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

Out of India

The first two days of Ramanujan’s travels were miserable because he suffered from seasickness. After the Nevassa reached its first port of call in Sri Lanka and he was able to disembark for a short time, things became increasingly less miserable for him. Ramanujan arrived in England on April 14, 1914. He was met at the docks in London by E. H. Neville, whose charity and hospitality and whose affiliation with Cambridge helped Ramanujan get himself situated to his new surroundings in a way that most other Indian newcomers would not have access to. He moved into Neville’s home, and Kanigel points out that while he shared the home with Neville and his wife, Ramanujan experienced an unprecedented degree of privacy there. Once settled in his living quarters, Ramanujan almost immediately went to work with Hardy and his associate John Littlewood.

Together

Kanigel discusses the work that Hardy and Ramanujan performed and goes into some detail about the math behind it. The more Hardy investigated Ramanujan’s theories, the more it became clear to him that he was in the presence of an especially gifted mathematical mind. Although some of Ramanujan’s theories had been proven for many years, the way he approached the problems were unorthodox and revealed to Hardy a uniqueness not found in English mathematics at the time. For Hardy, Ramanujan was nearly the embodiment of pure mathematics. Kanigel mentions that some of the work in Ramanujan’s notebooks are still studied today. Kanigel compares the approach of Leonhard Euler and Karl Gustav Jacob Jacobi, generally regarded as two of the most influential mathematicians of all time, to Ramanujan’s. Kanigel details Ramanujan’s publication history in 1914 and 1915, which officially put him on the map as a formidable mathematician. In this early time at Cambridge, Ramanujan had finally found his intellectual home.

The Flames of Louvain

Kanigel discusses the onset of World War I, which coincided with Ramanujan’s initial work at Cambridge. Many thought the war would be short; however, as it became clear that it would be a prolonged conflict, England had to adapt at home. To treat the thousands of wounded, Trinity was essentially turned into a military hospital. While England did not face the same level of catastrophe as the countries on the continent, there were still daily threats of bombing raids. Tensions were high. Against this historical backdrop, Ramanujan and Hardy continued to press forward with their work.

The Zeroes of the Zeta Function

Kanigel states that Ramanujan tended to see his mathematical insights as divine gifts, and that according to Hardy, this tendency ultimately imposed limits on his intellectual growth. Kanigel then outlines how Ramanujan approached a statement made by Hardy in his work Orders of Infinity. The central concern was to determine if there was a way to predict which among very large numbers would be prime. Ramanujan sought to discover the patterns of prime numbers. Kanigel explains how the prevalence of prime numbers tends to drop as the numbers get higher, a process that he calls a logarithmic drop-off (217). Much of the remainder of this section explores how Ramanujan arrived at the formulas that sought to further explain this process, and Kanigel makes clear throughout that Ramanujan was not always correct; in fact, he was often wrong. However, his approach to these mathematical puzzles was intuitive, which Hardy believed to be his special gift and which Hardy worked with rather than against. He harnessed Ramanujan’s creativity at the same time he taught him more orthodox methods and approaches.

S. Ramanujan, B.A.

Kanigel shifts gears once again in this section, providing more detail of how the war impacted daily life at Cambridge. In 1915, Littlewood joined the war effort, employed to provide his mathematical skills for the development of more precise and better functioning weaponry. The war also hampered the publication speed of Ramanujan’s work, something that he acknowledged in one of his regular letters home. In any event, his and Hardy’s work continued despite the omnipresent impacts of the ongoing war. In 1915, Ramanujan published a significant paper on composite numbers in Proceedings of the London Mathematical Society. This was a monumental accomplishment for him. In 1916, Ramanujan received his B.A. degree.