We are currently witnessing marked changes in the public perception and understanding of mathematics and the sciences. The most prominent recent example of mathematics inspiring popular consciousness is the proof of Fermat's Last Theorem by Andrew Wiles, which made headline news and has been the subject of television documentaries and even a musical. One panelist at a forum discussing public awareness of mathematics, held during last year's European Congress of Mathematicians in Barcelona, even spoke of a ``love affair of the American public with mathematics''. Yet in most western countries, student numbers in mathematics and the exact sciences are dropping dramatically. Pupils seem to leave school less well prepared for university studies, and the romanticised image of mathematics has hardly led to an increase in mathematical literacy of the general public.
In this context, Oxford Figures is a welcome contribution not only to popular writing on the history of science, but also to debates about the role of mathematics in school and university curricula and society at large.
The book focuses on periods in the 800 years of mathematical activity at Oxford University. One chapter is devoted to instrument making, and others contain portraits of mathematicacians at Oxford, including the Savilian professors John Wallis, Edmond Halley, Henry Smith, and James Joseph Sylvester. Henry Savile (1549--1622) was in many ways the most influential figure for the development of mathematics at Oxford. In his lectures on Ptolmey's Almagest he emphasised the intellectual nature of mathematics and astronomy within a liberal education. Savile illustrated his point by recounting the tale of the Socratic philosopher Aristippus (as recorded c. 30 BC by the Roman architect Vitruvius) who, shipwrecked on Rhodes, inferred the inhabitants' civilised nature from mathematical diagrams drawn in the sand. The founding of the Savilian chairs of geometry and astronomy in 1619 promoted these fields of study only on a didactic level. They became degree subjects much later. The reasons why this occured earlier at places such as Cambridge deserve more detailed analysis than can be given within the scope of this book. Nonetheless, these chairs contributed to realising Savile's vision of mathematics as an integral part of a humanistic education.
Late 13th-century Oxford witnessed some of the most sophisticated mathematical discussions of the period. Medieval scholars declared that ``he who knows not mathematics cannot know the other sciences nor the things of this world and ... those who have no knowledge of mathematics do not perceive their own ignorance and so do not look for a cure''.
By Savile's time, Oxford had lost this leading role in mathematics. To the average student, mathematics did not seem an important component of his education. Aware that mathematics could not be promoted on intrinsic value alone, Savile defended it by demonstrating its use to the state (meaning: military affairs) in a plea to the queen for continued patronage of the universities.
Wallis and Halley not only brought Oxford renewed international recognition as a centre for mathematical and astronomical research, they also taught mathematics on a practical level and recognised their duty to educate the public. Halley believed that ``one of the principal uses of mathematical sciences'' was that they were ``in many ways able to prevent the Superstition of the unskillful vulgar''.
By the early 19th century, interest in mathematics had again declined sharply. On taking up the Savilian chair of geometry in 1827, Baden Powell was advised not to give an inaugural lecture because he would almost surely not attract an audience. When Henry Smith could remark: ``It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstances can it be of the smallest possible utility'', we can infer that the late 19th century was again a happier time for mathematics.
Mathematicians usually regard the importance of their subject as self-evident. In a time of funding cuts and increased pressure to perform ``useful'' research, Oxford Figures provides insight into how the role of mathematics has been debated and defended over the centuries. This book, rich in illustrations and quotations, vividly shows mathematicians as social beings and gives a fascinating portrait of mathematics as a dynamic part of human culture. One hopes that it helps to attract more young people to this intellectual endeavour.
H. Geiges