Archimedes & The First Eureka, or, How to Weigh a Tyrant’s Crown

How many great ideas have you had in the shower? Probably quite a few. It is therefore not so surprising that history’s most famous spark of genius—the one that gave us the term “Eureka!”—came from a bathtub.

The occupant of that tub was Archimedes, the most prominent mathematician and scientist of his time (c. 287 BC – c. 212 BC). Archimedes had been tasked by his local tyrant, Hiero II, to determine whether his shiny new crown was made from solid gold or if it had been cut with far less kingly silver. But how could he find out without melting down the crown? Not wanting to disappoint the despot, Archimedes thought long and hard about a process. Eventually, needing a break, he went for a bath.

As Archimedes stepped into the tub, he noticed that the water level rose. His answer came with it! If he could measure the amount of water that an object displaced, he realized, then he could measure the volume of the object. If he took a piece of gold the same weight as the crown and noted how much water it displaced, he could measure whether the crown displaced the same. If it did, the crown was solid gold; if it didn’t, then it wasn’t. Simple!

This sudden shower of insight pleased Archimedes so much that he reputedly ran naked through the streets of Syracuse, shouting “Eureka!” (or more likely, εὕρηκα which is the Ancient Greek for “I have found!”). Archimedes’ plan worked: not only had he pleased his tyrant master, he’d had the first Eureka, and the human race was to have many more in the centuries to come.