I work across mathematics, physics, astronomy and optics. My Principia states the laws of motion and universal gravitation, I built calculus, and I showed that white light is a spectrum of colours.
My report of 21 September 1717 to the Treasury reset the exchange rate between gold and silver coin; the royal proclamation that followed capped a guinea at 21 shillings and in effect moved Britain to its first gold standard.
Critics said my gravity was an "occult agency". In the General Scholium of the 1713 second edition of the Principia I answered that the phenomena imply attraction, and that framing hypotheses beyond them is unnecessary and improper.
Appointed Warden of the Mint in 1696 and Master from 1699, I ran the Great Recoinage, prosecuted 28 counterfeiters and re-engineered minting: weekly output rose from 15,000 to 100,000 pounds and coin weights became far more precise.
Book II of the Principia gave the first comprehensive treatment of motion under resistance, defined what is now called a Newtonian fluid, and first analysed Couette flow — engineering science of motion as it is found in the world.
From 1679 I proved that an inverse-square force produces elliptical orbits, then expanded that proof into the Principia (5 July 1687): three laws of motion and universal gravitation, the foundation of classical mechanics and modern physical science.
I wrote this line to Robert Hooke in February 1675, during our dispute over optical discoveries. It is the sentence of mine most quoted about how science builds on earlier research.
Measuring Newton's rings in 1671, I averaged all the differences and compared the average with the first ring — a noise-reduction method no one else used then. By 1700 I extended it to equinox timings and wrote the first normal equation of least squares.
In late 1668 I built the first known functional reflecting telescope, about eight inches long, grinding my own speculum-metal mirrors to escape the chromatic aberration of lenses. It showed Jupiter's four Galilean moons and the crescent of Venus.
My prism experiments of 1666–1672 showed that white light is a mixture of colours, that a prism refracts each colour by a different angle, and that colour belongs to the light, not to the object. My 1672 paper underpins all later research on colour.
I began my method of fluxions in 1664; by 20 May 1665 I could compute the tangent and curvature at any point of a continuous curve, and by year's end I had a systematic calculus unifying differentiation and integration.
Beyond calculus I discovered the generalised binomial theorem, Newton's method, the Newton–Cotes formulas and the general Taylor series, classified the cubic curves and solved the brachistochrone in a night — tools science still uses.
An undistinguished Cambridge student, I taught myself from Aristotle, Descartes and Galileo through private notebooks; in 1669 I succeeded Isaac Barrow as Lucasian Professor, yet my lectures were almost always empty.
