Professor Emeritus Max Kelly was solely responsible for introducing into Australia a branch of mathematics known as category theory, which pervades almost all research in the fundamental structures of mathematics, allowing people in one branch of maths to understand others in a common form, not unlike Esperanto in languages. It is used in theoretical physics, computer architecture, software design, and banking and finance to connect ideas and streamline the management of information.

In 1966 Kelly and Samuel Eilenberg wrote the monograph Closed Categories, which set the stage for two more generations of Australian category theorists who flourish and are highly acclaimed worldwide. Kelly's book Basic Concepts of Enriched Category Theory (1982) is a standard in the field.

Gregory Maxwell Kelly, who has died at 76, showed his mathematical ability early. In 1946, he topped the state in the Leaving Certificate and took a Higher Exhibition in mathematics, after studying at Marist Brothers at Bondi. He graduated from Sydney University in 1950, with a science degree, first-class honours and the University Medal for mathematics and the James King of Irrawang travelling scholarship. He took his PhD at Cambridge in 1957.

Kelly was appointed a professor of pure mathematics at the University of NSW in 1967 and a fellow of the Australian Academy of Science at the age of 42. He returned to Sydney University in 1973 as a professor, staying 21 years until his retirement in 1994.

He was a true academic: erudite in the classics, a prolific researcher and publisher, editor for several journals, inspiring lecturer, PhD supervisor, successful department head, traveller, linguist, raconteur and bon vivant.

Some colleagues claim him as a logician in his passionate insistence on precision and clarity in mathematics and his belief in, and search for, the grand order at the heart of the world. Much of his work can be called higher-order universal algebra.

Aware of how fortunate his life had been, he felt obliged to give something back to the community. He happily gave time to aspiring young mathematicians and to all those keen to learn.

Always aware of what was going on in the world, he was once threatened with excommunication from the Catholic Church for challenging the priest in Mass about the morality of the Vietnam War. Another time, frustrated by bureaucracies, he enlisted the media to borrow for a blind girl in a Catholic school a mathematics textbook in braille that was gathering dust in a Department of Education office. He was involved with Action for World Development and in ways to help the Aboriginal community in Redfern.

In 1960 Kelly married Imogen Datson and they had four children, whom Kelly impressed with his range of knowledge - astronomy, languages, history, politics, theology and philosophy - as well as his ability to rebuild the lawnmower's carburettor and his habit of stopping in mid-conversation to admire his favourite flowering trees. Imogen took her PhD, in medieval drama, as a mature-aged student in 2002.

Kelly used mathematics in ordinary life, too, devising an ingenious way of encoding PINs on his credit cards that involved Greek symbols encrypted with mathematical transformations. One such card had a square matrix of dots and symbols drawn on the back. To most people it would have looked like a smudge or a doodle, but to Kelly it was as clear as four written numbers.

Kelly started learning ancient Greek recently and in his last months he was engaged in complex research on coherence theory, which he was typing despite failing eyesight. This research will be completed and published by collaborators in Canada and Italy.

Max Kelly is survived by Imogen, their children, Dom, Martin, Catherine and Simon, and 10 grandchildren.

**Ross Street**

April 11, 2007