Srinivasa Ramanujan — The Man Who Knew Infinity | Dr. Praveendra Singh

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

— Srinivasa Ramanujan

1887Year of Birth

32Age at Death

3900+Mathematical Results

100Pages — Lost Notebook

FRSFirst Indian Fellow

Introduction

In the history of mathematics, a few names rise above mere numbers and formulas to become enduring symbols of inspiration. Srinivasa Ramanujan is one such name — a man who, from a small town in South India, without formal training, without a laboratory, without any mentor, discovered mathematical truths that still astonish the world’s greatest mathematicians today.

Ramanujan’s story is not merely the story of a prodigy. It is the story of a man who found infinity in poverty, who refused to abandon mathematics despite hunger and illness, who nourished his genius through devotion to his mother, his wife, his culture, and his goddess Namagiri.

This article presents a detailed account of Ramanujan’s life, his family, his struggles, his mathematical discoveries, and his enduring legacy.

Birth and Early Life

Birth

Srinivasa Ramanujan Iyengar was born on 22 December 1887 in Erode, Tamil Nadu. His mother, Komalatammal, had come to her parents’ home for the delivery. Within days, the family returned to Kumbakonam, where Ramanujan spent most of his childhood.

Kumbakonam — A Sacred Town

Kumbakonam is an ancient, deeply religious town on the banks of the Kaveri river. Famous for its magnificent temples, learned priests and classical music, this environment shaped Ramanujan’s personality in profound ways.

Family Background

Ramanujan’s family was a Brahmin family of modest means. His father, Srinivasa Iyengar, worked as a clerk in a cloth merchant’s shop, earning around twenty rupees a month — barely enough even then for a large family.

His mother, Komalatammal, was a religious, spirited, and strong-willed woman. She sang devotional songs at the local Namagiri temple and was a devoted follower of the goddess Namagiri. Her influence on Ramanujan’s life was immense. The bond between mother and son was extraordinarily close.

Ramanujan had several siblings, but most died in infancy. This grief made the family centre itself even more deeply around Ramanujan.

Goddess Namagiri — His Spiritual Inspiration

Spiritual Source

The goddess Namagiri held a place of supreme importance in Ramanujan’s life. The Namagiri temple at Namakkal was his mother’s place of worship. Ramanujan himself attributed his mathematical gift to the goddess.

He often said that the goddess Namagiri would appear in his dreams and write mathematical formulas on his tongue. Upon waking each morning, he would immediately record those formulas in his notebook.

This was not mere superstition — it was a symbol of Ramanujan’s extraordinary power of intuition. His mind continued working on mathematical problems even in sleep, and answers came to him in dreams.

Mathematical Talent in Childhood

An Extraordinary Child

Ramanujan displayed exceptional talent from a very early age. His memory was phenomenal — once he saw or heard something, it was permanently etched into his mind.

Age 5

Began formal schooling. Stunned teachers with answers they had never seen before.

Age 10

Scored top marks in the district primary examination. Left everyone astonished.

Age 15

Obtained G. S. Carr's book — a moment that changed the direction of his life forever.

Age 16

Independently proved all 5000 theorems in Carr's book and extended many of them with new results.

Carr’s Book — A Life-Changing Moment

That Great Book

At age fifteen, Ramanujan obtained a copy of G. S. Carr’s “A Synopsis of Elementary Results in Pure and Applied Mathematics” — a collection of over 5000 mathematical theorems and formulas, most without proofs.

An ordinary student would have been discouraged. But Ramanujan took it as a challenge. He attempted to prove every single formula himself, and wherever he found them incomplete, he developed entirely new formulas. This book became his university of mathematics.

Failure in Formal Education — A Painful Truth

Struggle in College

Ramanujan’s obsession with mathematics meant he could not pay attention to any other subject.

1904

Entered Government Arts College, Kumbakonam. Won a mathematics scholarship. But failed in all other subjects — scholarship revoked.

1905

Ran away from home, reached Visakhapatnam. Family brought him back.

1906

Entered Pachaiyappa's College, Madras. Failed the F.A. examination twice.

