by Jonathan Kujawa

For mathematics, 1666 was the Annus Mirabilis (“wonderous year”). For the rest of humanity, it was pretty terrible. The plague once again burnt across Europe [1]. Cambridge University closed its doors and Issac Newton moved home.
Although only twenty-three years old, Newton was pretty well caught up to the state of the art in math and physics. Newton was brilliant, of course, but it also wasn’t so hard for an educated person to be at the cutting edge. After all, it was only thirty years earlier that Descartes and Fermat had introduced the notion of using letters (like x and y) for unknowns and had the insight that by plotting points on the xy-plane you could view algebra and geometry as two sides of the same coin.
With nothing better to do while quarantined at the family home, Newton settled back into the study of math and physics and, it turns out, ignited several world-changing revolutions in the process. Newton cracked open a 1000 page notebook he had inherited from his stepfather and got to work, recording his thoughts as he went. After reading Euclid’s Elements (still the gold standard after nearly 2,000 years!), Descartes, and the other books he had on hand, Newton began posing ever harder questions for himself which he then solved, inventing new math along the way.
Amazingly, Newton’s notebook (which he called his “Waste Book”) still exists! It is kept by the Cambridge University library along with thousands of pages of his other writings. In fact, you can read it for yourself online at the University’s website.
Some of the questions Newton posed could be considered standard, even for his day: computing roots, solving problems in geometry, and the like. Others are more open-ended: “If a Staffe bee bended to find the crooked line which it resembles.” or “To find such lines whose areas length or centers of gravity may bee found.”
In due course, Newton asks himself questions we recognize as the forerunners of calculus. Read more »