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Srinivasa Ramanujan

Srinivasa Ramanujan was an Indian mathematician born in 1887 in Erode, a small town in Tamil Nadu. His family was poor but educated. His father was a clerk and his mother was a devout Hindu. From a young age, he loved numbers. By the age of twelve, he was working through advanced mathematics books on his own. He had very little formal mathematical training. He failed his college exams because he spent all his time on mathematics and neglected other subjects. He lost his scholarship. He worked as a clerk in Madras and did mathematics in every spare moment. He filled notebooks with thousands of results, many of which were new and surprising. In 1913, he wrote a letter to G. H. Hardy, a leading mathematician at Cambridge University in England. The letter contained strange and beautiful formulas. Hardy was amazed. He invited Ramanujan to Cambridge in 1914. The two men worked together for five years. Ramanujan produced brilliant results on number theory, infinite series, and continued fractions. Life in England was hard. The climate was cold. The food was wrong for his vegetarian diet. He became very ill, possibly with tuberculosis or a parasitic infection. He returned to India in 1919 and died in 1920, aged only 32. His notebooks are still being studied today.

Origin
India (British Raj)
Lifespan
1887-1920
Era
Early 20th Century
Subjects
Mathematics Number Theory Infinite Series Colonial Science Intuition
Why They Matter

Ramanujan matters for three big reasons. First, his mathematics is deep and still useful. His formulas appear in modern physics, in computer science, and in the theory of black holes. Mathematicians are still proving things he only guessed a hundred years ago.

Second, he changed who mathematics belongs to. He was poor, self-taught, and from a country that was under British colonial rule. The leading universities of his time were not built for someone like him. Yet he became one of the great mathematicians of the twentieth century. His story broke the idea that world-class mathematics required the right background, the right school, or the right country.

Third, his way of thinking was different. He had almost no access to the modern proofs that European mathematicians relied on. He got his results through intuition, calculation, and what he called divine inspiration. This makes his work a puzzle for historians and mathematicians. How did he know? His method cannot be fully explained, but it produced truths that later mathematics has confirmed. He shows that there is more than one path to mathematical knowledge.

Key Ideas
1
Self-Taught Genius
2
The Letter to Hardy
3
Infinity and Patterns
Key Quotations
"An equation for me has no meaning unless it expresses a thought of God."
— Attributed, reported by his friend R. Srinivasan; widely quoted but exact source disputed
Ramanujan was a devout Hindu. He believed that mathematical truths were sacred. He often said that the goddess Namagiri showed him formulas in dreams. For him, mathematics was not just a human activity. It was a way of seeing divine patterns in the world. Not every mathematician agrees with this view. But the quote shows how personal and spiritual mathematics was for Ramanujan. It is a reminder that great mathematicians do not all think the same way.
"No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
— Response to G. H. Hardy about the number 1729, reported by Hardy in his obituary of Ramanujan, 1921
Hardy had visited Ramanujan in hospital and said the number of his taxi, 1729, was a dull number. Ramanujan instantly replied with this. The number equals 1 cubed plus 12 cubed, and also 9 cubed plus 10 cubed. This was not something Ramanujan worked out in the moment. He simply knew it. The story is now famous because it shows how differently he saw numbers. For him, every number had interesting features. The number 1729 is still called the Hardy-Ramanujan number.
Using This Thinker in the Classroom
Scientific Thinking When students learn about different ways of knowing in mathematics
How to introduce
Most mathematics classes teach proof: a step-by-step argument from given facts. Ramanujan often skipped this step. He wrote down truths he sensed were correct. Most of the time, he was right. Ask students: is a correct result without a proof still mathematics? Why do we need proof? What might be gained and lost by working like Ramanujan?
Cultural Heritage and Identity When celebrating National Mathematics Day (22 December) or discussing scientists from the Global South
How to introduce
India celebrates Ramanujan's birthday as National Mathematics Day. Use this moment to ask: why is it important to know about mathematicians from many countries? Students often hear names like Newton, Euler, or Gauss. Ramanujan adds another kind of story. Ask students to research mathematicians from their own region or heritage. Science belongs to the whole world.
Further Reading

For a first introduction, Robert Kanigel's biography The Man Who Knew Infinity, published in 1991, is the most popular account of Ramanujan's life. It was made into a film in 2015 with Dev Patel and Jeremy Irons. The film is accurate in broad outline, less so in detail. The BBC documentary Ramanujan: Letters from an Indian Clerk is a shorter watch. For children, The Boy Who Dreamed of Infinity by Amy Alznauer is a lovely picture book. The Indian government's website for National Mathematics Day has good introductory material.

