This exclamation is most famously attributed to the ancient Greek scholar Archimedes; he reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose — he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. This meant that the volume of irregular objects could be calculated with precision, a previously intractable problem. He is said to have been so eager to share his realisation that he leapt out of his bathtub and ran through the streets of Syracuse naked.
Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden crown. Equipment for weighing objects already existed, and now that Archimedes could also measure volume, their ratio would give the object's density, an important indicator of purity.
This story first appeared in written form in Vitruvius's books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: balance the crown against pure gold in air, and then submerge the scale with crown and gold in water to see if they still balance.
Another mathematician, Carl Friedrich Gauss, echoed Archimedes when in 1796 he wrote in his notebook, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive integer could be expressed as the sum of at most three triangular numbers.
The expression is also quoted as the state motto of California, referring to the momentous discovery of gold near Sutter's Mill in 1848. The California State Seal has included the word "eureka" since its original design by Robert S. Garnett in 1849; the official text from that time describing the seal states that this word's meaning applies "either to the principle involved in the admission of the State or the success of the miner at work". In 1957, the state legislature attempted to make "In God We Trust" the state motto, but this attempt did not succeed, and "Eureka" became the official motto in 1963.
The city of Eureka, California, founded in 1850, uses the California State Seal as its official seal. Eureka is a considerable distance from Sutter's Mill, but was the jumping off point of a smaller gold rush in Trinity County, California in 1850. It is the largest of at least eleven remaining US cities and towns named for the exclamation, "eureka!". As a result of the extensive use of the exclamation dating from 1849, there were nearly 40 locales so named by the 1880s in a nation that had none in the 1840s. Many places, works of culture, and other objects have since been named "Eureka"; see Eureka for a list.
"Eureka" was also associated with a gold rush in Ballarat, Victoria, Australia. The Eureka Stockade was a revolt in 1854 by gold miners against unjust mining license fees and a brutal administration supervising the miners. The rebellion demonstrated the refusal of the workers to be dominated by unfair government and laws. The Eureka Stockade has often been referred to as the 'birth of democracy' in Australia.
Hēurēka is the 1st person singular perfect indicative active of the Greek verb heuriskein, (Greek εὑρίσκειν) meaning "to find"; it means "I have found it", or more literally, "I am in a state of having found it". The English version of the word is pronounced /jʊˈriːkə/; in ancient Greek ηὕρηκα (later εὕρηκα) would have been pronounced [hɛːúhr̥ɛːka] in both former and later forms, while the modern Greek pronunciation is [ˈevrika]. The initial /h/ is dropped in many European languages; Finnish is one of those that preserve it (e.g. in Heureka), German is another one (cf. Heureka).