Student numbers increased by more than 50 per cent during Brown's time, postgraduate numbers more than doubled, income almost trebled and the numbers of international students multiplied fourfold.
There were also more completions of higher degrees than at any other university in Australia.
It was a period of major improvements in funding, research and infrastructure development at the university. The capital works included a new law school, an IT building, the student services centre, a 650-bed village for students and a multimillion-dollar restoration and refurbishment of heritage buildings.
Under Brown's stewardship, the university came to boast the United States Studies Centre, the Brain and Mind Research Institute and the Rio Tinto Centre for Mining Automation.
The university also became the first and only one to hold a graduation ceremony in the Great Hall of the People in Beijing.
Gavin Brown was born in Lundin Links, Scotland, on February 27, 1942, the only child of a bricklayer, Frank Brown, and his wife, Alexandria (nee Duncanson). His intellect marked him quickly.
He was so good at Scrabble that at the age of eight he was banned from playing the game in the local adult competition.
Brown went to school at Madras College in St Andrews, then attended the University of St Andrews, where he graduated as a master of arts in 1963 with first-class honours in mathematics and Latin.
In 1965 Brown became a junior research fellow at Edinburgh University. A year later, when he was awarded a PhD from Newcastle University, at Newcastle Upon Tyne, he joined the academic staff of the University of Liverpool. Brown also married that year, a geography teacher named Barbara Routh.
At Liverpool, he progressed to senior lecturer before accepting the post of professor of pure mathematics at the University of NSW in 1976.
He took up visiting professorships at the universities of Paris, Cambridge and Washington.
Brown had the misfortune, while swimming in 1977, of picking up a virus which so affected his right eye that he could not open it. But that was a mere annoyance.
In 1982 he won the Australian Mathematical Society Medal. Brown held a host of administrative and academic appointments at the University of NSW, including dean of the faculty of science from 1989 to 1992.
In 1992 Brown accepted the post of deputy vice-chancellor at the University of Adelaide. He became vice-chancellor in 1994. Two years later, he took up the appointment of vice-chancellor at Sydney University.
There was great sadness in his life when Barbara died in 2001. In 2004 Brown married the marketing director of health services at the university, Diane Ranck.
He also recovered the use of muscles in his eye.
The artist Judy Cassab painted his portrait while he was vice-chancellor at Adelaide University, with his eye shut. When she painted him at Sydney University, it was open.
Brown was active with the Australian Research Council as a chairman of various funding committees.
He held positions on many boards of management, including the Australian Graduate School of Management and the Australian Technology Park. He served on the Australian Vice-Chancellors' Committee and was also a committee member of the Association of Pacific Rim Universities.
Brown gave keynote addresses all over the world on topics beyond his research interests, at venues such as the universities of Freiburg, Tsinghua, Beijing, Nanjing, Tohoku and Fudan, the Thai Ministry of Education and the Stockholm World Forum.
In 2006 Brown, appointed an honorary fellow of the Royal Society of NSW, was awarded an Officer of the Order of Australia.
In 2008 he retired from the university and returned to Adelaide. He received the Royal Society NSW Medal and was appointed inaugural director of the Royal Institution of Australia.
Diane said he could write about anything, ''from Robbie Burns to an administrative piece on change management''.
His last paper, in April, was on ''Symmetric Cantor Measure, Coin-Tossing and Sum Sets''.
But not everything was ethereal; he listed his recreational interest in the Who's Who in Australia as racing.
Having suffered from a heart condition in his last years, Brown died suddenly from a heart attack after enjoying Christmas lunch with his family.
His funeral was held yesterday in Lutheran College in Adelaide's Immanuel College.
Gavin Brown is survived by Diane, his children, Janet and Colin, and stepchildren Benjamin and Oliver.