Sheila Scott's father was rector of Trinity Academy Edinburgh and she attended the school. She attended Edinburgh Ladies' College from 1926 until 1928 when she graduated as Dux in Mathematics.
In the same year, 1928, she entered the University of Edinburgh where she won several scholarships. She graduated M.A. with first class honours in mathematics and natural philosophy in 1932. It was usual for the top students in those days to study at Oxford or Cambridge University after taking their first degree at a Scottish University. Scott spent three years at Girton College at Cambridge. Her final year at Cambridge was one in which she undertook research under Cartwright's supervision. She published her first paper on the work she had done under Cartwright's supervision On the asymptotic periods of integral functions in 1935.
Scott returned to Scotland to train as a teacher and she taught for five years in a number of schools from 1934. She taught at St Leonard's, a girls' school in St Andrews, as well as James Allen's School for Girls and Stowe School.
During this period Whittaker introduced Sheila Scott to A J Macintyre who was a mathematics lecturer at Aberdeen University. They married in 1940 and the following year Sheila Macintyre was appointed as an assistant lecturer in the same department as her husband in Aberdeen.
At Aberdeen Sheila Macintyre completed her doctorate under E M Wright's supervision. Wright wrote:-
... good as her research was there would have been more of it had she not had a family to look after.
Between 1947 and 1958 she published another ten papers during a period when she brought up her two children (a third child died at age two in 1949).
Sheila Macintyre was an active member of the Edinburgh Mathematical Society and of the Mathematical Association. In 1958 she was elected a Fellow of the Royal Society of Edinburgh.
In 1958 Macintyre and her husband accepted visiting research professorships at the University of Cincinnati. There she taught until her early death from cancer.
In  Cartwright quotes R C Buck who wrote about Macintyre:-
In her chosen area of analysis, she introduced powerful refinements of techniques, and what is much harder, new and original problems for investigation.
Wright, writing in , says:-
Brilliant original mathematician though Sheila was, it is even more as the superb teacher and the gay helpful colleague that we remember her. Her clarity of mind made her a quite exceptionally able lecturer, but it was her warm-hearted interest in each of her students (conbined with a shrewd assessment of their abilities) that made her so successful a tutor and regent. They repaid her by a very real affection and respect.
Article by: J J O'Connor and E F Robertson