Why 1729?

1729

1729, also known as the original taxicab number, is named after the licence plate number of a taxi that a mathematician named G. H. Hardy took to see another genius mathematician Srinivasa Ramanujan, who was in a hospital. Hardy got interested in 1729 number but he thought it was a dull number. But Srinivasa Ramanujan was so smart that he told Hardy that 1729 is the smallest number that can be expressed as two different sums of 2 cubed numbers. One expression is 10³ + 9³. The other one is 12³ + 1³. And Hardy of course was surprised.

And that’s why I named my website jv1729.com.

10³ + 9³ = 12³ + 1³ = 1729

1729 is not the only number that can be expressed as such. Here are some more numbers that work the same way: two different sums of two cubes.

• 4104 = 2³ + 16³ = 9³ + 15³
• 13832 = 2³ + 24³ = 18³ + 20³
• 20683 = 10³ + 27³ = 19³ + 24³
• 32832 = 4³ + 32³ = 18³ + 30³
• 39312 = 2³ + 34³ = 15³ + 33³
• 40033 = 9³ + 34³ = 16³ + 33³
• 46683 = 3³ + 36³ = 27³ + 30³
• 64232 = 17³ + 39³ = 26³ + 36³
• 65728 = 12³ + 40³ = 31³ + 33³
• 110656 = 4³ + 48³ = 36³ + 40³
• 110808 = 6³ + 48³ = 27³ + 45³