General
The 'Boring' Taxi Number That Hid a Famous Math Secret
What is the smallest positive integer expressible as the sum of two positive integer cubes in two distinct ways?
People also ask
What is the answer to the Ramanujan taxicab riddle?
The answer is 1729 — the smallest positive integer that can be written as the sum of two positive cubes in two different ways: 1³ + 12³ and 9³ + 10³.
Why is 1729 called the taxicab number?
Mathematician G. H. Hardy mentioned arriving in a taxi numbered 1729, calling it dull. Ramanujan replied it was special — the smallest number expressible as a sum of two cubes in two ways.
What are the two ways to write 1729 as a sum of cubes?
1729 = 1³ + 12³ (1 + 1728) and 1729 = 9³ + 10³ (729 + 1000). Both pairs of cubes add up to the same number.