Brown then undertook postgraduate work at the University of Newcastle-upon-Tyne in the north of England supported financially by a Carnegie Scholarship. His thesis advisor was Frank Bonsall. He was awarded his Ph.D. in 1966 for his thesis Norm and stability properties of semi-algebras and in the same year he worked as a Junior Research Fellow at the University of Edinburgh. He accepted an appointment at the University of Liverpool starting at the beginning of academic year 1966-67 and remained at Liverpool until 1975, being promoted first to Lecturer and then to Senior Lecturer. During this period he spent the academic year 1967-68 as a Visiting Associate Professor at the University of Illinois, in the United States, and the academic year 1974-75 as a Visiting Lecturer at the University of Washington. Brown's first paper Relatively type 0 semi-algebras, based on the work of his doctoral thesis, was published in 1967. Further papers, all arising from his doctoral studies, followed in quick succession: Stability of wedges and semi-algebras (1968); Type 0 semi-algebras in Banach algebras (1968); Continuous functions of bounded n th variation (1969); and Norm properties of a class of semi-algebras (1969). These papers developed ideas of Frank Bonsall and, since they involve the notion of a semi-algebra, perhaps we should give a formal definition:
A semi-algebra in a Banach algebra B is a subset A of B such that x + y, αx and x.y belong to A whenever x and y are in A, and α ≥ 0 is real number.In 1975 Brown and his family emigrated to Australia when he accepted the Chair of Pure Mathematics at the University of New South Wales. He was honoured by the Edinburgh Mathematical Society for his outstanding mathematical work in 1977 when they awarded him their Sir Edmund Whittaker Memorial Prize. Further honours followed such as election as a fellow of the Australian Academy of Science in 1981. In the following year he became the second recipient of the Australian Mathematical Society Medal:-
... awarded to a member of the Society under the age of 40 years for distinguished research in the mathematical sciences. A significant portion of the research work should have been carried out in Australia.After being Head of the Department of Pure Mathematics and then Head of the School of Mathematics, Brown became Dean of the Faculty of Science of the University of New South Wales in 1989. He spent two years in England during his time on the staff at New South Wales, namely 1979 when he was Visiting Professor at the University of York and 1986 when he was Visiting Professor at the University of Cambridge.
In 1992 Brown moved to the University of Adelaide as Deputy Vice-Chancellor (Research) and then in January 1994 he became Vice-Chancellor of the University of Adelaide. Also in 1992 he became a member of the Council of the Australian Academy of Science, and was Vice-President of the Academy during 1993-1994. His biographical note  states:-
Features of Professor Brown's period as Vice-Chancellor included a major restructuring of University management, a strong focus on links with industry and a programmed return of the University's budget to surplus. Professor Brown was also very active in national and regional committees during his time at the University. The most notable of these was his service as Chair of the National Advisory Group on Science and Technology Awareness and Promotion.On 1 July 1996 Brown became Vice-Chancellor and Principal of the University of Sydney, a post which he continues to occupy. Given the tasks involved with his positions at the University of Adelaide and the University of Sydney it is remarkable that he has been able to continue his mathematical research and research collaborations at a very high level. For example during his ten-year period in Sydney, from 1996 to 2005, Brown published around 30 papers. To give an idea of the topics he now works on we give the titles of the four papers he published in 2004: The maximal Riesz, Fejér, and Cesàro operators on real Hardy spaces; Lebesgue measure of sum sets - the basic result for coin-tossing; The maximal Fejér operator on real Hardy spaces; and Approximation on two-point homogeneous spaces.
In addition to the honours we have mentioned above, Brown has received honorary degrees from the University of St Andrews (1997) and the University of Dundee (2004). In January 2006 Brown was appointed an Officer of the Order of Australia.
Gavin Brown married Diane Ranck in 2004, his first wife Barbara Routh having died in 2001. He has one son and one daughter by his first marriage.
Article by: J J O'Connor and E F Robertson