Life Without a Degree

Without any formal degree, Ramanujan spent years in a hand-to-mouth struggle. He gave private tuitions — sometimes in exchange for meals. Paper was expensive, so he worked on a slate, transferring only the most important results to his notebooks.

Marriage and Family Life

Marriage to Janaki

In 1909, when Ramanujan was 21, he was married. His wife’s name was Janaki Ammal. At the time of their marriage, Janaki was only nine years old (child marriage was common in that era).

Janaki was a quiet, gentle, and devoted woman. She did not understand Ramanujan’s mathematical genius, but she stood by him always. When Ramanujan left for England, Janaki stayed behind with her mother-in-law Komalatammal.

After Ramanujan’s departure, there arose tension between mother and daughter-in-law. Komalatammal prevented Janaki from going to England and also withheld Ramanujan’s letters from her. Ramanujan did not know whether his letters were reaching Janaki at all.

Mother Komalatammal — Strength and Conflict

The relationship between Ramanujan and his mother was complex and deep. It was she who instilled in him devotion to goddess Namagiri. She who taught him Sanskrit verses. Her lullabies held numbers in them; her devotional songs were threaded with mathematics.

Komalatammal was a woman of strong personality. All important family decisions were hers. She was deeply opposed to Ramanujan crossing the seas — in a strict Brahmin family, travelling across the ocean was considered a transgression of faith. But ultimately, after Goddess Namagiri appeared to her in a dream and gave her blessing, she granted her permission.

Struggles in Madras — In Search of Recognition

Meeting Ramachandra Rao

Around 1910–11, Ramanujan met Diwan Bahadur Ramachandra Rao, District Collector of Madras, and showed him his notebook. Rao was astounded.

“Before me sat a half-starved man holding a notebook. I opened it and saw — results I had never seen before, formulas that existed in no known text.” — Diwan Bahadur Ramachandra Rao

Clerk at Madras Port Trust

In 1912, Ramanujan was appointed as a clerk at Madras Port Trust. Monthly salary — thirty rupees. This was his first stable income. His supervisor S. Narayana Iyer recognised his talent and gave him time and encouragement for mathematics, eventually presenting him to the Indian Mathematical Society.

Connection with the Indian Mathematical Society

In 1911, Ramanujan’s first research paper was published — “On Some Properties of Bernoulli Numbers” — in the Journal of the Indian Mathematical Society. This was an important milestone. His name was now known in the world of mathematics.

The Letter to Hardy — That Historic Moment

16 January 1913 — A Date Immortalised in History

On this day, Ramanujan wrote a letter to Professor Godfrey Harold Hardy of Cambridge University — enclosing a list of over 120 theorems and formulas, without any proofs.

The Decision to Write

In his letter, Ramanujan wrote:

“I am a clerk in the Madras Port Trust. I am 23 years of age. I have had no university education. But I have found some mathematical results that might be of interest to you…” — Ramanujan’s letter to Hardy, 1913

Hardy’s Reaction

Hardy initially set the letter aside, thinking it the work of a crank. But that night he could not sleep. The formulas in the letter kept circling in his mind. In the morning he called his colleague John Edensor Littlewood.

Together they examined the formulas for hours. They found:

Some formulas were already known — but Ramanujan had discovered them independently
Some formulas were entirely new and of astounding validity
Some formulas were so complex that even Hardy and Littlewood could not immediately prove them

“They must be true because, if they were not true, no one would have had the imagination to invent them.” — Professor G. H. Hardy

Hardy wrote back immediately and invited Ramanujan to Cambridge.

Cambridge — A New World

The Journey to England

Travelling to England was not easy for Ramanujan. His mother strongly objected, fearing spiritual transgression. In strict Brahmin tradition, crossing the seas was considered religiously forbidden.

Eventually, Goddess Namagiri appeared to his mother in a dream and told her to let Ramanujan go. After this dream, she gave her blessing.

On 17 March 1914, Ramanujan departed Madras for England. The journey was long and difficult. For a strict vegetarian Brahmin, finding suitable food on board the ship was itself a challenge.

