Srinivasa Ramanujan (born December 22, 1887 in Erode, India) was an Indian mathematician who made substantial contributions to mathematics—including results in number theory, analysis, and infinite series—despite having little formal training in math.

### Fast Facts: Srinivasa Ramanujan

**Full Name:**Srinivasa Aiyangar Ramanujan**Known For:**Prolific mathematician**Parents’ Names:**K. Srinivasa Aiyangar, Komalatammal**Born:**December 22, 1887 in Erode, India**Died:**April 26, 1920 at age 32 in Kumbakonam, India**Spouse:**Janakiammal**Interesting Fact:**Ramanujan's life is depicted in a book published in 1991 and a 2015 biographical film, both titled "The Man Who Knew Infinity."

## Early Life and Education

Ramanujan was born on December 22, 1887, in Erode, a city in southern India. His father, K. Srinivasa Aiyangar, was an accountant, and his mother Komalatammal was the daughter of a city official. Though Ramanujan’s family was of the Brahmin caste, the highest social class in India, they lived in poverty.

Ramanujan began attending school at the age of 5. In 1898, he transferred to Town High School in Kumbakonam. Even at a young age, Ramanujan demonstrated extraordinary proficiency in math, impressing his teachers and upperclassmen.

However, it was G.S. Carr’s book, "A Synopsis of Elementary Results in Pure Mathematics," which reportedly spurred Ramanujan to become obsessed with the subject. Having no access to other books, Ramanujan taught himself mathematics using Carr’s book, whose topics included integral calculus and power series calculations. This concise book would have an unfortunate impact on the way Ramanujan wrote down his mathematical results later, as his writings included too few details for many people to understand how he arrived at his results.

Ramanujan was so interested in studying mathematics that his formal education effectively came to a standstill. At the age of 16, Ramanujan matriculated at the Government College in Kumbakonam on a scholarship, but lost his scholarship the next year because he had neglected his other studies. He then failed the First Arts examination in 1906, which would have allowed him to matriculate at the University of Madras, passing math but failing his other subjects.

## Career

For the next few years, Ramanujan worked independently on mathematics, writing down results in two notebooks. In 1909, he began publishing work in the Journal of the Indian Mathematical Society, which gained him recognition for his work despite lacking a university education. Needing employment, Ramanujan became a clerk in 1912 but continued his mathematics research and gained even more recognition.

Receiving encouragement from a number of people, including the mathematician Seshu Iyer, Ramanujan sent over a letter along with about 120 mathematical theorems to G. H. Hardy, a lecturer in mathematics at Cambridge University in England. Hardy, thinking that the writer could either be a mathematician who was playing a prank or a previously undiscovered genius, asked another mathematician J.E. Littlewood, to help him look at Ramanujan’s work.

The two concluded that Ramanujan was indeed a genius. Hardy wrote back, noting that Ramanujan’s theorems fell into roughly three categories: results that were already known (or which could easily be deduced with known mathematical theorems); results that were new, and that were interesting but not necessarily important; and results that were both new and important.

Hardy immediately began to arrange for Ramanujan to come to England, but Ramanujan refused to go at first because of religious scruples about going overseas. However, his mother dreamed that the Goddess of Namakkal commanded her to not prevent Ramanujan from fulfilling his purpose. Ramanujan arrived in England in 1914 and began his collaboration with Hardy.

In 1916, Ramanujan obtained a Bachelor of Science by Research (later called a Ph.D.) from Cambridge University. His thesis was based on highly composite numbers, which are integers that have more divisors (or numbers that they can be divided by) than do integers of smaller value.

In 1917, however, Ramanujan became seriously ill, possibly from tuberculosis, and was admitted to a nursing home at Cambridge, moving to different nursing homes as he tried to regain his health.

In 1919, he showed some recovery and decided to move back to India. There, his health deteriorated again and he died there the following year.

## Personal Life

On July 14, 1909, Ramanujan married Janakiammal, a girl whom his mother had selected for him. Because she was 10 at the time of marriage, Ramanujan did not live together with her until she reached puberty at the age of 12, as was common at the time.

## Honors and Awards

- 1918, Fellow of the Royal Society
- 1918, Fellow of Trinity College, Cambridge University

In recognition of Ramanujan’s achievements, India also celebrates Mathematics Day on December 22, Ramanjan’s birthday.

## Death

Ramanujan died on April 26, 1920 in Kumbakonam, India, at the age of 32. His death was likely caused by an intestinal disease called hepatic amoebiasis.

## Legacy and Impact

Ramanujan proposed many formulas and theorems during his lifetime. These results, which include solutions of problems that were previously considered to be unsolvable, would be investigated in more detail by other mathematicians, as Ramanujan relied more on his intuition rather than writing out mathematical proofs.

His results include:

- An infinite series for π, which calculates the number based on the summation of other numbers. Ramanujan’s infinite series serves as the basis for many algorithms used to calculate π.
- The Hardy-Ramanujan asymptotic formula, which provided a formula for calculating the partition of numbers—numbers that can be written as the sum of other numbers. For example, 5 can be written as 1 + 4, 2 + 3, or other combinations.
- The Hardy-Ramanujan number, which Ramanujan stated was the smallest number that can be expressed as the sum of cubed numbers in two different ways. Mathematically, 1729 = 1
^{3}+ 12^{3}= 9^{3}+ 10^{3}. Ramanujan did not actually discover this result, which was actually published by the French mathematician Frénicle de Bessy in 1657. However, Ramanujan made the number 1729 well known.

1729 is an example of a “taxicab number,” which is the smallest number that can be expressed as the sum of cubed numbers in*n*different ways. The name derives from a conversation between Hardy and Ramanujan, in which Ramanujan asked Hardy the number of the taxi he had arrived in. Hardy replied that it was a boring number, 1729, to which Ramanujan replied that it was actually a very interesting number for the reasons above.

## Sources

- Kanigel, Robert.
*The Man Who Knew Infinity: A Life of the Genius Ramanujan*. Scribner, 1991. - Krishnamurthy, Mangala. “The Life and Lasting Influence of Srinivasa Ramanujan.”
*Science & Technology Libraries*, vol. 31, 2012, pp. 230–241. - Miller, Julius. “Srinivasa Ramanujan: A Biographical Sketch.”
*School Science and Mathematics*, vol. 51, no. 8, Nov. 1951, pp. 637–645. - Newman, James. “Srinivasa Ramanujan.”
*Scientific American*, vol. 178, no. 6, June 1948, pp. 54–57. - O'Connor, John, and Edmund Robertson. “Srinivasa Aiyangar Ramanujan.”
*MacTutor History of Mathematics Archive*, University of St. Andrews, Scotland, June 1998, www-groups.dcs.st-and.ac.uk/history/Biographies/Ramanujan.html. - Singh, Dharminder, et al. “Srinvasa Ramanujan's Contributions in Mathematics.”
*IOSR Journal of Mathematics*, vol. 12, no. 3, 2016, pp. 137–139. - “Srinivasa Aiyangar Ramanujan.”
*Ramanujan Museum & Math Education Centre*, M.A.T Educational Trust, www.ramanujanmuseum.org/aboutramamujan.htm.