For more than two thousand years philosophers, mathematicians and
physicists have struggled to understand the nature of space. Kant studied
the role of the human mind, mathematicians examined the logical
ramifications of space and physicists investigated experimental phenomena.
Einstein showed how space and time are inextricably linked. The story
continues to the present day, with increasingly exotic scenarios of
vibrating strings in ten dimensional space-time. I will review the history
and present status of the great philosophical controversies in the light
of modern developments.
Michael Atiyah received both his BA and Ph.D.(1955) from Trinity College,
Cambridge, England. He held postdoctoral appointments at Cambridge and the
Institute for Advanced Study. He arrived in Oxford in 1961 as a Reader and
then from 1963 to 1969 he held the Savilian Chair of Geometry. He spent
3 years as Professor at the Institute for Advanced Study before returning
t o Oxford as a Royal Society Research Professor. In 1990 he became Master
of Trinity College and the first Director of the Newton Institute for
Mathematical Studies in Cambridge. He retired from these positions in 1997
and 1996 respectively. Professor Atiyah is currently an Honorary Professor
at the University of Edinburgh.
Atiyah has made many outstanding and
fundamental mathematical contributions, especially in areas involving
interactions between geometry, topology and analysis. In collaboration
with Hirzebruch he pioneered the development of K-theory, which is now
crucial to the solution of many important mathematical problems. His
celebrated "index theorem" with Singer led to new connections in
Differential geometry, topology and analysis. It has become an important
tool in theoretical physics. Many of the great results in 4-manifold
geometry rely on mathematical theories in which he made foundational
contributions. He has been very influential in bringing the ideas of
theoretical physicists to the attention of mathematicians and vice versa.
For these and other contributions he received numerous awards including
the Fields Medal (1966), Royal Medal (1968), De Morgan Medal (1980), King
Faisal Prize (1987), the Copley Medal (1988) and the Abel Prize in 2004.
He was Knighted in 1983 and made a member of the Order of Merit in 1992.
He has been elected to the national academies of about 20 nations and
received honorary degrees from over 30 universities. Professor Atiyah
served as President of the London Mathematical Society (1974-1976) and
President of the Royal Society (1990-1995) and is to become President of
the Royal Society of Edinburgh in October 2005. He also served as
President of the Pugwash Conferences (1997-2002), an international
organization dedicated to "reducing the danger of armed conflict and
seeking cooperative solutions for Global problems."
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