Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

All good problem-solvers know that hard problems become easier when they’re split into chunks. The truly radical and distinctive move of calculus is that it takes this divide-and-conquer strategy to its utmost extreme—all the way out to infinity.

Thus, calculus proceeds in two phases: cutting and rebuilding. In mathematical terms, the cutting process always involves infinitely fine subtraction, which is used to quantify the differences between the parts. Accordingly, this half of the subject is called differential calculus. The reassembly process always involves infinite addition, which integrates the parts back into the original whole. This half of the subject is called integral calculus.

Creation is intuitive; reason comes later.