Life at Cambridge

Arriving at Cambridge, Ramanujan found a new world — vast libraries, eminent professors, an environment of mathematical discussion. But there were hardships too.

Hardships

Food: Vegetarian food was almost impossible to find
Climate: Cold and fog — a stark contrast to South India's warmth
World War I: Life became even harder from 1914 onwards

Achievements

Access to vast libraries and resources
Mentorship from Hardy — the finest mathematician of his time
Five years of extraordinary discoveries

The Hardy–Ramanujan Partnership

The Hardy–Ramanujan partnership is one of the most remarkable in the history of mathematics.

Professor Hardy

Rationalist, atheist
Systematic, disciplined
Believed in rigorous proof

Ramanujan

Deeply religious, intuitive
Results often arrived without proof
Deeply emotional and spiritual

But both shared one thing — an indomitable love of mathematics. Hardy taught Ramanujan the formal language of mathematics. Ramanujan gave Hardy the insight that no textbook could ever provide.

The Great Mathematical Discoveries

Partition of Numbers — $p(n)$

One of Ramanujan’s most celebrated contributions is the theory of number partitions. The partition function $p(n)$ counts the number of ways a positive integer $n$ can be written as a sum of positive integers.

For example, the partitions of $n = 4$ are: $4 = 4 \qquad 4 = 3+1 \qquad 4 = 2+2 \qquad 4 = 2+1+1 \qquad 4 = 1+1+1+1$ So $p(4) = 5$.

Together, Hardy and Ramanujan developed the famous Hardy–Ramanujan asymptotic formula: $p(n) \sim \frac{1}{4n\sqrt{3}} \cdot e^{\pi\sqrt{\frac{2n}{3}}} \quad \text{as } n \to \infty$

Physics — Energy Levels String Theory Statistical Mechanics

Ramanujan’s Remarkable Formula for $\pi$

$\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^{\infty} \frac{(4k)!\,(1103 + 26390k)}{(k!)^4 \cdot 396^{4k}}$ Each term of this series adds approximately eight correct decimal places of $\pi$. Today’s supercomputers use this very formula to compute $\pi$ to trillions of decimal places.

Supercomputing Numerical Methods

The Taxicab Number — 1729

1729

$1729 = 1^3 + 12^3 = 9^3 + 10^3$

The smallest number expressible as the sum of two cubes in two different ways

Hardy was visiting Ramanujan in hospital and mentioned his taxi’s number was 1729, which seemed dull. Ramanujan instantly replied with the number’s remarkable property. This anecdote is the most celebrated demonstration of Ramanujan’s extraordinary number sense.

Infinite Series — A Startling Result

$1 + 2 + 3 + 4 + 5 + \cdots = -\frac{1}{12}$ This appears utterly impossible — yet it is true in the framework of the Riemann Zeta Function. Today this result plays a crucial role in quantum physics and string theory.

Quantum Physics String Theory

Ramanujan Primes

Ramanujan made important contributions to the theory of prime numbers. A Ramanujan prime $R_n$ is a special case of the Bertrand–Chebyshev theorem. He proved that there are at least $n$ prime numbers between $x$ and $2x$, whenever $x \geq R_n$.

Ramanujan Theta Function

$f(a,b) = \sum_{n=-\infty}^{\infty} a^{n(n+1)/2} \cdot b^{n(n-1)/2}$ This function is the foundation of the theory of Modular Forms.

Cryptography Digital Communications Quantum Computing

Mock Theta Functions — His Most Mysterious Legacy

The Final Letter — 1920

A few weeks before his death, Ramanujan wrote a final letter to Hardy introducing the concept of Mock Theta Functions. Mathematicians, including Hardy, could not fully understand these functions for 80 years.

In 2002, mathematician Sander Zwegers connected them to Harmonic Maass Forms — a landmark achievement of modern mathematics.

