Mathematician, born in Drumoak, Aberdeen, NE Scotland, UK. He graduated from Aberdeen University and went to London in 1662, and the following year published Optica promota (The Advance of Optics), containing a description of the Gregorian reflecting telescope he had invented in 1661. He went to Padua, Italy, and published Vera circuli et hyperbole quadratura (1667, The True Squaring of the Circle and of the Hyperbola), making use of convergent infinite series to find the areas of these figures. He became professor of mathematics at St Andrews University (1669--74) and at Edinburgh University (1674--5). Manuscripts discovered after his death showed that he had anticipated several discoveries in number theory, including the Taylor expansion.