Srinivasa Ramanujan - The Man Who Knew Infinity
In the grand tapestry of human intellect, few threads shine with the raw, untutored brilliance of Srinivasa Ramanujan. Born into poverty in colonial South India, with no formal training in higher mathematics, he emerged as one of history's most original and profound mathematical minds. His life, a brief but incandescent journey of 32 years, is a testament to the power of pure intuition and an unquenchable thirst for the hidden patterns of the universe. From the temple courtyards of Kumbakonam to the hallowed halls of Cambridge University, Ramanujan's story is not just one of numbers, but a deeply human saga of struggle, discovery, and a legacy that continues to unfold over a century later.
Early Life: A Mind Awakens in Kumbakonam
Srinivasa Ramanujan Iyengar was born on December 22, 1887, in Erode, in the Madras Presidency of British India. He was the son of K. Srinivasa Iyengar, a clerk in a sari shop, and Komalatammal, a housewife who supplemented the family's modest income by singing at a local temple. The family, devout Iyengar Brahmins, soon moved to the town of Kumbakonam, a place renowned for its ancient temples and scholarly traditions. It was here, amidst the rhythms of ritual and tradition, that Ramanujan's extraordinary mind began to stir.
His genius was not immediately apparent, but by the time he was 10, he was the undisputed mathematical prodigy of his town. He displayed an astonishing memory for numbers and an innate ability to manipulate complex formulae. By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. By 13, he was working on his own sophisticated theorems, mastering books on advanced trigonometry written for college students.
The pivotal moment of his young life came in 1903 when a friend lent him a copy of G. S. Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics. This book was not a conventional textbook but a dense compilation of over 5,000 theorems, stated one after the other with only the briefest of proofs. For a mind like Ramanujan's, this was not a limitation but a key. The book unlocked the vast world of Western mathematics for him. He did not simply read it; he independently proved every result and then began to go far beyond, using Carr's collection as a springboard for his own unparalleled explorations.
This single-minded obsession with mathematics, however, came at a cost. In 1904, he won a scholarship to the Government Arts College in Kumbakonam, but his focus on mathematics was so absolute that he neglected all other subjects, including English and history. He failed his examinations and lost his scholarship, a pattern that repeated itself when he later enrolled at Pachaiyappa's College in Madras. Without a university degree, the doors to a conventional academic career were firmly shut.
These were years of immense hardship. Living in extreme poverty, often on the brink of starvation, Ramanujan continued his mathematical research relentlessly. He filled notebooks with his discoveries, page after page of astounding formulae and theorems that poured from his mind, often without the formal proofs demanded by Western mathematics. These notebooks, which are now treasured artifacts, were the raw, unfiltered output of his genius. In 1909, he married Janaki Ammal, and the pressure to find employment to support his family became immense.
The Letter That Changed Everything
Despite his lack of credentials, Ramanujan's brilliance was recognized by a small circle of mathematics enthusiasts in Madras. With the encouragement of figures like V. Ramaswamy Aiyer, founder of the Indian Mathematical Society, he secured a menial clerical position at the Madras Port Trust in 1912. His superiors, notably Sir Francis Spring, the chairman of the Port Trust, and his chief accountant S. Narayana Iyer, recognized that their new clerk was no ordinary man. They encouraged him to pursue his research and to contact mathematicians in England.
In January 1913, Ramanujan took a leap of faith. He mailed a letter to G. H. Hardy, a leading mathematician at Trinity College, Cambridge. The unassuming package contained nine pages of dense mathematics, filled with around 120 theorems on infinite series, number theory, and continued fractions. Most mathematicians would have dismissed the letter as the work of a crank. The formulae were unfamiliar, presented without proofs, and written with an unconventional flair. But Hardy, a man of profound insight, saw something more.
After initially dismissing the letter, Hardy, along with his brilliant collaborator J. E. Littlewood, took a closer look. They were stunned. Some of the formulae were familiar, while others were entirely new and seemed almost impossible to conceive. As Hardy would later famously write, the theorems "must be true, because, if they were not true, no one would have the imagination to invent them." He recognized that he was looking at the work of a genius of the highest order, a natural talent on par with legends like Euler and Gauss.
