Shaw studied at King's College, Cambridge, where he studied mathematics; he was Wrangler and earned a B.A. in 1980. In 1981 he won the Mayhew Prize for his performance on the Cambridge Mathematical Tripos, and in 1984 he received a Ph.D. in physics from Wolfson College, Oxford. From 1984 to 1987 he was a research fellow at Cambridge and C.L.E. Moore Instructor at the Massachusetts Institute of Technology, from 1991 to 2002 he was a lecturer in mathematics at Balliol College, Oxford, and in 2002 he moved to St. Catherine's College, Oxford, where he was University lecturer in financial mathematics. In 2006 he moved to his present position at King's College London.

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