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

The Bernoulli numbers are named for the Swiss mathematician Jacob Bernoulli (1655-1705), although they were simultaneously discovered by the Japanese mathematician Seki Takakazu (c. 1642-1708). They are a sequence of numbers that can be used to compute the sum of consecutive numbers or the sum of consecutive numbers raised to a given power. Upon making his discovery, Bernoulli wrote excitedly, “With the help of this table, it took me less than [8 minutes] to find that the tenth powers of the first 1,000 numbers being added together will yield the sum 91,409,924,241,424,243,424,241,924,242,500.” Bernoulli numbers were the subject of Ramanujan’s first published paper.

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).