What is his number?

1729 is a rather interesting number, often referred to as the <a href="https://www.wikiwhat.page/kavramlar/Hardy–Ramanujan%20number">Hardy–Ramanujan number</a> or taxicab number. It is the smallest positive integer that can be expressed as the sum of two cubes in two different ways.

Specifically:

  • 1729 = 1³ + 12³ = 1 + 1728
  • 1729 = 9³ + 10³ = 729 + 1000

This property makes it a special case in <a href="https://www.wikiwhat.page/kavramlar/number%20theory">number theory</a>. The anecdote surrounding this number involves the mathematicians <a href="https://www.wikiwhat.page/kavramlar/G.%20H.%20Hardy">G. H. Hardy</a> and <a href="https://www.wikiwhat.page/kavramlar/Srinivasa%20Ramanujan">Srinivasa Ramanujan</a>. Hardy recounted that he had taken a taxi with the number 1729 to visit Ramanujan, who was ill. Hardy remarked that the number seemed rather dull. Ramanujan immediately pointed out its unique property of being the smallest number expressible as the sum of two cubes in two different ways, thus making it far from dull.