Number PatternsNumber TheoryEasy
The 1729 Secret
The 'dull' taxi number Ramanujan saw was the smallest sum of two cubes two ways.
Worked demonstration
When G. H. Hardy called the taxi number 1729 "rather dull", Ramanujan replied it was the smallest number that is a sum of two cubes in two different ways. Compute 1³ + 12³.
Try it yourself
Why it works
1729 = 1³ + 12³ = 9³ + 10³ — the smallest 'taxicab' number, expressible as a sum of two positive cubes in two different ways.
Background & Explore Further
From Hardy's well-attested anecdote about Ramanujan (1887–1920). Explore taxicab numbers further — Ta(3) = 87,539,319 is the smallest expressible three ways.