The Man Who Knew Infinity: A Life of the Genius Ramanujan

India’s caste system is a traditional Hindu social structure that dates back at least 3,000 years. It divides people into four main hierarchical groups that reflect the work done by each group. The highest caste, the Brahmins, are traditionally teachers and priests. Kshatriyas are warriors and politicians, Vaishyas are farmers and merchants, and Shudras are laborers. Dalits are outside the caste structure and have generally occupied the poorest and least desirable occupations. Kanigel explains that, during Ramanujan’s lifetime, the laws governing how castes could interact with each other, which ones were allowed to interact at all, and who ate with whom were based on the “Institutes of Manu, a Sanskrit work dating to the third century” (20). Recent scholarship indicates that before the 18th century, social movement between the castes was fairly fluid. However, British colonizers, wanting to simplify the system to make India easier to govern, solidified the distinctions between castes. In Ramanujan’s time, there was little mixing among castes. However, the divisions were more social than economic: Although Ramanujan was a Brahmin, his family was impoverished.

In mathematics, a partition refers to the different ways numbers can be added to arrive at the sum. Kanigel outlines the partitions for 4: 1 + 3, 2 + 2, 1 +1 + 2, 1 + 1 + 1 + 1, and 4 itself—all are different ways of adding numbers to arrive at 4. According to Kanigel, “the problem is that the number of partitions rises fast” the higher you go (246). Ramanujan and Hardy were working on a formula that could predict how many partitions were in numbers of the highest magnitude.

Kanigel chronicles the legend behind this number. Apparently, it was the number of a taxi that Hardy took to visit Ramanujan while he was at a nursing home. Hardy notified Ramanujan of the number and said that it was “rather a dull number,” to which Ramanujan explained why it was actually “an interesting number” (312). The reason given is that “it is the smallest number expressible as the sum of two cubes in two different ways” (312). 12³ + 1³ and 10³ + 9³ both equal 1729.