You say it at the moment the answer suddenly arrives — the problem you have been stuck on cracks open and you see it. 'Eureka! That's why the code kept crashing.' As a plain exclamation it is now half a joke: real people shout it playfully, or a writer uses it to mark a discovery, but nobody says it seriously in an office. Its more useful modern life is as a describing word in front of a noun, especially 'a eureka moment' — the instant an idea lands. That phrase is completely ordinary in business and teaching English, and it is the form learners should actually own. You will also see 'the eureka effect' for the psychology of sudden insight, and occasionally the bare noun 'a eureka' for the discovery itself. The word is Greek for 'I have found it', and the story attached to it is worth telling students: Archimedes, asked whether a crown was really solid gold, is said to have noticed how his own body pushed the water up as he got into a bath, understood how to measure the crown's volume, and run out shouting heúrēka. The story may not be true, but it is why the word means what it means — insight arriving all at once, sideways, when you were not sitting at your desk.