Key Ideas
1
Partitions and the Hardy-Ramanujan Formula
2
Mock Theta Functions
3
Colonial Context and the Journey to Cambridge
Key Quotations
"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing."
— Reported conversation, in S. R. Ranganathan, Ramanujan: The Man and the Mathematician, 1967
Ramanujan described receiving mathematical results in visions and dreams. He credited the goddess Namagiri for many of them. Western mathematicians found this unusual. Today we might explain it as the mind working on problems during sleep. Whatever the mechanism, the results Ramanujan wrote down were often correct. The quote raises interesting questions about where mathematical ideas come from. For Ramanujan, they came from a spiritual source. Others may describe the same experience in different language.
"I have found a friend in you who views my labours sympathetically."
— Letter to G. H. Hardy, 16 January 1913
This was part of Ramanujan's first letter to Hardy. He had tried to reach other British mathematicians before, without success. Hardy was the first to take him seriously. The quote shows both Ramanujan's gratitude and his isolation. Before Hardy, he had no mathematical colleagues who could understand his work. This loneliness was one cost of his unusual path into mathematics. The quote also shows the human side of science: great work needs not just talent but connection, encouragement, and trust.
Using This Thinker in the Classroom
Critical Thinking When examining myths around 'lone geniuses'
How to introduce
Ramanujan is often told as a lone genius story. The truth is more complex. He had a supportive family, Indian patrons, and a clerk's job that gave him time to work. Without Hardy's invitation, he might have been forgotten. Ask students: what does Ramanujan's story need from other people to be possible? How does the lone genius myth hide the role of supporters, teachers, and chance?
Research Skills When teaching students about keeping a research notebook
How to introduce
Ramanujan's notebooks are legendary. He filled them with thousands of results, often without explanation. The notebooks are still being studied today. Show students a page from his notebooks (available online from the Tata Institute). Ask: what can we learn about how he thought? Encourage students to keep their own mathematical notebooks: write down problems, partial solutions, strange results, questions for later.
Problem Solving When introducing the concept of partitions or pattern-finding
How to introduce
Start with partitions. Ask students: in how many ways can you write the number 5 as a sum of smaller positive whole numbers? They can work it out: there are 7 ways. Then ask about 10, 20, 50. The numbers grow fast. Tell students that Ramanujan and Hardy found a formula that almost exactly predicts the count for any number. Their method started a whole new field. This shows how a simple counting problem can lead to deep mathematics.
Further Reading

Bruce C. Berndt, one of the leading scholars of Ramanujan's notebooks, has written a series of books called Ramanujan's Notebooks (five volumes). These are serious but accessible for people with some university mathematics. S. R.

Ranganathan's biography Ramanujan

The Man and the Mathematician, published in 1967 by an Indian librarian who knew people close to Ramanujan, offers an Indian perspective that Kanigel's book does not have. G. H.

Hardy's Ramanujan

Twelve Lectures is the classic mathematical appreciation. The Ramanujan Mathematical Society in India publishes regularly on his work.

Key Ideas
1
Proof, Intuition, and Epistemology
2
Illness, Death, and What Was Lost
3
Ramanujan's Legacy in Modern Science
Key Quotations
"The limits of my language mean the limits of my world."
— Not Ramanujan's own words; this is a famous line from Wittgenstein often mistakenly attributed to him. For a real Ramanujan quote on his approach: 'My method is the scientific method.'
This entry is included as a warning. Ramanujan is sometimes quoted with sayings he never said. The first line here is by the philosopher Ludwig Wittgenstein. A real Ramanujan quote, reported by colleagues, is simpler: he thought of his mathematical intuition as a form of scientific method, even if not the European kind. For advanced students, this is a lesson in source criticism. Famous figures attract false quotes. Always check where a quote really comes from.
"I am extremely sorry for not writing you a single letter up to now... I discovered very interesting functions recently which I call Mock theta-functions."
— Last letter from Ramanujan to G. H. Hardy, 12 January 1920
Ramanujan wrote this letter from his sickbed, three months before his death. He described the mock theta functions he had discovered. He gave examples but no complete theory. Hardy kept the letter. For nearly 80 years, mathematicians tried to understand what Ramanujan meant. In 2002, Sander Zwegers finally placed mock theta functions inside modern theory. The quote is a message from a dying 32-year-old to the future. It shows how much was still inside him when he died. Whatever else we say about his short life, he never stopped working.
Using This Thinker in the Classroom
Creative Expression When exploring mathematics as an art form
How to introduce
Hardy said his greatest contribution to mathematics was Ramanujan. He also said mathematics was like poetry: beautiful patterns of ideas. Ramanujan saw his formulas as expressing divine thoughts. Ask students to compare mathematical creativity with artistic creativity. Show them a Ramanujan formula, like one of his pi series. Ask: what makes it beautiful? What makes any equation beautiful?
Ethical Thinking When studying the history of science under colonialism
How to introduce
Ramanujan worked inside the British Empire. His talent was discovered partly because British mathematicians had access to Indian minds that the other way around was less true. At Cambridge, he was celebrated but also isolated. He fell ill partly because the support he needed was not there. Ask students: who benefits from stories like Ramanujan's? What does the British Empire owe for the scientific work of its colonial subjects? How should we remember this history today?
Common Misconceptions
Common misconception

Ramanujan was a magical genius whose work cannot be explained.

