In mathematics, the nth taxicab number, typically enoted Ta(n) or Taxicab(n), is defined as the smallest number that can be expressed as a sum of two positive cubes in n distinct ways, up to order of summands. G. H. Hardy and E. M. Wright proved in 1954 that such numbers exist for all positive integers n, and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-generated numbers are the smallest possible and is thus useless in finding Ta(n). So far, only the following six taxicab numbers are known (sequence A011541 in OEIS):