The Man Who Knew Infinity

The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel, Washington Square Press, 1991. 

Tamil Nadu:

This book is a biography of an autodidact from India, and one of the deepest mathematicians of the twentieth century, with magical powers of intuition. Srinivasa Ramanujan was born in 1887 Tamil Nadu in Tamil Nadu in Southern India. He excelled at mathematics from an early age, but was unable to obtain a college degree, because he refused to study subjects that did not interest him. Some scholars in India helped foster his talent, but none could understand his results. 

Hinduism:

Ramanujan was a Brahmin and took his Hindu religion very seriously. He was deeply religious, not just with respect to ritual and traditions, but also in the sense of Einstein. Mathematics was a way to understand the divine. Ramanujan also liked to intrepret his dreams. 

Voyage to England: 

Ramanujan wrote to several mathematicians in England. One of them, G. H. Hardy, recognized his talent, and invited Ramanujan to come to England to complete his education at Cambridge University. Traveling across the seas was forbidden to observant Hindus, but the Cambridge mathematicians were able to persuade Ramanujan to come. 

Culture Shock:

The English reserve was strange to Ramanujan, who was use to people being more friendly. The weather was cold, unlike South India. The English loved sports, especially cricket, but Ramanujan had no interest in sports. At the time there were few Indians in London, and even fewer in Cambridge.

G. H. Hardy and Trinity College, Cambride:

Hardy was one of the best mathematicians in England, known for reforming the Tripos mathematics examination and for bringing more rigor into English mathematics. Ramanujan had intuition; Hardy had rigor. They complemented each other. Ramanujan would write down an equation and Hardy would prove that it was true. 

Mathematics:

Ramanujan did work on:

(a) quickly converging infinite series for pi,

(b) a particular kind of infinite series called continued fractions, 

(c) the number of different ways to write an integer as a sum of smaller integers (called a partition), 

(d) the distribution of prime numbers, 

(e) the relationship between the calculus of complex numbers and number theory (the study of the integers), 

(f) generalizations of trigonometric functions called elliptic functions, 

(g) elliptic curves in complex projective space, 

(h) the foundations for the subject area of modular forms, which describe symmetry in algebraic geometry. 

Food:

Fresh fruits and vegetables were in short supply during World War I. He could not obtain the food he was use to in India, such as mangos and bananas. Ramanujan was a strict vegetarian because of his religion. He could not eat anything fried in lard, so he avoided eating meals at the college, which diminished his social life. Unlike his youth in India, in England Ramanujan had to cook for himself, because his wife Janaki did not accompany him to England. 

Health:

During the Spring of 1917, Ramanujan became ill, probably from tuberculosis, brought on by malnutrition, in particular, by a lack of Vitamin D. Not only was his diet low in vitamin D, he spent little time in the sunshine. The body manufactures vitamin D when ultraviolet light falls on the skin. Ramanujan became lonely and depressed, and he returned to India after the war. Back home, his wife Janaki nursed him, but it was too late. Ramanujan died in 1920 at age 32..