Behind this text, six points are following the same three equations. They start almost exactly together; within seconds they go their separate ways. Three short lines of calculus, and the shape of weather itself appears.
Three stages, from the language of functions to the frontier of Further Pure. Each is built module by module; a lesson lights up the moment it is ready.
Every idea here was once a breakthrough. Some of them still run the world around you.
Napier's tables cut astronomers' work from months to days. Today the same idea measures earthquakes, sound in decibels and acidity in pH: scales where each step means “ten times more”.
Newton used it to explain why planets move in ellipses. The same derivatives and integrals now steer spacecraft, price options and train neural networks.
Once called “imaginary”, they now describe alternating current in every power grid and the waves that carry your phone calls and music.
From the cooling of a cup of tea to the spread of an epidemic: write down how fast something changes, and solve for what happens next.
The book of nature is written in the language of mathematics.