Who is credited with saying 'Eureka' after making a scientific discovery in his bathtub?

The famous exclamation "Eureka!" is widely attributed to the ancient Greek scholar Archimedes, following a breakthrough he made while bathing. The story begins in Syracuse, where King Hiero II suspected his goldsmith had defrauded him by substituting some of the gold in a newly crafted crown with a cheaper metal, likely silver. The king tasked Archimedes with determining the crown's purity without damaging it, a perplexing problem at the time.

While pondering this challenge, Archimedes stepped into a bathtub and observed the water level rise as his body displaced it. This seemingly ordinary event sparked a profound realization: the volume of water displaced by an object is equal to the volume of the object itself. This insight provided him with a method to accurately measure the volume of irregularly shaped objects, like the crown. Overcome with excitement at having found the solution, he reportedly leaped from the bath and ran naked through the streets of Syracuse, exclaiming "Eureka! Eureka!" which is Ancient Greek for "I have found it!"

This pivotal moment led to the formulation of what is now known as Archimedes' Principle, a fundamental concept in fluid mechanics. By measuring the volume of the crown and comparing its density to that of pure gold, Archimedes was able to prove that the goldsmith had indeed mixed in other metals. The tale, first recorded by the Roman architect Vitruvius, not only highlights Archimedes' genius but also cemented "Eureka" into popular culture as an expression of sudden, joyful discovery.