Every Map Needs Only 4 Colors

Grab any map, any map at all. States, countries, made-up regions, whatever. Now try to color it so that no two neighboring regions share the same color. You might think you'd need dozens of colors, but you don't. You only ever need four. That's the four color theorem. No matter how complicated the map, no matter how many regions, four colors is always enough. And people tried to prove this for over a hundred years. This was noticed in flag patterns in around the 1850s. But the proof didn't come until 1976, and the wild part, the proof required a computer. This team reduced every possible map to 1,936 special cases, and then a computer checked each one. It was the first major theorem proved by a computer. Mathematicians were furious, and some refused to accept it. But it's true. Four colors, every single map, always enough.