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Ioan Mackenzie James

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23 May 1928

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Ioan James was a Foundation Scholar at St Paul's School. From there he won an Open Scholarship to the University of Oxford where he studied mathematics at Queen's College in the topology school of Henry Whitehead .

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.

James has been a governor of St Paul's School and St Paul's Girls School since 1970.

Source:School of Mathematics and Statistics University of St Andrews, Scotland