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Oxford Figures: 800 Years of the Mathematical Sciences

John Fauvel, Raymond Flood, and Robin Wilson, editors
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Eisso Atzema
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History of science, or — more specifically — history of mathematics, can be approached in a variety of ways. Traditionally, the focus is on the history of the "great" themes or the "great" minds. In many ways, this emphasis on greatness makes a lot of sense. Unfortunately, however, the adjective "great" is rather ill-defined and leaves a lot of room for the furthering of contemporary agendas such as patriotism or the validation of one's own discipline. More importantly, whatever "great" means exactly, the traditional approach tends to overlook the social and institutional contexts in which the great minds lived and in which the great themes took shape.

More recently, the history of mathematics has been approached from a more institutional point of view as well. Several studies on the history of mathematics at German universities exist (Leipzig, Rostock, Tübingen) and the history of various mathematical societies has been studied (Circulo Matematico di Palermo, AMS, Finnish Mathematical Society). Obviously, this approach allows for more attention to societal and cultural context, but it does have its drawbacks too. Indeed, the institutional approach leaves very little room for whatever greatness might mean and the inevitable attention to minor themes and minor minds (whatever "minor" means exactly) could obscure the view on the bigger picture. The book under review here is another example of the recent crop of studies into the history of mathematics from an institutional point of view and exemplifies both the strengths and the weaknesses of its genre.

As the pun in the title already indicates, the editors of the book want to show that Oxford has played a more than marginal role in the history of mathematics. And indeed, this claim is fully warranted for a university that can boast of the likes of John Wallis, Edmund Halley, David Gregory, J.J. Sylvester, G.H. Hardy and Michael Atiyah among its professors. At the same time, the book is replete with names of mathematicians that very few people are likely to have heard of.

It was probably a wise decision to dedicate separate chapters to the major figures on the Oxonian mathematical scene. Thus, John Wallis, Edmond Halley, Henry Smith, James Joseph Sylvester and (as an astronomer) Thomas Hornsby each received their own chapter. Particularly in the case of Wallis and the little-known, but very influential, Smith, these chapters provide very welcome quick introductions to their subjects' life and work. In the remaining chapters ample space is devoted to the more picturesque characters of which in good English style Oxford had its share as well. Obviously, Charles Ludwig Dodgson, student and mathematical lecturer of Christ Church, shows up in several of the later chapters as Oxford's most famous, if not — by whatever definition — greatest, mathematician.

As hardly more than a footnote, the Balliol College student Charles Hinton is mentioned as another writer of fantasy stories, in his case on life in higher and lower dimensions, and as the source of inspiration for both Abbott's Flatland and some of Wells' fiction. The same Hinton married Mary Boole, the oldest daughter of the mathematician George Boole and his niece and wife, the math educator Mary Boole. As it turned out, while still being married to Mary, he managed to marry one Maud Weldon as well. After serving a short conviction for bigamy, he fled the country and by way of Japan ended up in Princeton, where he invented a gun-powder based baseball pitcher which was actually used, for a while, by the Princeton team. Although not mentioned in the book, his marriage to Mary Boole also made him a brother-in-law to George and Mary's third daughter Alicia, the colorful pioneer in the study of higher-dimensional polygons. One might wonder about Hinton's influence on her, given that he experimented widely with models for polyhedra and their higher-dimensional analogs. Indeed, as the book does mention, he is also the inventor of the word tesseract for a four-dimensional hypercube. Other minor characters to receive mention are Leonard Rogers of Rogers-Ramanujan fame and John Campbell of Campbell-Baker-Hausdorff fame. Of course, the chapter on early 20th-century Oxford mathematics is mostly about G.H. Hardy, but there is room for others such as Mary Cartwright as well.

As far as the connections of mathematics to the other sciences are concerned, several chapters are devoted to the history of astronomy, although astronomy is only mentioned in passing in the later chapters. Particularly, mention is made of at least one Hardy student who switched to astrophysics (Edward Arthur Milne), but there is tantalizingly little on the position of astronomy with respect to mathematics in Oxford at the time. Similarly, other than a reference to the work of Coulson in quantum mechanics, the book does not give much insight into the relations between physics and mathematics at Oxford. Just out of curiosity, for instance, I would like to know what brought the mathematician Ida Busbridge and the physicist and astronomer Madge Adam together in one picture (p.250). But who really cares? After all, this is a book about mathematics and mathematicians and does not claim to be more than that.

In conclusion, even up to the pun in the title, this book is very similar in style to Möbius and his Band, the other book edited by Fauvel, Flood and Wilson that was published by Oxford University Press. Both make for very good bed-side reading and any reader who will want to know more will readily find pointers to further study. Indeed, both books clearly bear the stamp of the late John Fauvel. Not only did he serve as an editor, but he also contributed several chapters. This book must have been one of the last books John was involved in and I think I can fairly summarize its merits by concluding that it is a true loss to the history community that we will never have another book from his hand again.

Eisso Atzema ( is Lecturer in Mathematics at the University of Maine at Orono.

800 years of Oxford mathematics [Alfred the Great, Roger Bacon, Christopher Wren, Edmond Halley, Florence Nightingale, G. H. Hardy, Roger Penrose]
Medieval Oxford [Richard of Wallingford, Robert Grosseteste, Thomas Bradwardine]
Renaissance Oxford [Henry Savile, Thoms Harriot, Henry Briggs]
Mathematical Instruments [Robert Boyle, Edmund Hunter, Robert Hooke]
The Mid-Seventeenth Century [Christopher Wren, John Locke, Robert Hooke]
John Wallis [Seth Ward, Thoms Hobbes, Robert Wood]
Edmond Halley [Isaac Newton, John Flamsteed, David Gregory]
Oxford's Newtonian school [James Bradley, John Whiteside, John Keill]
Georgian Oxford [James Stirling, Nathaniel Bliss, Stephen Rigaud, William Gladstone]
Thomas Hornsby and the Radcliffe Observatory [John Radcliffe, John Bird, James Bradley]
The Mid-Nineteenth Century [Baden Powell, Henry Smith, Charles Darwin, Benjamin Jowett, Florence Nightingale, Francis Galton, Charles Dodgson, Bartholomew Price]
Henry Smith [Frederick Temple, Charles Hermite, Hermann Minkowski]
James Joseph Sylvester [Arthur Cayley, Augustus de Morgan, David Hilbert, Felix Klein]
The Twentieth Century [William Esson, G.H. Hardy, E.C. Titchmarsh, Henry Whitehead, Charles Coulston]
Some Personal Reminiscences
Appendix's Mathematical Chair