Meanings
plural happy numbers
- mathematicsAny number that eventually reaches 1 after some number of iterations of replacing each of its digits by the sum of that digit's squares.
13 is a happy number because 1² + 3² is 10, and 1² + 0² is 1.
Antonyms: sad number, unhappy number
Synonyms & antonyms
nounAny number that eventually reaches 1 after some number of iterations of replacing each of its digits by the sum of that digit's squares.
Origin
Popularised by the British mathematician Reginald Allenby in the 1960s, who developed this concept from his daughter, while similar mathematical formulas may have existed earlier in Russia. The number was called "happy" because the iteration to reach 1 was treated like a game of numbers, where reaching 1 is compared to "winning" that game.
Full word history & related roots →Translations
Polish liczba wesoła
- liczba wesołanumber
Cite this entry
happy number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/happy%20number
“happy number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/happy%20number. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “happy number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/happy%20number.
Source: happy number on Wiktionary, CC BY-SA 4.0.