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

“They were townspeople. They were poor, but they were urban poor; they inhabited not just the ground on which they lived but a wider world of the mind and spirit.”

The quote here describes Ramanujan’s family and their social position. Although they belonged to the Brahmin caste, his family was poor. Kanigel uses this detail to explain to Western readers—who may associate social status with wealth—that the Indian caste system is different, and Ramanujan’s high social status did not spare him from the struggles of poverty.

“In India, strong ties between son and mother are legendary; close indeed must have been the relationship between Ramanujan and his mother that even his Indian biographers invariably saw fit to comment upon it.”

Kanigel uses the Indian biographers’ portrayal of Ramanujan’s relationship with his mother to support his claim that the attachment between the two was indeed very strong. He prepares readers to discover the impacts that Komalatammal had on her son’s life, both positive and negative.

“Ramanujan absorbed such dos and don’ts of Brahmin life as naturally as he learned to walk and talk.”

Kanigel devotes much time early in the book to showing how religion influenced Ramanujan’s worldview. To fully understand him as a person, one must acknowledge the impact religion had on his upbringing, even though his intellectual life depended on the rigorous logic of mathematical theorems.

“But is zero divided by zero also one? If no fruits are divided among no one, will each still get one?”

Kanigel attributes this quote to 11-year-old Ramanujan; it showcases the kind of complex thinking he was capable of at a young age. Ramanujan posed this question to his math teacher, who might have preferred that the boy follow his lead in the classroom, but Ramanujan always had his own creative perspective on mathematics.

“It was goddess Namagiri, he would tell friends, to whom he owed his mathematical gifts. Namagiri would write the equations on his tongue. Namagiri would bestow mathematical insights in his dreams.”

This passage highlights the way Ramanujan attributed his gifts to divine origin. Although the question of Religion Versus Reason is often seen as binary, for Ramanujan, faith and intellect coexisted without conflict.

“They suggest an almost pathological sensitivity to the slightest breath of public humiliation.”

Ramanujan would often overreact to a perceived humiliation, highlighting another aspect of his character: His reputation mattered tremendously to him, and he cared about what others thought of him. In this passage, Kanigel is describing Ramanujan’s extreme reactions to events like not getting the highest score on a math exam or finding out that a discovery he made was not wholly original.

“Ramanujan was an artist. And numbers—and the mathematical language expressing their relationships—were his medium.”

Kanigel’s analogy here helps readers who are not well versed in mathematics to understand Ramanujan’s genius in a different way. The description emphasizes the creativity and beauty of mathematical thought, which to some readers may seem mechanical and dry.

“He was like a species that had branched off from the main evolutionary line and, like an Australian echidna or Galápagos tortoise, had come to occupy a biological niche all his own.”

Kanigel employs another analogy here to highlight Ramanujan’s unique personality and the way it informed his work. The gist of the comment is that he was one of a kind, but it also hints at the loneliness Ramanujan sometimes experienced when others, even fellow mathematicians, did not understand or appreciate him.

“People, as individuals, appreciated and respected Ramanujan; but the System failed to find a place for him.”

Kanigel draws attention to the academic system of India at the time, which prioritized the acquisition of a degree over all other intellectual pursuits. To graduate from college, Ramanujan needed to demonstrate proficiency in multiple disciplines. Kanigel points out that India’s educational system was meant to “churn out bright, well-rounded young men who could help their British masters run the country” and not to nurture creative genius.

“An equation for me has no meaning unless it expresses a thought of God.”

Using another quote attributed to Ramanujan, Kanigel illustrates once again how Ramanujan made sense of his own genius in the context of his religious faith. This sentiment foreshadows Ramanujan’s working relationship with G. H. Hardy, who also revered pure mathematics.

“His work was not well enough understood to classify as either the fulminations of a crank or the outpourings of a genius.”

The inability of people to understand Ramanujan’s work created suspicion of it. This would create the conditions for Ramanujan’s eventually reaching out to mathematics scholars at Cambridge. The greatest minds in India honestly could not discern whether Ramanujan’s work was valuable.

“My elbow is making a genius of me.”

These are Ramanujan’s words. He usually did his work on a slate tablet that he would continually erase with his elbow. The quote shows an interesting visual for how he worked through and past mistakes to arrive at his final result.

“It was this ‘great gulf’ that, in the succeeding months and years, Ramanujan would, of necessity, confront.”

