# Andrew Paul Guinand

### Born: 3 March 1912 in Renmark, South Australia, Australia

Died: 22 March 1987 in Peterborough, Ontario, Canada

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**Andrew Guinand**, always known as Andy, went to school at St Peter's College, Adelaide from 1924 to 1929. He then entered St Mark's College of the University of Adelaide in 1930 to study mathematics, graduating in 1933. He was a great sportsman in his university days, described in [1] as follows:-

In 1934 Guinand won a Rhodes Scholarship to attend the University of Oxford in England. This was the typical route for the top Australian academics at that time, and Guinand studied at Oxford for his doctorate under Titchmarsh's supervision. On of the examiners for his thesis was Hardy and [1]:-... it is recorded that he was a proficient gymnast, he rowed with the Torrens Rowing Club, and he competed in bicycle races with the South Australia Amateur Cycling Association.

In session 1937/38 Guinand studied at Göttingen, then in 1939/40 at Princeton in the United States. In 1940 he joined the Royal Canadian Air Force, returned to England and was a navigator on many missions. When he was stationed 70 km from Oxford he would ride there on his bicycle to continue his mathematical research.Andy in later years treasured a note from Hardy asking him to postpone his oral examination because he(Hardy)had been asked to play in a cricket match for the Trinity College Servant's Team.

After being an assistant at Cambridge, he became a lecturer at the Royal Military College of Science in 1947. He was promoted to Associate Professor of Mathematics before returning, in 1955, to a chair at the University of New England at Armidale which lies on the valley slopes of Dumaresq Creek in the New England Range in New South Wales, Australia.

During his two years at Armidale he was Head of Department, then he left to take up a post in Edmonton, Canada at the University of Alberta. His next appointment was to the University of Saskatchewan in 1960, then in 1964 he became the first chairman of the mathematics department at Trent University in Peterborough in south-eastern Ontario, Canada. Trent University, 115 km east-north-east of Toronto, had been founded in 1963.

Guinand worked on summation formulae and prime numbers, the Riemann zeta function, general Fourier type transformations, geometry and some papers on a variety of topics such as computing, air navigation, calculus of variations, the binomial theorem, determinants and special functions. In [1] W N Everitt writes:-

As a student of Titchmarsh in Oxford in the years immediately before the second world war it was natural that Guinand's research interests should be directed into the field of Fourier analysis and the Riemann zeta function. ...[In an important paper in1948]the main application of the general result yields a deep-seated connection between the distribution of the prime numbers and the location of the zeros of the Riemann zeta function on(or near to it if the Riemann hypothesis is false)the critical line in the complex plane... Guinand was convinced that these results could lead to more information about the Riemann zeta function, and he was disappointed that he was not able to advance further in this area and that others did not take up the possibility themselves.

**Article by:** *J J O'Connor* and *E F Robertson*

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