The Payoff of Weird

The holdout was philosophical: numbers were supposed to count real things, and you cannot have −3 apples.

But accepting negatives cracked open the next door. To solve x² = −1, mathematicians invented i, defined so that i² = −1 — a number that looked even more absurd than a negative.

Without it, electrical engineering, quantum physics, and signal processing would not exist. The pattern repeats: each time a "weird" number is finally accepted, a whole field opens up later.