principles.fyi · the brain · concept

e (Euler’s number)

A special number, about 2.718 — nature’s base for smooth growth.

e ≈ 2.71828 = (1 + 1/n)^n as n → ∞

e ≈ 2.718 is a constant like π. It falls out of compounding: grow by 100% but split it into infinitely many tiny steps and you land exactly on e. Its trick is that the curve e^x grows at a rate equal to its own height, which keeps the math clean — so e is the base used in exp, log, and inside softmax.