Isaac Newton · 1665
ẋ · ẍ · ẏ
Called it "The Method of Fluxions." Used dot notation. Built to describe motion and physics.
Gottfried Leibniz · 1675
dy/dx · ∫ f dx
Called it "Calculus." Used elegant notation. Built for pure mathematics. His symbols survive today.
Rectangles (n)
4
Approx. Area
—
True Area
—
4
x²
The ancient question: how do you find the area under a curve? Fill it with rectangles. Make them thinner and thinner. As n → ∞, the approximation becomes exact. Newton and Leibniz both saw this truth — independently, simultaneously, across a continent. This is the fundamental theorem of calculus.