Mathematics in Victorian Britain edited by Raymond Flood, Adrian Rice, and Robin Wilson (review)

The title of this book, Mathematics in Victorian Britain, suggests a narrow compass. Most of the important developments in mathematics between 1837 and 1901 happened in continental Europe. But this work manages to address a larger and more worthwhile topic by widening the scope of the title. “Mathematics” is taken to mean any field in which mathematical notions are applied. Thus there is a whole chapter on astronomy; others on theoretical physics, statistics in public health, calculating machines, and logic. As well, the meaning of “Britain” is extended to all of the British Empire, and even to some British mathematicians who emigrated to the United States.

Because of this wider reach, the book is more useful than it might have been otherwise. It draws connections between mathematical ideas and their applications in related fields. Many important mathematical developments were not so much new ideas as new applications of known concepts. Works more narrowly focused on the history of mathematics might not have reported on applications, while works focusing on the history of science might have skimped on the mathematics.

The book is organized in two sections. The first is geographical, with chapters on Cambridge, Oxford, London, Scotland, Ireland, and the rest of the British Empire. The second section goes into more depth by mathematical topic. A very interesting final chapter by Jeremy Gray is itself in a way a review of the entire book; it suggests that perhaps British mathematicians have been overrated and throws some cold water on claims made earlier in the book.

Britain was the engine of the Industrial Revolution during Victoria’s reign, but not a powerhouse in mathematics. Still it managed to train some excellent mathematicians who then staffed growing university mathematics departments all around the world, and some of those departments did notable research. Beyond that, Britain produced some important and totally new mathematical thinking that seemed to come out of nowhere. Britain had a renowned educational program in mathematics at one university, Cambridge. So revered was this program that graduates in mathematics from other British universities would often enroll at Cambridge for a second bachelor’s degree and take the competitive examinations, the mathematical tripos, in hopes of achieving firstclass honors and being designated as “wranglers” (20). To be a wrangler was a great honor, and it could get you a position in mathematics almost anywhere in the world.

The Cambridge system reflected what was the best and the worst of British education. The program was rigorous and uncompromising. But it was questionable whether it had kept up with advances in mathematics in the rest of the world. Possibly the worst aspect of the program was that it was essentially a contest. As Tony Crilly’s chapter reports, the top students spent three years cramming. Usually they hired a coach and spent the vast majority of their time getting ready for the six-day examination that would determine their fate. Students would naturally enough display little curiosity about mathematical questions that were unlikely to arise in the examination. Cambridge seems to have had very little interest in research and made little attempt to remedy how far British mathematics had fallen behind until quite late in the century.

There is not space here to comment upon the discussion of the other mathematical centers in this book. Suffice it to say that they all stood in the shadow of Cambridge and struggled to find an identity of their own. The most successful were those that concentrated on applied mathematics.

But as so often is the case, if there is a logjam somewhere, breakthroughs will occur elsewhere. And there are some very interesting cases of British originality that did not come out of the Cambridge system. Consider George Boole, a self-taught schoolmaster who saw that the compact notation of algebra might be applied to logic, and by doing so, he thought he could make headway...