Srinivasa Ramanujan (1887-1920), self-taught Indian mathematician. Known for number theory, infinite series, partition functions. Read his complete story.
Srinivasa Ramanujan stands among history’s most extraordinary mathematical minds. Born on December 22, 1887, in Erode, Tamil Nadu, he revolutionized mathematics despite having almost no formal training. His intuitive grasp of numbers and patterns continues to influence modern mathematics, physics, and computer science a century after his death.
The self-taught genius made groundbreaking contributions to number theory, infinite series, continued fractions, and partition functions. His collaboration with British mathematician G.H. Hardy at Cambridge University produced work that mathematicians still study today. Tragically, illness cut short his life at just 32 years, but his notebooks contain thousands of formulas that researchers continue to explore and prove.
Quick Facts About Srinivasa Ramanujan
| Detail | Information |
|---|---|
| Full Name | Srinivasa Ramanujan Iyengar |
| Date of Birth | December 22, 1887 |
| Date of Death | April 26, 1920 |
| Age at Death | 32 years |
| Birthplace | Erode, Tamil Nadu, India |
| Profession | Mathematician |
| Spouse | Janaki Ammal (m. 1909) |
| Education | Largely self-taught; briefly attended University of Madras |
| Famous For | Number Theory, Infinite Series, Partition Functions |
| Major Honor | Fellow of the Royal Society (1918) |
Early Life and Family Background
Ramanujan was born into a Tamil Brahmin Iyengar family of modest means in British-ruled India. His father, Kuppuswamy Srinivasa Iyengar, worked as a clerk in a sari shop in Kumbakonam after originally hailing from Thanjavur district. His mother, Komalatammal, was a housewife who sang devotional songs at a local temple.
When Ramanujan was just one year old, his mother took him to Kumbakonam, located about 160 kilometers from Madras. The family faced hardship early when young Ramanujan contracted smallpox in December 1889. He survived the illness that claimed many children’s lives in that era.
At nearly five years old, Ramanujan entered primary school in Kumbakonam. He attended several different primary schools before enrolling at Town High School in January 1898. Teachers quickly noticed his exceptional memory and mathematical abilities.
Educational Journey and Self-Learning
By age ten, Ramanujan scored top marks in his district examinations. He demonstrated remarkable abilities beyond mathematics, including the capacity to recite pi to many decimal places and recall Sanskrit word roots. His exceptional memory became legendary among classmates and teachers alike.
At fifteen, a pivotal moment changed his life trajectory. He obtained a copy of “A Synopsis of Elementary Results in Pure Mathematics” by G.S. Carr. The book contained thousands of theorems presented with minimal proof. Ramanujan systematically verified each theorem and began developing his own mathematical ideas.
When he graduated from high school at seventeen, his mathematical prowess earned him a scholarship to Government Arts College in Kumbakonam. However, his obsession with mathematics proved problematic. He neglected all other subjects, eventually failing his examinations and losing his scholarship. He briefly attended the University of Madras in 1903 but again failed due to poor performance in non-mathematical subjects.
Struggling Years and Marriage
Without a university education, Ramanujan faced difficult years. He developed his mathematical research in isolation, working on slate and scraps of paper because he couldn’t afford proper materials. Financial hardship plagued his family during this period.
On July 14, 1909, Ramanujan married Janaki Ammal, a ten-year-old girl his mother had selected. Child marriage was common in that era and culture. As was customary, Janaki remained with her parents until reaching puberty, joining Ramanujan’s household in 1912.
After marriage, Ramanujan developed a hydrocele testis requiring surgical treatment. His family couldn’t afford the operation until a doctor volunteered to perform it at no cost in January 1910. These health and financial struggles characterized his early adult years.
Finding Recognition in Madras
Despite his lack of credentials, Ramanujan’s mathematical abilities began attracting attention from local mathematicians and academics. In 1910, he met V. Ramaswamy Aiyer, deputy collector and founder of the Indian Mathematical Society. Ramaswamy viewed Ramanujan’s notebooks and recognized genuine talent but couldn’t secure him a scholarship.
Friends introduced Ramanujan to R. Ramachandra Rao, district collector for Nellore and secretary of the Indian Mathematical Society. Initially skeptical, Rao eventually became convinced of Ramanujan’s genius and provided financial support for his mathematical research. This patronage allowed Ramanujan to continue his work without immediate financial pressure.
