ELI5: theorem

// eli5

What is a theorem?

A theorem is a math rule that someone has proven to be true using logic and reasoning [3]. Think of it like a magic trick that always works the same way every time—once a mathematician shows why it works, everyone can trust it [3].

Why do we need theorems?

Without theorems, we'd have to figure out math problems from scratch every time [3]. But when someone proves something is always true, we can use that rule over and over again to solve new problems [3].

What's a famous example?

The Pythagorean theorem is probably the most famous one—it's a rule about triangles that works every single time [6]. It tells you how the sides of a right triangle always relate to each other [6].

How do mathematicians prove theorems?

They use step-by-step logical reasoning, kind of like following a recipe, to show that something must always be true [3]. Once they prove it works, it becomes a rule that everyone can use [3].