Black Hole Physics Particle Physics

Fellowship — India’s Pride

1918 — A Historic Honour

Ramanujan was elected Fellow of the Royal Society (F.R.S.) — the first Indian ever to receive this honour. In the same year he was also elected Fellow of Trinity College, Cambridge.

In 1918, Ramanujan was elected Fellow of the Royal Society (London) — the highest recognition in science and mathematics at the time, and he was the first Indian to receive it.

The news was celebrated across India like a festival. A clerk without a degree, from a poor family, from no metropolitan city — had received the world’s highest mathematical honour.

Illness and Return

The Attack of Tuberculosis

While in England, Ramanujan’s health gradually deteriorated. In 1917, he was admitted to Matlock Sanatorium with serious illness, suspected to be tuberculosis.

Mathematics Even in Hospital

Even in hospital, Ramanujan continued doing mathematics. Even in fever, he would open his notebook and write formulas. It was here that Hardy came to visit him and mentioned the taxicab number 1729.

Return to India

On 27 February 1919, Ramanujan left England for India. Five years had passed — and he was returning as a celebrated mathematician. But his condition on arrival was extremely weak. He went to Madras and then to Chetput for treatment.

Final Days and Legacy

Death

26 April 1920

At only 32 years of age, Srinivasa Ramanujan passed away. Even in his final days he was doing mathematics. His wife Janaki recalled that until the very end he would wake at night and write on his slate.

“Mathematics has lost its most romantic figure.” — Professor G. H. Hardy

The Lost Notebook — A Miraculous Discovery

1976 — The Lost Notebook Found

Mathematician George Andrews discovered Ramanujan’s 100-page lost notebook in the Wren Library, Cambridge — now known as the “Lost Notebook”. It took mathematicians over 30 years of research to fully explore it.

Ramanujan’s Contributions in Modern Mathematics

Ramanujan’s discoveries live on vibrantly in today’s science and technology:

💻

Computer Science

His formula for $\pi$ is used in supercomputers to compute trillions of decimal places.

🔐

Cryptography

His Modular Forms theory underpins modern data security and encryption.

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Physics

His work appears in String Theory and Quantum Gravity.

📊

Statistics

Partition theory is used in Statistical Mechanics and Thermodynamics.

Ramanujan and Indian Culture

Ramanujan was not merely a mathematician — he was the embodiment of the meeting point between Indian spirituality and mathematical genius.

He demonstrated that mathematics and spirituality are not opposites. When he said “the goddess gave me the formulas,” he was speaking of the power of his intuition — that deep concentration which we call meditation or sadhana.

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Talent is Innate

It does not depend on any university or institution.

💪

Struggle Refines Genius

Hardship did not break Ramanujan — it made him stronger.

🏠

Family as Foundation

His mother's devotion and culture kept his inspiration alive.

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Mathematics is Universal

It sees no caste, no country, no religion.

Relevance to CSIR NET, GATE and IIT JAM

Ramanujan’s work connects directly to your examination syllabus:

Topic	Ramanujan's Contribution
Number Theory	Partition function, prime numbers, taxicab numbers
Infinite Series	Convergence tests, special series
Complex Analysis	Theta functions, Modular Forms
Real Analysis	Infinite series, continued fractions
Applied Mathematics	Computation of $\pi$, numerical methods

Conclusion

Ramanujan’s story does not end — it continues to grow. The formulas in his notebooks continue to inspire new research. His discoveries continue to strengthen the foundations of mathematics and science.

He was a man who turned poverty into opportunity, struggle into devotion, and from the soil of a small Indian town, flung open the doors of infinity.

National Mathematics Day

22 December is celebrated as National Mathematics Day in India — in honour of Ramanujan’s birthday.

Whenever you study mathematics, whenever a problem seems too difficult, whenever you feel you cannot go on — remember Ramanujan. A man who, through hunger, through illness, through loneliness — knew infinity.

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

— Professor G. H. Hardy

Recommendation: To learn more about Ramanujan’s life, watch the 2015 film “The Man Who Knew Infinity” — a deeply inspiring portrayal of his extraordinary journey.

Srinivasa Ramanujan — The Man Who Knew Infinity