He is the Sir James Lighthill Professor of Mathematics and Computational Science & Engineering at the Florida State University, United States.
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When a team of students of Trinity College, Cambridge, won University Challenge in 1974 (Christopher Vane, Frederick 'Wynn' Jolley, Simon Schaffer, and Paul Hopkins), Gallagher was part of a Trinity fellows team ( Sir James Lighthill, Dr Bradfield, Mr JA Weir) which defeated them in a contest on live television.