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He is contributing major results in such a wide range of different areas. Yet he has produced such a fantastic collection of results, leading to the award of all the top prizes in mathematics, that one must try to at least give a vague picture of the work of this remarkable mathematician. Before looking at his contributions we note the prizes and awards he has received (although again this list is bound to become rapidly outdated as he continues to receive awards). These include: the Salem Prize (2000); the Bôcher Memorial Prize from the American Mathematical Society (2002); the Clay Research Award from the Clay Mathematical Institute (2003); the Levi L Conant Award from the American Mathematical Society (2005); the Australian Mathematical Society Medal (2005); the ISAAC Award from the International Society of Analysis, its Application and Computation (2005); the SASTRA Ramanujan Prize (2006); the Fields Medal (2006); the Ostrowski Prize from the Ostrowski Foundation (2007); the Alan T Waterman Award from the National Science Foundation (2008); the Onsager Medal(2008); the Information Theory Society Paper Award (2008); the Convocation Award from Flinders University Alumni Association (2008); the King Faisal International Prize (Mathematics) (2010); the Nemmers Prize in Mathematics from Northwestern University (2010); and the George Polya Prize from the Society for Industrial and Applied Mathematics (2010). In addition he has received a Sloan Foundation research Fellowship (1999-2001), a Foundation Fellowship from the David and Lucille Packard Foundation (1999-2006), and a MacArthur Fellowship from the MacArthur Foundation (2007-11). He has been elected to the Australian Academy of Sciences (2006), to a fellowship of the Royal Society (2007), to the National Academy of Sciences (2008), and to the American Academy of Arts and Sciences (2009). He was a finalist in Australian of the Year in 2007.
Physics and Mathematics