Mathematics
Why the Intermediate Value Theorem Guarantees a Root
Quick fact
The Intermediate Value Theorem was first formalized by Bernard Bolzano in 1817 and independently by Augustin-Louis Cauchy, establishing a rigorous foundation for calculus.
Why this is interesting
Picture walking up a hill; to get from the valley up to the peak, you must pass through every height in between. Now imagine a function that goes from negative to positive — how can you be absolutely sure it hits zero?