In high school, I studied advanced mathematics. This has two uses: Firstly, I can tell people that I once studied advanced mathematics. Secondly, I know about Euler’s equation.

Euler’s equation should not exist. A science fiction author would never imagine a formula so mind-blowingly perfect; it’s far too neat to seem real in an imaginary world. And yet it’s true, and absolutely true in the way only mathematics can be. I may have forgotten how to derive Euler’s equation from first principles (along with nearly every other detail from my high school classes), but I will always remember the resulting formula. It is irrefutable proof of mathematical perfection, and a reminder that we will never be able to fully grasp the meaning and reasons behind math.

Lo, here is the equation:

𝑒

^{𝑖𝜋}= -1

If it’s been a while since you studied math, perhaps this doesn’t look like much. But breaking it down reveals its beauty.

Firstly, in honor of pi day, take pi, or 𝜋: An irrational number, so-called because it goes on infinitely without repeating, 𝜋 was first discovered as the number that describes the relationship between a circle’s circumference and its diameter (circumference = 𝜋 x diameter.) In the centuries since, scientists have determined that 𝜋 also describes the way rivers wind and ripples of light in physics. Originally, though, 𝜋 belonged to the realm of mathematics that deals with shapes and sizes: geometry.

Another famous irrational number, 𝑒, comes from logarithms, which are a part of calculus—a totally different branch of mathematics. The full significance of 𝑒 takes a while to explain, but one key detail, forming the basis of its role in logarithms, is that the rate at which 𝑒^{x} grows is 𝑒^{x}. Like pi, *e* is the basis of many different formulas. Numerically, it equals 2.71828… going on continually, without repeating.

Then there’s 𝑖, which is an imaginary number. It’s a theoretical concept that can never practically exist. 𝑖 signifies the square root of -1, which is impossible. No two identical numbers can be multiplied together to get a negative, meaning there is no numerical square root of -1. The square root of 4 is 2, and you can have 2 apples. But you can never have √-1 apples.

And yet, take these three utterly different, complicated numbers and bring them together in Euler’s equation and you get a magically neat result: *e* to the power of (𝑖 multiplied by pi) equals -1. Or:

𝑒

^{𝑖𝜋}= -1

You can also write this as:

𝑒

^{𝑖𝜋}+ 1 = 0

The number one, of course, is the first natural number, the first positive integer, and the most common lead in sets of data: Quite simply, it’s how we start counting. And the number zero is the only non-positive natural number, the smallest non-negative quantity, signifying nothing.

In other words, one short equation includes five of the most important numbers in all of mathematics.

It’s almost unnerving. Taken alone, numbers like *e, *𝑖, and 𝜋 seem like the results of an imperfect human effort to understand the complexity of the world through mathematical relationships. Euler’s equation, though, shows there’s a unity behind these numbers. The sum total of human mathematic knowledge is no more than a tiny fraction of the complete, perfect system. And every number or equation we discover is a reflection of this abstract, inherent truth, rather than a human invention. Humans can hope to uncover mathematical truths, but we cannot create them.