Meaning of Eureka

“Eureka” means “I have found it” in Greek. According to legend, it is what the great Greek mathematician Archimedes shouted when he solved a particularly vexing problem posed to him by King Hieron II of his native Syracusa (Syracuse), Sicily.

King Hieron II (to whom some say Archimedes was related) commissioned a gold crown. He gave the goldsmith a known amount of gold with which to fashion the crown. When it was finished, however, the king came to suspect that the goldsmith had cheated him by mixing some of the gold with another less valuable metal (probably silver) and keeping the remainder for himself. The King asked Archimedes to determine whether he had been cheated, but without damaging the crown.

The problem came down to determining the volume of the crown, because then its density could be calculated (by dividing the weight of the crown by its volume) and compared to the known density of pure gold. But, how could he determine the volume of such an irregular solid as a crown? (For pictures of Greek gold crowns, click here.)

The legend is that one day when Archimedes was stepping into the public bath, he observed that the water rose (in some versions of the story it is suggested that some of the water overflowed the tub). In a brilliant insight, he concluded that the volume of water displaced must be equal to the volume of the object immersed (in this case his foot or however much of his body was already in the tub). He is said to have leapt from the tub and run naked through the city yelling, “eureka!” (I have found it!) Since then, it has come to be common for someone to cry “eureka!” when she or he finds the solution to a particularly vexing problem.

By the way, it should be noted that, in a time when people frequented public baths, and when man commonly exercised in the nude in public, the sight of a man running naked through the streets would not have had the same impact as it might have today. One of Archimedes prominence and stature, crying “eureka!” would have been noticed, however.