Unique among celebrated scientists, Newton was equally gifted at theoretical physics, experimental physics and pure mathematics. He was also exceptional in another, less well-recognised sense. No one has come near to equalling his extraordinary analytical power.Analytically-derived truths are controversial because such truths can only be established by extended experimental verification or by their success in generating further truths by systematic development. While Newton's optics was ultimately established by the first method and his theory of gravity by the second, much of his work on other subjects, though equally powerful and innovative, has never been totally established as part of this analytical context. This book discusses why the innovations matter today and why they were, and sometimes still are, controversial.