Mathematics
Continuity and the Intermediate Value Theorem in Real Analysis
Quick fact
The Intermediate Value Theorem is so intuitive that it was used by ancient civilizations to find roots of equations, but it was only rigorously proven in the 19th century by mathematicians like Bolzano and Cauchy.
Why this is interesting
Imagine drawing a continuous line on a piece of paper. If you start at one point and end at another, is there always a point where the line crosses a horizontal line halfway between? The answer is yes, and that's the Intermediate Value Theorem.