5. Identifying Metrics

In the 1920s, the great British mathematician G. H. Hardy paid a call on his ailing protégé, the self-taught prodigy Srinivasa Ramanujan. En route to Ramanujan’s home in Putney, London, he noted the number of the cab: 1729. On his arrival, he noted to Ramanujan that the number “seemed to me rather a dull one, and that I hoped it was not an unfavorable omen” for Ramanujan’s health. But the Indian mathematician—still seen as one of the world’s greatest mathematical geniuses today—countered instantly that the number had immense significance. “It is the smallest number expressible as the sum of two cubes in different ways.”

A few fortunate souls find numbers as easy to understand and manipulate as a high-school graduate finds ...

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