After graduating in 1933, Guinand attended the University of Oxford on a Rhodes Scholarship, where Edward Charles Titchmarsh supervised his doctoral research.
[1] Guinand worked as an assistant at the University of Cambridge, and then as a lecturer at the Royal Military College of Science, where he was eventually promoted to Associate professor of Mathematics.
In 1964, he moved once more, becoming the first chairman of the mathematics department at Trent University which had been founded the previous year.
[1] Guinand's research included work in number theory (particularly prime numbers and the Riemann hypothesis), as well as generalizations of the Fourier transform, in addition to publications on assorted topics including air navigation and the computation of pi.
[4][5] Guinand's work on this problem was largely forgotten and remained in obscurity until it was re-discovered by Yves Meyer in 2015.