Eureka Moment Meaning

(idiomatic) The moment of a sudden unexpected discovery.

Example: 2002, Evolutionary biology's 'Eureka!' moment supposedly took place some time in September or October 1835, during the Beagle's five-week visit to the Galapagos Islands. — London Review of Books, 7 Mar 2002
2002, The dreams of a farm boy, the eureka moment in a potato field, the confession to a teacher, the confidence in him shown by businessmen and bankers and investors, the breakthroughs in the laboratory, all the years of work, the decisions of the official patent examiners, those hard-fought victories, all of those demonstrations that had come and gone, the entire vision of the future. — The New Yorker, 27 May 2002
2003, In “Higher,” Bascomb’s account of the race at the end of the nineteen-twenties to build the tallest building in the world, we get one wonderful origin myth and eureka moment: an engineer sees his wife resting a heavy book on the family birdcage and realizes that a lightweight girded structure can carry an immensely heavy load. — The New Yorker, 15 Dec 2003
2004, Melnik said, “Jesus Christ, if I didn’t jump three feet in the air! It was totally a eureka moment.” — The New Yorker, 7 Jun 2004
2004, Historians teach us to be suspicious of "Eureka" moments, but there are moments when something happens to make one say "Eureka" — The New Yorker, December 6, 2004, p.104