Gregory's major contributions include:
(i) being one of the three founders of calculus (with Newton and Leibniz), including discovering Taylor series (40 years before Taylor) and giving the first proof of the fundamental theorem of calculus;
(ii) inventing the gregorian telescope and probably laying down in the King James library what would have been one of the first astronomical meridian lines in the world;
(iii) discovering the diffraction grating by shining a light through a bird's feather (possibly a seagull's picked up on the west sands).
Locations where Gregory is being acknowledged in St Andrews include:
(i) a major permanent exhibition of his life and work in the physics department up the stairs outside the main lecture theatre,
(ii) an artist's impression of his discovery of the diffraction grating by a local artist (Helen Firth) in the Mathematics building on the main corridor,
(iii) an interpretation board in St Mary's quad describing his work in the King James library
(iv) a plaque inside the King James library together with a later replica of a meridian line across the floor and a bracket that is likely to have supported his telescope
(v) a continuation of the meridian line across the pavement in South Street outside Parliament Hall, together with a plaque on the wall
(vi) Gregory's pillar on schooniehill, which is he likely to have used to line up his telescope when making astronomical measurements
Further information about James Gregory can be found at:
(i) MacTutor History of Mathematics site
(set up by Edmund Robertson and John O'Connor).
This includes details of his history, his contributions to mathematics, astronomy and physics, his observatory, his clock, the King James library, and his correspondence with John Collins.
(ii) James Gregory Public Lectures on Science and Religion
(iii) A Lecture by Edmund Robertson (Aug, 2013) entitled "James Gregory: Regius Professor of Mathematics"