The identity comes from Euler’s formula
Start with Euler’s formula:
Now let x = π. Since cos π = −1 and sin π = 0, the right side becomes −1. Rearranging gives eiπ + 1 = 0. The famous identity is therefore a special case of a more general formula, not an isolated coincidence.
Why people find it beautiful
The equation brings together e, the natural base of exponential growth; i, the imaginary unit; π, the circle constant; and the additive and multiplicative identities 0 and 1. It also uses addition, multiplication through the exponent, exponentiation, and equality with almost no visual clutter. That compression makes it memorable.
Beauty is not the only reason it matters
Euler’s formula links exponential behavior to rotation in the complex plane. That link is foundational in complex analysis and enormously useful in differential equations, Fourier methods, wave physics, electrical engineering, and signal processing. The identity is the poster child; the underlying formula is the workhorse.
Why wear it?
Because this is one of those Expressions that can be recognized from across a room by exactly the people most likely to care about it. It is mathematical elegance without explanation text. If you know why the line is remarkable, the line is enough.
Wear what you know.
You are not wearing a random graphic. You are wearing something you know, understand, believe, study, build, play, or find worth thinking about. That is the idea behind every NerdWear Expression.