At first sight, the instantaneous realization of this fact on a hospital bed seems incredible, too amazingly bright to be humanly possible. But in fact a minute of reflection suggests a simple way in which the Indian mathematician could have recognized this fact. Having worked for decades with numbers, Ramanujan evidently had memorized scores of facts, including the following list of cubes:

1x1x1 = 1

2x2x2 = 8

3x3x3 = 27

4x4x4 = 64

5x5x5 = 125

6x6x6 = 216

7x7x7 = 343

8x8x8 = 512

9x9x9 = 729

10x10x10 = 1000

11x11x11 = 1331

12x12x12 = 1728

Would it be farfetched to suggest that we could all match Ramanujan's feat with sufficient training? Perhaps that suggestion would seem less absurd if you consider that any high school student, even one that is not considered particularly bright, knows at least as much about mathematics as the most advanced mathematical scholars of the Middle Ages. We all start out in life with very similar brains, all endowed with an elementary number sense which has some innate structure, but also a degree of plasticity that allows it to be shaped by culture.

Back to the philosophy of mathematics, then. What are numbers, really? If we grant that we are all born with a rudimentary number sense that is engraved in the very architecture of our brains by evolution, then clearly numbers should be viewed as a construction of our brains. However, contrary to many social constructs such as art and religion, number and arithmetic are not arbitrary mental constructions. Rather, they are tightly adapted to the external world. Whence this adaptation? The puzzle about the adequacy of our mathematical constructions for the external world loses some of its mystery when one considers two facts.

• First, the basic elements on which our mathematical constructions are based, such as numbers, sets, space, and so on, have been rooted in the architecture of our brains by a long evolutionary process. Evolution has incorporated in our minds/brains structures that are essential to survival and hence to veridical perception of the external world. At the scale we live in, number is essential because we live in a world made of movable, denumerable objects. Things might have been very different if we lived in a purely fluid world, or at an atomic scale � and hence I concur with a few other mathematicians such as Henri Poincare, Max Delbruck, or Reuben Hersh in thinking that other life forms could have had mathematics very different from our own.
• Second, our mathematics has seen another evolution, a much faster one: a cultural evolution. Mathematical objects have been generated at will in the minds of mathematicians of the past thirty centuries (this is what we call "pure mathematics"). But then they have been selected for their usefulness in solving real world problems, for instance in physics. Hence, many of our current mathematical tools are well adapted to the outside world, precisely because they were selected as a function of this fit.