After completing his education at Oxford, James went to the United States for the year 1954-55. He did this having been awarded a Commonwealth Fund Fellowship which enabled him to spend time at Princeton University, the University of California at Berkeley and the Institute for Advanced Study at Princeton. Returning to England, James was Tapp Research Fellow at Gonville and Caius College in Cambridge in 1956 before returning to the University of Oxford.
Back at Oxford in 1957, James was appointed Reader in Pure Mathematics, a post which he held until 1969. From 1959 until 1969 he was a Senior Research Fellow at St John's College. In 1970 James was appointed to the famous chair of Savilian Professor of Geometry. The chair was founded by Savile in 1619 and first occupied by Briggs.
James was elected a Fellow of New College Oxford in 1970 when he became Savilian Professor of Geometry and he continues to hold the fellowship. He retired from the Savilian Professor of Geometry in 1995 and became professor emeritus.
James has done wide ranging work in topology, particularly in homotopy theory. His first publication was in 1953, followed by four publications in 1954 which were all written jointly with Henry Whitehead. These papers were on fibre spaces and the homotopy theory of sphere bundles over spheres. James then published on suspensions, on multiplication on spheres, on cup-products, and, another publication with Henry Whitehead, Homology with zero coefficients. He then wrote many papers on homotopy groups and Stiefel manifolds.
The mathematical works of J H C Whitehead appeared in four volumes in 1962 and 1963 edited by James. These volumes covered Henry Whitehead's work in differential geometry, complexes and manifolds, homotopy theory, and algebraic and classical topology.
In 1976 James published The topology of Stiefel manifolds which was based on his lecture notes. A reviewer wrote:-
There are a number of fascinating problems concerning the Stiefel manifolds which are of importance in the geometric applications of homotopy theory, and in homotopy theory itself. These lecture notes present, and solve, some of these problems (many of which the author has worked on), bringing in the necessary tools (e.g. K-theory characteristic classes, J-theory, Samelson products) as needed.general topology and homotopy theory (1984), another book by James which was based on his lectures, is described as follows:-
In this monograph, based on a set of sixteen lectures to students, the author expounds certain parts of general topology which are particulary relevant to homotopy theory. His book is reasonably self-contained. It is tightly written and elegant. ... This is a beautifully written and much needed book, both as a text and as a reference. It will probably become a classic.In 1987 James published Topological and uniform spaces which was written for advanced undergraduates or new graduate students. Fibrewise topology (1988) is a treatise on general topology, uniform spaces, and homotopy theory from the point of view of fibres. Introduction to uniform spaces (1989) is again based on lectures given by James at the University of Oxford. James published Handbook of algebraic topology in 1995.
In the late 1950s Henry Whitehead approached Robert Maxwell, the chairman of Pergamon Press, to start a new journal Topology although Whitehead never lived to see the first part appear. James became an editor of Topology in 1962 and he has continued in that role ever since. On the 25th anniversary of the founding of the journal, James gave an address in which he related much of the early history of the publication with which he has been so closely associated. The address has been published, see .
James has received many honours for his major contributions to mathematics. In 1968 he was elected a fellow of the Royal Society of London. Other honours have been the Junior Berwick Prize from the London Mathematical Society in 1959 and the Senior Whitehead Prize from that Society in 1978. He served the London Mathematical Society in a number of ways, in particular as treasurer from 1969 to 1979 and as the 62nd president of the Society from 1984 to 1986.
Among other honours he has received have been an honorary fellowship from St John's College Oxford in 1988, an honorary professorship from the University of Wales in 1989 and an honorary doctorate from the University of Aberdeen in 1993.
Over the last ten years, James has produced a number of outstanding historical studies. In 1999 he edited History of topology and contributed three chapters to the book: From combinatorial topology to algebraic topology; Topologists at conferences; and Some topologists. In 2001 he published Portrait of Alexander (1888-1971). The introduction reads:-
The first half of the twentieth century was a golden age for Princeton mathematics. This was especially true of topology, and the prince of Princeton topologists for most of that time was James Waddell Alexander. What has hitherto been published about him hardly does justice to one of the most interesting and important American mathematicians of that period. The available material is not only scanty and fragmentary but also quite hard to find. The following short memoir will, I hope, go some way towards filling the gap.In 2002 James published Remarkable mathematicians : From Euler to von Neumann. This excellent collection of sixty biographies makes very enjoyable reading. A deeper look at twenty mathematical personalities occurs in James' book The mind of the mathematician (2007) written jointly with Michael Fitzgerald. One of the main themes of the book is that most mathematical geniuses showed some symptoms of the Asperger syndrome. This theme is explored in another recent book by James, Asperger's Syndrome and High Achievement : Some Very Remarkable People (2005). James' Remarkable mathematicians is in fact the first of a "Remarkable" collection of books by James. He published Remarkable Physicists : From Galileo to Yukawa in 2004, Remarkable Biologists : From Ray to Hamilton in 2009, and a further work Remarkable Engineers : From Riquet to Shannon is about to be published. Another recent book by James Driven to Innovate : A Century of Mathematicians and Physicists:-
... celebrates the extraordinary contribution made by Jewish people in mathematics and physics, from the mathematician Norbert Wiener, the founder of cybernetics, to distinguished nuclear physicist and Nobel Prize-winner Niels Bohr. He tells the life-stories of thirty-five men and women, born in the nineteenth century, who were at the forefront of research in the closely related fields of mathematics and physics, often in the face of various kinds of anti-Semitism.
Article by: J J O'Connor and E F Robertson
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