As well, in Hungary there were severe restrictions on places for minority groups and only two places were open to the Jewish students from her school; her friend Marta Sved took the mathematics place and Esther the physics spot. George was part of a Budapest group of brilliant students, including Paul Erdos, who became the most prolific mathematician of all time; Paul Turan, who also became a famous mathematician; and Esther Klein. One of the problems the group considered was proposed by Esther and solved by George to declare his suit. Erdos called it the "Happy Ending Problem", as it led to the pair marrying in 1937.

After six years working in Budapest as an analytical chemist, George took work as a leather chemist in Shanghai to escape the threat of Nazi persecution. The factory closed a year later, and the Szekeres family became part of the Shanghai community of 15,000 Jewish refugees from central Europe. They lived through the rigours of World War II, the Japanese occupation and the start of the Chinese Communist revolution. These were desperate times and they were lucky to survive: their son Peter, who was born in Shanghai, tells of being whisked up by George as they ran for their lives to escape Japanese bombing. Offered a post as a lecturer at the University of Adelaide, George arrived in Australia in June 1948 with Esther and Peter. For the first three years they shared a flat with Esther's schoolfriend Marta, her husband George and their two children. Daughter Judy was born some years after their arrival. Adelaide in the 1950s was very different from Budapest, or Shanghai, but George and Esther quickly fell in love with the Australian bush and were happy to make their home here. Esther's time was taken up with raising their young family, though she tutored in mathematics at the university. George flourished as a professional mathematician.

The Szekeres family moved to Sydney in 1964, when George took up the post of foundation professor of pure mathematics at the University of NSW. This was the time of the notorious Bogle-Chandler murders, and the Turramurra house of one of the victims was for sale. It was almost unsaleable because of the publicity. But the association meant nothing to George and Esther. They bought the house and lived there until last year. The block, large, with many native trees, a cliff and a small creek, was a haven for birds and animals. George wrote to a friend that he had found paradise.

Last year, George lost his driver's licence. As they were three kilometres from the nearest shops they decided to move back to Adelaide to be close to their family. Paradise had become a little too isolated. For most of his life, George published mathematical papers of great originality and impact. His work broke new ground in an unusually broad range of fields - from algebra, combinatorics and number theory, to mathematical analysis, numerical analysis, relativity and cosmology. One of his most famous and far-sighted papers provided a key mathematical tool for understanding black holes in cosmology theory. An idea of the importance of the so-called "Kruskal-Szekeres co-ordinate system" (the technique was independently discovered by Joseph Kruskal) can be gleaned from Carl Sagan's book Contact, where it is featured. George is also well known for his work in combinatorics, where he laid the foundations of what is now known as Ramsey Theory. That he became the leading Australian mathematician of his day is all the more remarkable because he studied at the Technical University of Budapest, which specialised in engineering, and he attended only one undergraduate mathematics course in his life, on calculus. This proved to be an impediment later when his employers wanted him to take out a doctorate of philosophy in mathematics. Under George's leadership, the new department of pure mathematics at the University of NSW earned national and international recognition. In large measure through his example and influence, the school of mathematics became one of the top schools in Australia.

After he officially retired in 1975 as an emeritus professor, he continued to work at the university most of the week well into his 90s. He published more than 20 scientific papers in "retirement", and was seen regularly around the corridors and in the common room talking about the latest problems of mutual interest to young students and academic staff. In 1956 he was a foundation member of the Australian Mathematical Society, served on its council for many years, and was president from 1972 to 1974. The society devoted a volume of its journal to papers written in honour of his 65th birthday, and later named its most prestigious award the George Szekeres Medal.

George was elected a fellow of the Australian Academy of Science in 1963 and was awarded its Thomas Rankin Lyle Medal in 1968. He received an honorary doctorate from the University of NSW in 1976 and membership of the Order of Australia in 2002, but perhaps he was proudest of being one of the very few foreign members of the Hungarian Academy of Science. George was an inspiring leader for generations of talented young Australians. At the University of NSW he established the high school journal Parabola, and he was the source of many problems for both the university's Schools Mathematics Competition and SUMS, the Sydney University Mathematics Society competition, which continue to challenge high school and undergraduate students. He helped establish a training program for the first Australian team to compete in the International Mathematical Olympiad and was a key member of the Australian Mathematical Olympiad program in the 1980s.

In 1983, George and Esther attended a meeting to arrange weekly mathematics problem sessions for talented high school students in Sydney. As a result, weekly mathematics enrichment classes were started at Mercy College in Chatswood in 1984. These classes were free and open to any student from any school system. Esther supplied geometry problems for the first session and continued to do so for 21 years. She also attended the classes each week until 2002, when it became too difficult for her to get there. George and Esther both loved art and music. George, who was a passionate, active and very able musician, played the violin and the viola in the Ku-ring-gai Philharmonic Orchestra and the North Sydney Symphony Orchestra. He was treasurer of the Ku-ring-gai orchestra from its inception until 2000; as he said, "They thought that I was good at sums."

He was also a very keen bushwalker. Even when he was well into his 80s he and his daughter would walk a substantial section of the Great North Walk from Sydney to Newcastle every week. George and Esther were a wonderful and unpretentious couple who contributed richly to Australia for more than 50 years. They were together when they died - Esther had been in Wynwood Nursing Home in Adelaide for a year and George had joined her, sharing a room, seven weeks before their deaths. They are survived by their children Peter and Judith, Peter's wife, Angela, and his stepdaughter, Jorji.

Michael Cowling Much of this obituary was contributed by Garth Gaudry, Terry Gagen, Peter Szekeres and David Tacon. Michael Cowling is a professor of mathematics at the University of NSW.