What happens if you start counting and never stop? That’s how you get to infinity, a mathematical idea that has puzzled people for centuries, and even driven some mad. Take the following question, posed by the Greek philosopher Zeno: An arrow is shot, and first travels half the distance to the target. It then must travel half the distance that is left, then again half the remaining distance, and so on. How can it ever reach the target? The answer: An infinite number of events can happen in a finite amount of time. If you find yourself confused by this sort of thing, don’t worry – most mathematicians are too.

Despite its strangeness, infinity is very useful. It’s what makes calculus work, and therefore underpins many principles of modern engineering. The universe is not infinite – just really big. However, the theoretical concept of infinity is nonetheless important for understanding physics, including quantum mechanics and black holes.