In 1911, Ramanujan published his first paper in the Journal of the Indian Mathematical Society. His knowledge of mathematics, developed independently, startled those who reviewed his work. He had rediscovered results in continued fractions, elliptic integrals, and hypergeometric series that European mathematicians had taken decades to develop.
The Journey to Cambridge
In early 1912, Ramanujan secured a temporary position in the Madras Accountant General’s office. By March 1912, he was appointed as a clerk at the Madras Port Trust. The Chief Accountant, S. Narayana Aiyar, had mathematical training and became a lifelong supporter.
Seeking recognition beyond India, Ramanujan began writing to prominent British mathematicians in 1912. Most ignored his unconventional letters filled with theorems presented without proofs. The presentations seemed too novel and unfamiliar to established mathematicians who couldn’t be bothered to investigate further.
On January 31, 1913, Ramanujan sent a letter to G.H. Hardy at the University of Cambridge. The letter contained about 120 theorems and formulas. Hardy initially thought it might be an elaborate fraud. After careful examination with his colleague J.E. Littlewood, Hardy realized these results could only come from a mathematician of extraordinary talent.
Hardy later wrote that he had never seen anything like Ramanujan’s formulas. They “defeated me completely,” he admitted. A single look revealed they could only have been written by a mathematician of the highest class. If they weren’t true, Hardy reasoned, no one would have the imagination to invent them.
The Cambridge Years
Hardy arranged a special scholarship at the University of Madras and a grant from Trinity College, Cambridge. In March 1914, Ramanujan left India for England, traveling alone. His wife Janaki, then fifteen, had hoped to accompany him but was deemed too young. This decision would later haunt Ramanujan.
Overseas travel violated orthodox Hindu customs, and Ramanujan faced social ostracism from his community. He resolved the dilemma religiously, claiming his family deity Namagiri Thaayaar had blessed the journey in his prayers. His father did not support the decision and their relationship remained strained.
The collaboration between Hardy and Ramanujan proved extraordinarily fruitful. Hardy recognized that Ramanujan possessed intuitive mathematical insights that others simply couldn’t access. Hardy, himself a mathematical giant, reportedly quipped that his greatest contribution to mathematics was discovering Ramanujan.
Their work together produced significant advances in modular forms, prime number theory, and partition functions. The famous anecdote about the Hardy-Ramanujan number illustrates their relationship. When Hardy visited the hospitalized Ramanujan in a taxi numbered 1729, he remarked it seemed a dull number. Ramanujan immediately replied it was fascinating—the smallest number expressible as the sum of two cubes in two different ways.
Major Mathematical Contributions
Ramanujan’s contributions span multiple mathematical domains. His work on partition functions calculated how many ways a number can be expressed as the sum of positive integers. Together with Hardy, he developed the circle method, providing the first approximations for partitions beyond 200.
His infinite series for pi, discovered in 1914, forms the basis for many modern algorithms. These series converge incredibly fast, allowing rapid approximations of pi. Computer scientists still use Ramanujan’s formulas in computational mathematics.
The Ramanujan theta function generalized earlier work by German mathematician Carl Jacobi. This function now determines critical dimensions in bosonic string theory, superstring theory, and M-theory. His mathematical visions continue finding applications in theoretical physics decades later.
Ramanujan discovered remarkable congruences for partition functions and worked extensively on mock theta functions. His “lost notebook,” containing work from his final year, caused tremendous excitement when rediscovered in 1976. Mathematicians continue proving theorems from these notebooks.
His work touched elliptic functions, hypergeometric series, continued fractions, and divergent series. He invented techniques that anticipated modern mathematical developments. Hardy noted that each new point mentioned to Ramanujan caused him to produce original ideas, making systematic instruction nearly impossible.
Struggles in England
Life in England proved challenging for Ramanujan. The cold climate affected his health significantly. As a strict vegetarian bound by religious dietary restrictions, he struggled to find suitable food, especially during wartime rationing from 1914-1918.
Social isolation compounded his difficulties. Ramanujan was socially awkward with few friends outside the mathematics department. The darkness of wartime Cambridge, where streets stayed unlit to protect against attacks, made his apartment feel like a prison.
His wife Janaki sent letters that never reached him—his mother intercepted them. The silence from home distressed Ramanujan deeply. Janaki, only seventeen and under her mother-in-law’s control, couldn’t protest this manipulation.
