He was employed by Australia's CSR Company from 1961 to 1965, before joining the University of New South Wales as a Lecturer. After several promotions, he was appointed to a Personal Chair in Mathematics in 1983. He was Head of the School of Mathematics from 1986 to 1990 and from 1992 to 1993. He completed a term as Chair of the Chemistry, Mathematics and Physics Panel of the Australian Research Council and member of the ARC's Research Grants Committee, and is a former President of the Australian Mathematical Society .
He was elected a Fellow of the Australian Academy of Science in 1993. In 1997 he was awarded the ANZIAM Medal by Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), and in 2001 was awarded the Thomas Ranken Lyle Medal of the Australian Academy of Science. In 2002 he was awarded the Szekeres Medal of the Australian Mathematical Society, and in 2005 was awarded the Information Based Complexity Prize. In 2008 he was appointed an Officer of the Order of Australia (AO).
He is a member of the editorial board of a number of international journals, including SIAM Journal of Numerical Analysis, Numerische Mathematik, Advances in Conmputational Mathematics, Journal of Integral equations and Applications and the new International Journal of Geomathematics, and is a Senior Editor of the Journal of Complexity.
From 2003 to 2007 he was President of the International Council for Industrial and Applied Mathematics, Before that he was the Chair of the International Program Committee for ICIAM 2003, the fifth International Congress on Industrial and Applied Mathematics, held in Sydney in 2003. He is currently Deputy Director of MASCOS, the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.