Day 22 · Jan 22

Ramanujan's Taxi

On this day in 1887, Srinivasa Ramanujan was born in Erode, Tamil Nadu. When G.H. Hardy visited him in hospital and mentioned arriving in taxi number 1729, Ramanujan replied instantly: 'No, it is a very interesting number — the smallest expressible as the sum of two cubes in two different ways.' 1³ + 12³ = 1729 and 9³ + 10³ = 1729. Hardy later wrote: 'I realised that I was in the presence of a man of altogether exceptional originality and power.' The number 1729 is now called the Hardy–Ramanujan number.

Can you verify that 1³ + 12³ = 9³ + 10³ = 1729 without a calculator?

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