Questions to ask Srinivasa Ramanujan

Ramanujan's life in short, and National Mathematics Day

Srinivasa Ramanujan was born on 22 December 1887 in Erode, in what is now Tamil Nadu, and grew up in Kumbakonam, where his father was a clerk in a cloth shop. With almost no formal training beyond school, he filled notebooks with thousands of results on infinite series, continued fractions, partitions and number theory. He spent 1914 to 1919 at Trinity College, Cambridge, working with G. H. Hardy, was elected a Fellow of the Royal Society in 1918, returned to India ill in 1919 and died on 26 April 1920, aged 32.

India marks his birthday, 22 December, as National Mathematics Day. It was declared in 2011, for his 125th birth anniversary the following year, and schools hold quizzes, talks and projects around it. See our article on National Mathematics Day.

Tips before you start

Ramanujan's own words survive mainly in his letters and in the mathematics itself. That means the best questions ask about decisions and events he wrote about, not about his inner feelings, which biographers often guess at. Be careful with mathematics: never put a formula in his mouth unless you copied it from a published source. His illness, his marriage at 21 to a bride of about ten (child marriage was common then and is now illegal in India), and his religious faith should be handled plainly and respectfully.

You can rehearse your questions with an AI recreation of Ramanujan on Yuga, by voice or text, in English, Tamil, Hindi and other languages. It is built from his letters and the historical record, but it is not him and it can be wrong, especially about mathematics. Cite his letters and papers, not the app.

Kumbakonam and the borrowed textbook

What the record says: as a teenager he worked through G. S. Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics, a book of about 5,000 results with few proofs, which shaped his own habit of writing results without proofs. He won a scholarship to the Government College in Kumbakonam in 1904 but lost it because he neglected every subject except mathematics, and later failed exams at Pachaiyappa's College in Madras.

1. What did you find in Carr's Synopsis that excited you so much?
2. Why did you write down results without proofs?
3. How did it feel to lose your scholarship because of the subjects you ignored?
4. Why did you write your work on a slate and copy only the results into notebooks?
5. Who in your family supported your mathematics, and who worried about it?

Madras, the Port Trust and the letter

What the record says: after years of looking for a patron, he became a clerk at the Madras Port Trust in 1912, where his superiors encouraged his work. He published in the Journal of the Indian Mathematical Society from 1911. On 16 January 1913 he wrote to Hardy, enclosing pages of theorems. Hardy and his colleague J. E. Littlewood studied them and concluded he was a mathematician of the highest class, though a few results, such as his claim about counting primes, were wrong.

1. Why did you write to Hardy, a stranger in Cambridge?
2. Which results did you choose to send, and why without proofs?
3. What did you hope Hardy would do for you?
4. How did you feel when Hardy wrote back?
5. Why were you reluctant at first to travel to England?

On the last question: for an orthodox Brahmin, crossing the sea raised serious religious objections. He sailed in March 1914 after his mother gave her consent.

Cambridge, the war and the Royal Society

What the record says: in Cambridge he worked with Hardy on partitions, producing their 1918 paper on an asymptotic formula for the number of ways to write a number as a sum. He received a degree by research in 1916 for his work on highly composite numbers. During the First World War, food was scarce and he cooked his own vegetarian meals. He fell seriously ill in 1917. In 1918 he was elected a Fellow of the Royal Society and of Trinity College.

1. How did you and Hardy work together when you thought so differently?
2. What was it like when Hardy and Littlewood asked you to learn formal proofs?
3. What is the partition of a number, and what did you find about it?
4. What was it like to be a vegetarian in Cambridge in wartime?
5. What did it mean to you to become a Fellow of the Royal Society?
6. Is the story about the taxi number 1729 true?

The 1729 story comes from Hardy. Visiting Ramanujan when he was ill, Hardy said his taxi's number, 1729, seemed dull; Ramanujan replied that it is the smallest number expressible as the sum of two cubes in two different ways (1 cubed plus 12 cubed, and 9 cubed plus 10 cubed). We have it only in Hardy's telling.

The last year and the lost notebook

What the record says: he went home in 1919. In January 1920, months before he died, he wrote to Hardy about a new class of functions he called mock theta functions. His illness was diagnosed at the time as tuberculosis; a 1994 study suggested hepatic amoebiasis, and doctors still debate it. In 1976 the mathematician George Andrews found a bundle of his last papers, the “lost notebook”, in the library of Trinity College.

1. What are mock theta functions, as you described them to Hardy?
2. How did you keep working while you were so ill?
3. What did you want to happen to your notebooks?
4. How were you received when you came home to India in 1919?
5. What would you tell a student who loves one subject and struggles with the rest?

Sample answers in Ramanujan's words

Q: Who are you, and what do you do?

Q: How did you learn mathematics without a degree?

Q: What does mathematics mean to you?

Q: What were you working on at the end? In his last letter to Hardy (January 1920) he wrote, in substance, that he had found functions that behave like theta functions near the edge of their domain without being theta functions, and called them mock theta functions.

Questions he could not answer

He never knew that his mock theta functions would be understood properly only in 2002, when Sander Zwegers connected them to a wider theory, or that physicists would later use related ideas. He did not see National Mathematics Day, the 2015 film The Man Who Knew Infinity, or Hardy's essay A Mathematician's Apology (1940), which mentions him. Ask instead what he hoped later mathematicians would do with his unproved results.

Where to read Ramanujan's work

• Collected Papers of Srinivasa Ramanujan, edited by Hardy, P. V. Seshu Aiyar and B. M. Wilson (1927).
• The Notebooks of Srinivasa Ramanujan, a facsimile published by the Tata Institute of Fundamental Research, Bombay (1957).
• Bruce Berndt and Robert Rankin, Ramanujan: Letters and Commentary (1995), with the 1913 letters in full.
• G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940).
• Robert Kanigel, The Man Who Knew Infinity (1991), the standard biography.

He also appears in our lists of Indian scientists in history and famous mathematicians.