The story of Euler’s Number.
A passionate engineer discussing it to a colleague over coffee.
In 1683, a Swiss mathematician named Jacob Bernoulli was trying to solve a problem that had absolutely nothing to do with the secrets of the universe. He was just thinking about money.
Specifically, he was dreaming up a hypothetical, completely unrealistic bank account that paid 100% interest every single year.
Bernoulli realized something interesting about compound interest: the more frequently the bank pays you, the more money you make, because your interest starts earning its own interest. If they pay you once a year, your 1 coin becomes 2. If they split it and pay you every six months, you end up with 2.25. If they pay you every single month, you get 2.61.
So, Bernoulli asked the ultimate greedy question: What if the bank compounds my money continuously? Every day, every second, every millisecond?
Human intuition tells us that if you compound something an infinite number of times, you should end up with infinite wealth. But Bernoulli did the math and hit a brick wall. He discovered that as you chop time into infinitely smaller pieces, the growth fundamentally stalls out. It hits an invisible speed limit of exactly 2.71828…
He had found something incredibly strange, but he didn’t really know what to do with it. To him, it was just a quirky financial puzzle. He didn’t even give the number a name.
Fast forward about fifty years.
Enter Leonhard Euler, one of the most brilliant minds in the history of mathematics. Euler wasn’t looking at bank accounts; he was obsessed with calculus and the physics of motion. He was hunting for a very specific, “perfect” curve.
Think about how things grow in nature. Usually, how tall a curve is on a graph doesn’t perfectly match how fast it’s growing. Euler wanted to find a mathematical anomaly that a specific curve where its height was perfectly equal to its rate of change at every single microscopic point. If the curve was at a height of 10, it was growing at a speed of exactly 10.
Euler dug into the calculus and realized that there was only one number in the entire universe that created this perfect, self-replicating curve. It was Bernoulli’s bizarre bank number: 2.71828…
Because Euler needed a shorthand variable to write out this massive, infinite decimal in his proofs, he assigned it the letter e.
Despite the rumor, he almost certainly didn’t name it after himself he wasn’t that arrogant. He was just already using a, b, c, and d for other variables, so e was the next available letter. But his proofs were so staggering that the mathematical community permanently crowned it “Euler’s Number.”
And here is the beautiful part: once Euler proved what e actually was the ultimate mathematical engine of continuous growth scientists suddenly started finding it everywhere.
Because e represents a system whose growth is perfectly tied to its current size, it is the exact blueprint nature uses to run the physical world.
When bacteria multiply in a petri dish, their growth rate is calculated using e.
When a hot cup of coffee cools down in a room, the rate of temperature loss is governed by e.
When radioactive uranium decays, its half-life is dictated by e.
Bernoulli thought he was looking at a quirk about money. But Euler proved that he had accidentally stumbled upon the mathematical heartbeat of the universe.