Hardy immediately began a correspondence and made arrangements to bring Ramanujan to Cambridge. This was a monumental step for Ramanujan. As a Brahmin, crossing the ocean was considered a religious taboo, and he was a strict vegetarian with deeply ingrained cultural and religious habits. After overcoming his own and his family's reservations, he set sail for England, arriving in April 1914, just as the world was teetering on the brink of the First World War.
A Fruitful and Tragic Collaboration
The five years Ramanujan spent at Cambridge were the most productive of his life, marking one of the most remarkable collaborations in the history of science. The partnership between the intuitive, mystical Ramanujan and the rigorous, formal Hardy was a study in contrasts. Hardy taught Ramanujan the importance of formal proof, the language of modern mathematics, while Ramanujan provided a torrent of new ideas and conjectures that astounded Hardy and Littlewood.
Together, they made groundbreaking discoveries. Their most famous work was on the partition function, p(n), which counts the number of ways an integer 'n' can be written as a sum of positive integers. For example, p(4) = 5 because 4 can be written as 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. While the concept was simple, finding a formula for p(n) was incredibly difficult. Hardy and Ramanujan developed a stunningly accurate asymptotic formula that could approximate the value of p(n) for large numbers, a landmark achievement in number theory.
Beyond this, Ramanujan's contributions were vast:
- Infinite Series for Pi (π): He discovered extraordinary and rapidly converging series for calculating the value of pi, some of which are now fundamental to computer algorithms that compute pi to trillions of digits.
- Ramanujan's Notebooks: The work he had done in India before leaving for Cambridge was compiled into his famous notebooks. These three volumes contain nearly 3,900 results, most of which have since been proven correct, and continue to inspire new mathematical research.
- Mock Theta Functions: In his final year, while gravely ill, Ramanujan wrote a last, cryptic letter to Hardy describing a new concept he called "mock theta functions." This was his final gift to the world. For decades, their meaning was a mystery, but today they have found profound applications in fields like physics (to compute the entropy of black holes), computer science, and combinatorics.
His unparalleled contributions earned him the recognition he deserved. In 1918, he was elected a Fellow of the Royal Society, one of the youngest in its history. Shortly thereafter, he became the first Indian to be elected a Fellow of Trinity College, Cambridge. These were monumental honours, but they came as his health was failing.
Legacy: The Echoes of a Genius
The cold, damp English climate, the difficulty of maintaining a strict vegetarian diet during wartime rationing, and relentless work took a severe toll on Ramanujan's health. He was diagnosed with tuberculosis (though a 1994 analysis of his medical records suggests a more likely cause was hepatic amoebiasis, a parasitic infection). In 1919, weakened and frail, he returned to India.
Even on his deathbed, his mind was ablaze with mathematics. He continued to work, scribbling down new ideas that would later be collected in what is known as his "lost notebook." On April 26, 1920, in Chetput, Madras, Srinivasa Ramanujan passed away. He was only 32 years old.
Though his life was short, his legacy is immeasurable. Ramanujan is a towering figure in the history of mathematics, a symbol of pure, unadulterated genius. His work did not just solve existing problems; it opened up entirely new fields of research that mathematicians are still exploring today. The "lost notebook," discovered in the Trinity College library by mathematician George Andrews in 1976, has proven to be a particularly rich source, containing profound results that have kept mathematicians busy for decades.
In India, Ramanujan is a national hero, an icon of intellectual achievement against all odds. His birthday, December 22nd, is celebrated annually as National Mathematics Day to honour his contributions. His life story, popularized by Robert Kanigel's biography The Man Who Knew Infinity and its subsequent film adaptation, has introduced his incredible journey to a global audience.
Srinivasa Ramanujan's work remains a cornerstone of number theory and has found surprising applications in fields he could never have imagined, from particle physics and string theory to computer science and cryptography. He stands as a powerful reminder that genius can be found anywhere, and that the language of numbers is a universal one, capable of being spoken by a humble clerk from Kumbakonam with a voice that echoes through the ages.