In 1917, Ramanujan’s health deteriorated dramatically. He was diagnosed with tuberculosis and severe vitamin deficiency, then confined to a sanatorium. His suffering became so intense that he attempted suicide in late 1917 or early 1918 by jumping onto London Underground tracks. Scotland Yard arrested him, but Hardy intervened to secure his release.
Recognition and Return to India
Despite his declining health, Ramanujan achieved significant recognition. In 1918, he became the second Indian elected Fellow of the Royal Society, a tremendous honor. His mathematical papers appeared in prestigious English and European journals.
By 1919, his health in pieces but with considerable distinction, Ramanujan returned to India. When he arrived in Bombay on March 27, 1919, his first words were “Where is she?” He wanted to see Janaki. His mother had “forgotten” to inform her daughter-in-law of his arrival—Janaki learned from newspapers that her husband had returned.
Ramanujan was offered a university professorship at Madras University, which he promised to accept when his health improved. Janaki finally joined him and nursed him devotedly. During their final year together, Ramanujan expressed regret that he hadn’t taken her to England. Perhaps he wouldn’t have felt so lost and alone.
Those final months held tender moments despite his deteriorating condition. Their marriage, previously unconsummated due to separation and family interference, finally gained emotional substance. Ramanujan told his mother to step back so Janaki could care for him.
Final Days and Death
Even on his deathbed, Ramanujan continued working. He filled sheet after sheet with numbers and formulas. His last letters to Hardy, written in January 1920, contained new mathematical ideas including the mysterious mock theta functions.
On the morning of April 26, 1920, Ramanujan lapsed into unconsciousness. Janaki sat with him for two hours, feeding him sips of diluted milk. Around midmorning, he died peacefully surrounded by his wife, parents, brothers, and friends. He was just 32 years old.
His early death robbed mathematics of decades of potential discoveries. Yet his brief life produced an astounding body of work. Hardy compared Ramanujan favorably to legendary mathematicians Leonhard Euler and Carl Jacobi.
Legacy and Continuing Impact
Ramanujan’s influence extends far beyond his lifetime. December 22, his birthday, is celebrated as National Mathematics Day in India and Ramanujan Day at institutions worldwide. The Government Arts College in Kumbakonam and IIT Madras hold annual commemorations.
The International Centre for Theoretical Physics created the Ramanujan Prize for young mathematicians from developing countries. SASTRA University established the SASTRA Ramanujan Prize of $10,000, awarded annually to mathematicians under 32 for contributions in areas influenced by Ramanujan’s work.
More than a century after his death, mathematicians continue catching up to Ramanujan’s genius. His formulas appear unexpectedly in diverse mathematical areas—statistical mechanics, knot theory, string theory, algebraic geometry, and representation theory. Research published in 2024 discusses how his work on partition identities connects to modern physics and geometry.
Professor Bruce Berndt spent over forty years proving theorems from Ramanujan’s notebooks. Nearly all have been verified as correct, confirming the extraordinary accuracy of Ramanujan’s mathematical intuition. His methods anticipated developments that wouldn’t emerge until decades later.
Ramanujan in Popular Culture
Several films have portrayed Ramanujan’s life. “The Man Who Knew Infinity” (2015), starring Dev Patel as Ramanujan and Jeremy Irons as Hardy, brought his story to international audiences. Indian documentaries and docudramas have explored his mathematical legacy and personal struggles.
The play “Partition” by Ira Hauptman and “First Class Man” by Alter Ego Productions dramatized Ramanujan’s complex relationship with Hardy. His life inspires novels, including “The Steradian Trail” which weaves Ramanujan’s discoveries into plots connecting religion, mathematics, and economics.
Google honored him with a doodle on his 125th birth anniversary. Educational institutions worldwide use his story to inspire students, demonstrating that genius can emerge from unexpected circumstances and that passion can overcome lack of formal training.
Janaki Ammal’s Later Life
After Ramanujan’s death, Janaki moved to Bombay before returning to Madras in 1931, settling in Triplicane. She supported herself through a small pension from Madras University and income from tailoring. In 1950, she adopted a son, W. Narayana, who became a State Bank of India officer.
