# The 17 equations that changed the world, according to Ian Stewart

In his 2012 book, mathematician Ian Stewart tells the story of 17 equations, from Pythagoras to Black–Scholes, that transformed science, technology and even finance. Which one matters most?

- 12 votes · 17 items
- Jan 7, 2019 · Amandine Durand
- https://even.best/en/l/2717/the-17-equations-that-changed-the-world-according-to-ian-stewart

## Top 17

1. **The Pythagorean theorem** (2 · ▲2 ▼0) — a² + b² = c², the basis of geometry and mapping.
2. **Calculus** (2 · ▲2 ▼0) — Newton and Leibniz's derivative.
3. **The normal distribution** (1 · ▲1 ▼0) — The bell curve of statistics.
4. **The second law of thermodynamics** (1 · ▲1 ▼0) — Entropy only ever increases.
5. **E = mc²** (1 · ▲1 ▼0) — Einstein's relativity and nuclear energy.
6. **The Black–Scholes equation** (1 · ▲1 ▼0) — Pricing financial options, and its excesses.
7. **Logarithms** (0 · ▲1 ▼1) — Turning multiplication into addition.
8. **The wave equation** (0 · ▲1 ▼1) — Vibrations, sound and music.
9. **Newton's law of gravity** (0 · ▲0 ▼0) — The force that makes the apple fall and the Moon go round.
10. **The square root of minus one** (0 · ▲0 ▼0) — Complex numbers.
11. **Euler's formula for polyhedra** (0 · ▲0 ▼0) — Vertices minus edges plus faces equals two.
12. **The Fourier transform** (0 · ▲0 ▼0) — Breaking a signal into frequencies: from JPEG to MRI.
13. **The Navier–Stokes equations** (0 · ▲0 ▼0) — The motion of fluids, from aircraft to weather.
14. **Maxwell's equations** (0 · ▲0 ▼0) — Electromagnetism, radio and television.
15. **The Schrödinger equation** (0 · ▲0 ▼0) — Quantum mechanics, from lasers to chips.
16. **Shannon's information theory** (0 · ▲0 ▼0) — Measuring information: the basis of digital technology.
17. **Chaos theory** (0 · ▲0 ▼0) — The logistic map and the butterfly effect.

How is this ranking ordered? By people's votes: each ▲ adds a point and each ▼ takes one away. Anyone can vote and add what is missing.