Draw the wildest pattern of shapes you can. No matter how crazy your drawing, you can always color it in using four colors without any of them touching each other. Don't believe me? Try it out for yourself.
This idea was first discovered 1852 and to this day no human has proven that it's true nor found a counter-example showing that it's false. Though in the 1960's a computer was used to prove it is true, it used methods that some people don't fully accept because a human can't go back and check it. Either way, this was historically the first conjecture that was tackled by a computer.