What to teach instead

His work is now well understood by mathematicians. Most of his results have been proved. A few have been shown to be wrong. His methods, though unusual, can be studied. He had absorbed a huge amount of calculation and pattern recognition. His intuitions were trained by thousands of hours of work. Calling him magical makes him less real. He was a human being with extraordinary talent and discipline.

Common misconception

Ramanujan's mathematics is old-fashioned and no longer relevant.

What to teach instead

His mathematics is more relevant today than ever. His mock theta functions connect to black holes and string theory. His partition formulas are used in modern combinatorics. His formulas for pi are used in computers. The Ramanujan Journal publishes new research inspired by his ideas every year. Mathematicians are still proving things he only guessed. His work is not historical decoration. It is living mathematics.

Common misconception

Without G. H. Hardy, Ramanujan's talent would have been lost.

What to teach instead

Hardy was crucial, but he was not the first to support Ramanujan. Indian patrons, including Ramaswamy Iyer, Ramachandra Rao, and Narayana Iyer, recognised his talent first. They gave him jobs, money, and encouragement. They helped him prepare the letter to Hardy. This misconception centres the British part of the story and erases the Indian part. The full story is about a network of people, both Indian and British, who saw what he could do.

Common misconception

Ramanujan died of tuberculosis from the cold English climate.

What to teach instead

This was the long-accepted story but is now questioned. In the 1990s, Dr D. A. B. Young and others studied the medical evidence. They argued that Ramanujan more likely had hepatic amoebiasis, a parasitic infection he probably picked up in India years before. It was treatable but not diagnosed at the time. Cold weather and stress in England made things worse, but they were probably not the root cause. This correction matters because it changes the moral: his death was less about racial mismatch and more about missed medical care.

Intellectual Connections
In Dialogue With
Emmy Noether
Ramanujan and Noether worked at roughly the same time but in very different ways. Noether sought abstract structure and formal proof. Ramanujan sought patterns through intuition. Together they show that mathematics can be done in many styles. Both were outsiders: Ramanujan as a colonial subject, Noether as a Jewish woman. Both found paths into a profession that was not designed for them.
Complements
Pāṇini
Both Ramanujan and Pāṇini came from Indian traditions of precise, rule-based thinking. Pāṇini, over 2000 years earlier, built a formal system for Sanskrit grammar. Ramanujan built formulas for numbers. Both worked with elegance and economy. Their shared Indian intellectual heritage, focused on pattern and rule, is worth exploring. It suggests a longer history of formal thinking in South Asia than Western histories often acknowledge.
Influenced
Rabindranath Tagore
Ramanujan and Tagore were contemporaries and both became global symbols of Indian genius in the early 20th century. Tagore won the Nobel Prize in Literature in 1913, the same year Ramanujan wrote to Hardy. Both challenged the idea that India could only receive Western knowledge. Both were celebrated in Britain but remained rooted in Indian culture. Their parallel stories changed how India was seen in the world.
Anticipates
Dorothy Hodgkin
Hodgkin worked a generation later at Oxford but shared with Ramanujan a pattern-based way of seeing. She solved molecular structures by reading crystallographic images. Ramanujan saw patterns in numbers. Both used visual and intuitive thinking in scientific work. Their connection suggests that intuition and pattern recognition are essential parts of scientific discovery, not just formal deduction.
Complements
Marie Curie
Both Ramanujan and Curie worked outside the mainstream of their fields because of who they were: he a colonial subject, she a Polish woman in France. Both moved to centres of power (Cambridge for him, Paris for her) and changed those centres. Both paid a heavy price in their health. Their stories together show what science loses when access is unequal, and what it gains when barriers can be crossed.
Influenced
Ada Lovelace
Lovelace and Ramanujan share a kind of visionary mathematics. She saw that computers could do more than calculate; he saw that numbers had patterns others missed. Both were ahead of their time in ways that later generations are still catching up with. Both died young. Both are now central to conversations about who gets to do mathematics and whose contributions get remembered.
Further Reading

For research-level study, Bruce Berndt and Robert Rankin's two-volume Ramanujan: Letters and Commentary and Ramanujan: Essays and Surveys are essential. Ken Ono and Amir Aczel's My Search for Ramanujan describes modern work on the mock theta functions. Zwegers's 2002 Utrecht thesis is available online for those wanting to read the key breakthrough on mock theta functions. For the medical reassessment, see D. A. B. Young, Ramanujan's Illness, Notes and Records of the Royal Society, 1994. For colonial and cultural context, Gyan Prakash's Another Reason: Science and the Imagination of Modern India places Ramanujan within the broader history of science under British rule.