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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.
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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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