#### Making sense of complex numbers

NOEL BAKER was a mathematician who specialised in complex analysis. Within mathematics, analysis deals with limiting processes such as those of the calculus. When the setting is complex rather than real (that is, when not only ordinary or real numbers appear, but also

*i*, the mathematical symbol for the square root of -1), one obtains a theory of great power, which was developed by Cauchy in the 19th century.

Complex dynamics studies the effect of repeatedly applying a complex function (a rule for transforming one complex number into another). As the number of applications grows indefinitely, a sequence of points in the complex plane is obtained. The study in depth of such sequences goes back to the French mathematicians Julia and Fatou in the 1920s, but has enjoyed a great revival in recent years, through its links with modern ideas of chaos, fractals, and the work of Mandelbrot. Modern computer graphics have greatly helped to popularise the field.

Baker devoted the bulk of his long career to this field, even when it was quite unfashionable, and wrote more than 70 papers, some quite influential (the term "Baker domains" commemorates some aspects of his work).

He was a modest, unassuming man, whose loves outside maths were music and his family. He had no small talk, but was blessed with a pleasantly self-deprecating sense of humour. A mathematician of the old school, he lacked the computer skills of the younger generation, and in his inaugural lecture thanked his students for having led him "to the very brink of the computer age".

Irvine Noel Baker was born in Adelaide, and began to study mathematics there in 1949 at the age of 16. His early work in Adelaide was done under George Szekeres, an early specialist in complex dynamics and "functional iteration", as the repeated application of a function is known. He also wrote the first of his papers there. He did his doctoral work at Tüb- ingen in Germany under the direction of Helmut Kneser. There he met his future wife, Gillian, who had come from England to study German and its literature. Both were fine pianists, and their duets, particularly of Schubert, gave joy to many colleagues at departmental concerts.

Baker spent two years in Edmonton, Canada, during which time he and Gillian were married. Following an excellent talk at the International Congress of Mathematicians in Edinburgh in 1958, he was appointed lecturer in mathematics at Imperial College, London in 1959, and he remained there for the rest of his career. He retired as professor of pure mathematics in 1997, but remained active until the day he died.

He is survived by his wife, Gillian, and their two sons.

Professor Noel Baker, mathematician, was born on August 10, 1932. He died on May 21, 2001, aged 68.

© The Times, 2001