// the mystery
Unreasonably effective
In 1960 the physicist Eugene Wigner wrote an essay called The Unreasonable Effectiveness of Mathematics in the Natural Sciences. His point: mathematicians often invent ideas purely because they're beautiful, and decades later physicists discover that the universe runs on exactly those ideas.
- Imaginary numbers started as a "useless" trick for solving equations. Now quantum mechanics can't be written without them.
- Curved geometry was a 19th-century curiosity. Then Einstein needed it to describe gravity as bent spacetime.
- Maxwell's four equations describe electricity and magnetism. Solve them, and out pops a wave moving at exactly the speed of light. Light, it turned out, is electricity and magnetism.
// the most beautiful equation
eiπ + 1 = 0
Euler's identity links five of the most important numbers in maths, each from a completely different corner:
| number | where it comes from |
|---|---|
| 0 | nothing; the starting point of counting |
| 1 | one; the building block of every other number |
| π ≈ 3.14159 | circles: how many diameters fit around the edge |
| e ≈ 2.71828 | growth: compound interest, populations, radioactive decay |
| i = √−1 | the imaginary number nobody believed in at first |
The simple version: multiplying by i means "turn 90°". Raising e to an imaginary power means "walk around a circle". So eiπ means "walk halfway around a circle of radius 1", which lands you exactly at −1. Add 1, and you get 0.
Circles, growth and rotation, all secretly the same idea. That's what I mean by poetry.
// go deeper