Srinivasa Ramanujan · Mathematics

The Taxicab Number and the Structure of the Integers

1729 as the smallest number that is a sum of two cubes in two different ways - the famous hospital story - together with Ramanujan’s deep work on highly composite numbers and the theory of the partition function, all expressions of his intimacy with the whole numbers.

What you'll be able to recall

You learned that 1729 is the smallest number expressible as a sum of two cubes in two ways, that Ramanujan saw this instantly from his hospital bed, and that he did deep work on highly composite numbers and on partitions. Explain what these have in common about how Ramanujan ‘knew’ numbers.

Leads to Diophantus of Alexandria.

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