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1729 is the natural number following 1728 and preceding 1730 .. natural number. natural number. 1728 ( number ). It is known as the Hardy -- Ramanujan number , after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital .. G. H. Hardy. G. H. Hardy. Srinivasa Ramanujan. Srinivasa Ramanujan. He related their conversation  :. The two different ways are  :. 1729 = 13 + 123 = 93 + 103. The quotation is sometimes expressed using the term `` positive cubes '' , since allowing negative perfect cubes -LRB- the cube of a negative integer -RRB- gives the smallest solution as 91 -LRB- which is a divisor of 1729 -RRB-  :. negative. negative number. integer. integer. 91 ( number ). divisor. divisor. 91 = 63 + -LRB- − 5 -RRB- 3 = 43 + 33. 91 ( number ). Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways have been dubbed `` taxicab numbers '' .. The number was also found in one of Ramanujan 's notebooks dated years before the incident , and was noted by Frenicle de Bessy in 1657 .. Frenicle de Bessy. Frenicle de Bessy. The same expression defines 1729 as the first in the sequence of `` Fermat near misses '' defined as numbers of the form 1 + z3 which are also expressible as the sum of two other cubes .