Andrew Paul Guinand (known as Andrew Guinand) was an Australian mathematician and a professor at the

University of New England University of New England may refer to: * University of New England (Australia), in New South Wales, with about 26,000 students * University of New England (United States), in Biddeford, Maine, with about 6,000 students See also * New England Coll ...

Early life and education

Guinand attended St Peter's College,

Adelaide Adelaide ( , ; ) is the list of Australian capital cities, capital and most populous city of South Australia, as well as the list of cities in Australia by population, fifth-most populous city in Australia. The name "Adelaide" may refer to ei ...

from 1924 to 1929. In 1930, he entered St Mark's College of the

University of Adelaide The University of Adelaide is a public university, public research university based in Adelaide, South Australia. Established in 1874, it is the third-oldest university in Australia. Its main campus in the Adelaide city centre includes many Sa ...

to study mathematics. After graduating in 1933, Guinand attended the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

on a

Rhodes Scholarship The Rhodes Scholarship is an international postgraduate award for students to study at the University of Oxford in Oxford, United Kingdom. The scholarship is open to people from all backgrounds around the world. Established in 1902, it is ...

, where

Edward Charles Titchmarsh Edward Charles "Ted" Titchmarsh (June 1, 1899 – January 18, 1963) was a leading British mathematician. Education Titchmarsh was educated at King Edward VII School (Sheffield) and Balliol College, Oxford, where he began his studies in October 1 ...

supervised his doctoral research. From 1937 to 1938, he studied at

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, after which he studied at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, until in 1940 he joined the

Royal Canadian Air Force The Royal Canadian Air Force (RCAF; ) is the air and space force of Canada. Its role is to "provide the Canadian Forces with relevant, responsive and effective airpower". The RCAF is one of three environmental commands within the unified Can ...

and served as a navigator. Guinand worked as an assistant at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

, and then as a lecturer at the

Royal Military College of Science The Royal Military College of Science (RMCS) was a British postgraduate school, research institution and training provider with origins dating back to 1772. It became part of the Defence Academy of the United Kingdom in 2009, and ceased to exis ...

, where he was eventually promoted to

Associate professor Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''. In the ''North American system'', used in the United States and many other countries, it is a position ...

of Mathematics. In 1955, he was named Head of department at the

Armidale Armidale is a city in the Northern Tablelands, New South Wales, Australia. Armidale had a population of 23,967 as of the 2021 census. Estimated resident population, 30 June 2018. It is the administrative centre for the Northern Tablelands reg ...

. After two years at Armidale, he moved to the

University of Alberta The University of Alberta (also known as U of A or UAlberta, ) is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford, the first premier of Alberta, and Henry Marshall Tory, t ...

Edmonton, Alberta Edmonton is the capital city of the Provinces and territories of Canada, Canadian province of Alberta. It is situated on the North Saskatchewan River and is the centre of the Edmonton Metropolitan Region, which is surrounded by Central Alberta ...

, and in 1960 moved again to the

University of Saskatchewan The University of Saskatchewan (U of S, or USask) is a Universities in Canada, Canadian public university, public research university, founded on March 19, 1907, and located on the east side of the South Saskatchewan River in Saskatoon, Saskatch ...

. In 1964, he moved once more, becoming the first chairman of the mathematics department at

Trent University Trent University is a public liberal arts university in Peterborough, Ontario, with a satellite campus in Oshawa, which serves the Regional Municipality of Durham. Founded in 1964, the university is known for its Oxbridge college system, sma ...

which had been founded the previous year.

Work

Guinand's research included work in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

(particularly

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s and the

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

), as well as generalizations of the

Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

, in addition to publications on assorted topics including air navigation and the computation of pi. In 1959, he published a paper on the

Poisson summation formula In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function (mathematics), function to values of the function's continuous Fourier transform. Consequently, the pe ...

for which he presented a simpler solution. (HTML 117 kB) Guinand's work on this problem was largely forgotten and remained in obscurity until it was re-discovered by

Yves Meyer Yves F. Meyer (; born 19 July 1939) is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017. Biography Born in Paris, Yves Meyer studied at the Lyc ...

in 2015.

References

External links

mathoverflow.net: Have the explicit Poisson-type formulas of Guinand and Meyer been observed before?
(2016-03-26) 1912 births 1987 deaths 20th-century Australian mathematicians {{Mathematician-stub