# Never a Dull Number

Brian Hayes in American Scientist:

It all begins with a taxi ride. In 1918 the Cambridge mathematician G. H. Hardy goes to visit his protégé Srinivasa Ramanujan and mentions that the number of his taxicab was rather dull: 1,729. Not dull at all, Ramanujan replies; 1,729 is the smallest number that can be written as the sum of two cubes in two different ways (123 + 13 and 103 + 93).

From this famous anecdote springs a mathematical joke. If 1,729 is not a dull number, then which numbers are dull? In particular, what is the smallest number that has no interesting traits—nothing to make it stand out in the endlessly receding line of undistinguished integers? The joke is this: Whatever number you choose as the smallest dull number immediately becomes highly interesting because it’s the smallest dull number.

Those Fascinating Numbers, a collection of numerical lore by Jean-Marie De Koninck, can’t escape the pseudo-paradox of dull numbers. The book is essentially a list of the counting numbers, presented in the usual order, with notes on curious facts about each of them: 1 is the only number that divides all the others; 2 is the only even prime number; 3 is the smallest triangular number.

Clearly, this can’t go on forever.

More here.