Son of Robert Paman, he was born at his father's estate of Chevington, Suffolk.
He entered as a sizar at Emmanuel College, Cambridge, on 22 June 1643, where William Sancroft was his tutor.
On 20 June 1656 he kept an act for a medical degree before Professor Francis Glisson, maintaining the thesis Morbis acutis convenit dieta tenuissima In the same year he was senior proctor, and in 1658 he graduated M.D., being incorporated M.D.
He was elected public orator at Cambridge on 5 March 1674, ahead of Isaac Newton,[2] and held office till 9 July 1681.
On 21 June 1679 he was appointed Professor of Physic at Gresham College, and on 1 December 1679 he was elected Fellow of the Royal Society.