'Eureka!' — 'I have found it!' — is the most famous exclamation in the history of science. According to the story, Archimedes shouted it while running naked through the streets of Syracuse after making a breakthrough in his bathtub. But what was he actually solving?
The story comes from the Roman writer Vitruvius, writing over 200 years after Archimedes' death. King Hiero II of Syracuse had commissioned a gold crown and suspected the goldsmith had mixed in silver. He asked Archimedes to determine whether the crown was pure gold without melting it down.
The problem was density. Gold is denser than silver, so an equal weight of gold takes less volume than silver. The challenge was measuring the irregular volume of a crown. While stepping into a bath, Archimedes noticed that water displaced was proportional to his body's volume — and realized he could use the same principle on the crown.
The principle he discovered — that a submerged object displaces its own volume of water — allowed him to compare the crown's density to pure gold. If the crown displaced more water than an equal weight of pure gold, it contained a less dense metal mixed in.
Whether the naked street-running happened is uncertain — Vitruvius is not the most reliable historian. But Archimedes' Principle of buoyancy is real and correct, and it remains foundational in physics and engineering today. The 'Eureka moment' has become a cultural symbol for the flash of sudden insight.
Frequently Asked Questions
What did Archimedes discover in the bathtub?
Archimedes discovered the principle of buoyancy — that an object submerged in fluid displaces a volume of fluid equal to the object's own volume, and experiences an upward buoyant force equal to the weight of that displaced fluid.
Is the Eureka story true?
The basic premise — Archimedes solving a density problem using water displacement — is plausible and consistent with his known work. The naked running through streets comes from Vitruvius, writing over 200 years later, and is considered a colorful embellishment.
