IVT
A mathematician explains the Intermediate Value Theorem with a growth-chart example; a skeptic asks why something so obvious needed a proof.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2018-07-12-ivt/ (CC BY-NC 4.0)Transcript
A: "The Intermediate Value Theorem says that if you're 3 feet tall, and later 5 feet tall, then sometime in between you must have been 4 feet tall! Huge breakthrough when Cauchy proved it."
B: "But... isn't it obvious?"
A: "Oho! Not if you rephrase it in abstract technical language! Then it takes YEARS to pin down!"
B: "So... a mathematician's job is to make pointless and trivial accomplishments sound impressive?"
A: "See? We're just like everybody else!"