for graduate
students, were aimed at professional certification (for example,
teaching mathematics or science at secondary schools) and were
administered by academics for the entire state, as had been
similar examinations in forestry, architecture and civil engineering
in the 18th century. So to the degree that individuals such as the
theoretical physicist Franz Neumann complained about the absence of
questions on physics (or other subjects) on the Prussian teaching
examination, they were expressing a desire for greater career
opportunities for their own pupils, not for a material culture of
pen and paper, which in any event was already well established, as
18th-century German textbooks for mathematically technical subjects
indicate. For this reason, and others, the more significant
implications of Warwick's work lie, I believe, beyond both the
material culture of pen and paper and the examination system that
relied upon it.
If one measure of the value of a book is the number of new avenues
of research it suggests, Warwick's succeeds remarkably: He
tantalizingly hints at several implications of his study, all of
which warrant further investigation. The most pressing concerns the
actual percentage of Tripos examinees who went on to become
professional physicists or teachers of physics (or mathematics) at
any level, a statistic that would also be useful for understanding
why a research school in mathematical physics emerged at Cambridge
in the 1870s but not earlier. Another issue concerns the
relationship between the techniques of the Tripos and experimental
results. Warwick calls his Tripos examinees "masters of
theory," but because he does not delve into their conception of
physical reality, they seem more like "masters of
technique." The establishment of the Cavendish Laboratory in
1874 and the appearance of Maxwell's Treatise on Electricity and
Magnetism in 1873 are important starting points for
understanding how empirical results, especially ones based on
precision measurement, meshed with the intellectual perspectives
cultivated in the Tripos and its attendant lectures, coaching
sessions and textbooks.
Finally, given the profound and lasting influence of the
Mathematical Tripos on the development of mathematical physics in
Great Britain, it is important to learn why, precisely, a technical
subject came to dominate Cambridge undergraduate studies by the end
of the 18th century. The link between Newton's work and Anglicanism,
detailed by Warwick, is certainly part of the reason. Warwick's
book, like Joan Richards's Mathematical Visions: The Pursuit of
Geometry in Victorian Britain (1988), motivates us to take
a broader look at the cultural role of mathematics in building
character, in transforming merit into a social phenomenon, and in
achieving social mobility and status in a world that was rapidly
changing—economically, politically and socially.
The most important conclusions of Warwick's study, however, concern
everyday practices in science, especially those that are involved in
the regeneration of the discipline and the reproduction of its
personnel. Pace Thomas Kuhn (and even Ludwik Fleck), "normal
science" issues not from a canonical textbook, but rather from
specific pedagogical practices repeated over time that may
eventually become the foundation of a textbook, although not
necessarily. Those pedagogical practices—which undergird the
successful transmission of technical skills—are for Warwick a
form of life-sustaining sociability necessary for disciplinary
survival (an observation also made by Sharon Traweek in her 1988
book Beamtimes and Lifetimes: The World of High Energy Physicists).
Thus the broader significance of Warwick's book lies in its
articulation of the complex social systems required to keep science
operating. Science does not simply exist as a body of knowledge
perched on a library shelf and poised to survive no matter what. It
requires forms of sociability to exist and persist: a cadre of good
teachers, attention to the introductory stages of learning in any
subject, the coordination of secondary and higher education, a
system of values that holds scientific and mathematical education in
high regard, and finally, the assignation of social prestige not
only to a scientific career but also (and perhaps more importantly)
to science teaching. In this, Masters of Theory is a sober
admonition to policy makers that the neglect of science education
can only spell the demise of science itself.