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.
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.
Late in life I described my whole body of research as a boy finding smoother pebbles on the shore while the great ocean of truth lay undiscovered — a measure of how much science still had to find.
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.
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.
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.
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.
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.
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.
