Born in Edmonton, near London, Taylor studied at Cambridge University, and was secretary to the Royal Society during the period 1714–18. He made important contributions to the development of the differential calculus in his Methodus incrementorum directa et inversa (1715; Direct and Indirect Methods of Incrementation). This contained the formula known as Taylor's theorem, which was recognized by Joseph Lagrange in 1772 as being the principle of differential calculus. The Methodus also contributed to the calculus of finite differences, which Taylor applied to the mathematical theory of vibrating strings.

Outside mathematics Taylor was an accomplished artist and this led him to an interest in the theory of perspective, publishing his work on this subject in Linear Perspective (1715). Taylor expansions are named for him.