The Hardy-Ramanujan number is 1729, the smallest number that can be expressed as the sum of two cubes in two different ways: 1³ + 12³ = 1 + 1728 = 1729; and 9³ + 10³ = 729 + 1000 = 1729. While many readers can wonder, ‘okay, so what?’, it is the way Ramanujan saw the number that is interesting. Story continues below this adWhat does the Hardy –Ramanujan number reveal about Ramanujan? The number 1729 appears in Ramanujan’s works in yet another context, this time related to Fermat’s last theorem. Now if 9³ + 10³ had equalled 1728 and not 1729, it would violate Fermat’s theorem, because 1728 is 12³.

Source: Indian Express December 23, 2025 06:05 UTC