The “gulf” mentioned here refers to the cultural gap between Indians and the English. After Ramanujan moved to England, negotiating the different culture was a monumental challenge for him. His struggles in this context help develop the book’s theme of Achievement in the Face of Adversity.

“Hardy judged God, and found Him wanting. He was not just an atheist; he was a devout one.”

As Chapter 4 moves into a biography of G. H. Hardy, Kanigel points out the stark contrast between Hardy’s and Ramanujan’s views on religion. The fact that the two men became such close colleagues shows how their common devotion to pure mathematics overshadowed all other differences between them.

“I have never done anything ‘useful’.”

These are words attributed to Hardy. How he means “useful” in this context is not what the word normally suggests. For him, it was synonymous with practical matters, and he was not interested in finding practical uses for mathematics. Like Ramanujan, Hardy felt that the value of mathematics lay in its formal beauty, not its usefulness in solving engineering problems.

“For all his confidence in his mathematical prowess, Ramanujan needed outside approval, affirmation. Now he had it. Hardy’s letter took him seriously.”

Kanigel provides further insight onto Ramanujan’s personality here, specifically in his need to have his work validated. Readers can empathize with his struggle to have someone recognize the genius of his work, which he had been conducting in solitude for many years.

“I have never met his equal, and I can compare him only with Euler or Jacobi.”

Hardy’s words express his impressions of Ramanujan. Leonhard Euler and Karl Gustav Jacob Jacobi were considered two of the greatest mathematicians of all time. Hardy’s recognition of Ramanujan’s unique gifts was a turning point in Ramanujan’s career and a dramatic change after all the years when no one knew what to do with his ideas.

“One gift it has which no one can deny—profound and invincible originality.”

Hardy says this of Ramanujan’s work; though it showed some flaws, what impressed Hardy the most was its originality. Finally, someone was judging Ramanujan’s work not according to a predetermined set of standards but with a fresh eye open to brilliant new ideas.

“Ramanujan, Intuition Incarnate, had run smack into Hardy, the Apostle of Proof.”

Kanigel contrasts the stylistic differences between Ramanujan and Hardy, though he does not mean to suggest that either man was one-dimensional. Ramanujan and Hardy’s successful collaboration proved that bringing together two different approaches to a problem can be the most effective way to solve it.

“Indeed, though Hardy deemed Ramanujan’s natural mathematical ability superior to his own, no hint survives of so much as a wisp of envy tainting his relationship with him.”

Painting Hardy in a positive light, Kanigel suggests that his ability to work alongside Ramanujan without envy is an impressive feat and likely enabled their work to be as productive and important as it was. While academia is often marked by bitter competition among ambitious people, Hardy’s love of pure mathematics and his basic humanity allowed him to acknowledge and promote Ramanujan’s genius without jealousy.

“Hardy, in short, was a stern taskmaster. His was a personality of expectations, of high performance. From him, Ramanujan could get encouragement and, in those ways in which Hardy could express it, friendship—but little in the way of pure, uncritical nurturing.”

While Hardy was a great friend to Ramanujan, the relationship between the two was centered on their work. Though his intellectual hunger was provided for in his work with Hardy, Ramanujan was isolated in a foreign land without emotional support. This observation reminds readers that Ramanujan, as focused as he was on his work, had the same human needs as any other person, and that in many ways those needs were not being met in Cambridge.

“He was uncomfortable discussing it, uncomfortable thinking about it. That mathematics was a ‘creative’ activity was not the question; it was among the most creative. But as to its source—there he didn’t care to delve.”

Kanigel describes Hardy's reluctance to investigate the source of creative energy that is required for the kind of work he and Ramanujan did. As a “devout atheist,” Hardy did not have the language to describe the source of his mathematical insights, and perhaps trying to explain it took some of the joy from it.

“Ramanujan’s work during the year before he died could be seen to support an old nostrum of the tuberculosis literature—that the tuberculous patient, as he succumbed, was driven to an ever-higher creative pitch; that approaching death inspired a final flurry of creativity impossible during normal times. The idea has been soundly trounced by modern scholars quick to cite artists and other creative workers whose greatest work long preceded their illness and whose deathbed productivity was nil.”

Though Ramanujan was gravely ill, he still produced astonishing work, leading many to claim that this was a symptom of his illness, and that the insights had a mystical source. It is a somewhat romantic notion that Kanigel feels compelled to refute with more recent scientific thinking.