Janaki received pensions from various organizations including the Indian National Science Academy and state governments of Tamil Nadu, Andhra Pradesh, and West Bengal. She remained devoted to preserving Ramanujan’s memory and participated in efforts to increase his public recognition.
Prominent mathematicians including George Andrews, Bruce Berndt, and Béla Bollobás visited her while in India. When Andrews discovered Ramanujan’s “lost notebook” in 1976, Janaki expressed regret that no statue honored her husband. Mathematician Richard Askey organized support to create a bronze bust, presented to Janaki in 1985.
She lived a life of quiet dignity, using her modest resources to help poor students with school fees. Some children sought her blessing for examinations, considering it auspicious. She passed away peacefully on April 13, 1994, at age 94, having spent 74 years preserving and celebrating her husband’s legacy.
Final Thoughts
Srinivasa Ramanujan’s story transcends mathematics. It embodies the power of human intellect, the importance of recognizing talent regardless of credentials, and the tragedy of potential cut short by circumstance. His rise from poverty and isolation to international mathematical fame remains inspirational.
The collaboration between Ramanujan and Hardy demonstrates how mentorship can unlock genius. Hardy’s willingness to look beyond unconventional presentations and lack of formal proofs allowed Ramanujan’s gifts to flourish. Their partnership produced work that continues shaping modern mathematics and theoretical physics.
Ramanujan’s legacy reminds us that genius exists everywhere, not just in elite institutions. His intuitive approach to mathematics—often attributed to divine inspiration—actually reflected incredible dedication and countless hours of work on slate and scraps of paper. Behind the mysticism was perspiration, not just inspiration. His life stands as testament to what the human mind can achieve when passion meets opportunity, even for too brief a time.
Frequently Asked Questions
Q1: Who was Srinivasa Ramanujan?
Srinivasa Ramanujan was a self-taught Indian mathematician born on December 22, 1887, in Erode, Tamil Nadu. Despite minimal formal training, he made revolutionary contributions to number theory, infinite series, continued fractions, and partition functions. He died in 1920 at age 32 but left behind notebooks containing thousands of theorems that mathematicians continue studying today.
Q2: What is Ramanujan most famous for?
Ramanujan is famous for his work on partition functions, infinite series for pi, the Hardy-Ramanujan number (1729), mock theta functions, and numerous mathematical formulas. His intuitive mathematical insights continue influencing modern mathematics, physics, and computer science. He became the second Indian elected Fellow of the Royal Society in 1918.
Q3: How did Ramanujan learn mathematics without formal education?
Ramanujan taught himself mathematics primarily from one book—”A Synopsis of Elementary Results in Pure Mathematics” by G.S. Carr, which he obtained at age 15. He systematically verified the theorems and developed his own ideas. His exceptional memory, intuitive understanding of numbers, and relentless dedication allowed him to rediscover results that took European mathematicians decades to develop.
Q4: What is the Hardy-Ramanujan number?
The Hardy-Ramanujan number is 1729, which Ramanujan identified as the smallest number that can be expressed as the sum of two cubes in two different ways: 1729 = 1³ + 12³ = 9³ + 10³. When G.H. Hardy visited Ramanujan in hospital and mentioned arriving in taxi number 1729, Ramanujan immediately recognized this mathematical property.
Q5: Was Ramanujan married?
Yes, Ramanujan married Janaki Ammal on July 14, 1909, when he was 21 and she was 10 years old. Child marriage was common in that era. Janaki joined his household at age 13 in 1912. They were separated for five years when Ramanujan went to Cambridge. Their marriage was finally consummated in the year before his death when Janaki nursed him devotedly.
Q6: How did Ramanujan die?
Ramanujan died on April 26, 1920, at age 32 in Kumbakonam, India. His death resulted from what is now believed to be hepatic amoebiasis, a complication from earlier dysentery episodes, though he was initially diagnosed with tuberculosis and severe vitamin deficiency. His health deteriorated during his time in England due to the cold climate, dietary difficulties, and wartime conditions.
Q7: Why is December 22 celebrated as National Mathematics Day in India?
India declared December 22 as National Mathematics Day in 2012 to honor Ramanujan’s birthday and commemorate his extraordinary contributions to mathematics. Prime Minister Manmohan Singh made the declaration on December 26, 2011, during Ramanujan’s 125th birth anniversary year. The day celebrates mathematical sciences and inspires students across India to pursue mathematics.
