# Srinivasa Ramanujan: Indian Mathematician Who Stunned Cambridge

## Who Was Srinivasa Ramanujan?

Srinivasa Ramanujan was a pioneering mathematician who made significant contributions to the fields of mathematical analysis, number theory, and continued fractions. Despite having limited access to formal education in mathematics, he possessed a natural talent for the subject.

Ramanujan was a largely self-taught mathematician who made significant contributions to mathematical analysis, number theory, and infinite series. He did not have a formal education in mathematics but instead learned on his own and developed his skills through self-study and correspondence with other mathematicians. Despite the lack of formal training, Ramanujan was able to make significant contributions to the field and is now considered one of the most brilliant mathematicians in history.

## Ramanujan's Early Years

Ramanujan was born on December 22, 1887, in Erode, a small town in the Madras Presidency (now Tamil Nadu) in India. He was the son of K. Srinivasa Iyengar, a clerk in a cloth merchant's office, and Komalatammal, a housewife. Ramanujan's family was poor and struggled financially, but they placed a great value on education and encouraged their children to pursue their studies.

As a child, Ramanujan showed a strong interest in mathematics and spent much of his time studying and solving mathematical problems. He excelled in his studies and was considered a prodigy by his teachers and peers. However, due to his family's financial struggles, Ramanujan was unable to continue his formal education beyond primary school. Despite this, he continued to study mathematics independently and developed his skills and understanding of the subject.

It is known that Ramanujan sometimes struggled to buy paper and so preferred to use chalk and slate for the workings and only used paper once he had the answer. This led to the lack of working out on his scripts, which is how he thought mathematics was done. A consequence of recording less of his process on paper was that he did more in his head, leading to his extraordinary thinking processes, which were remarkable. Ramanujan was able to remember irrational constants to many decimal places.

Ramanujan's problem was that in British India, he struggled to use his mathematical skills or find appropriate employment because those roles were reserved for the British ruling over India.

## Ramanujan's Breakthrough

In 1903, Ramanujan enrolled in the Government College in Kumbakonam, where he studied mathematics and other subjects. He excelled in his studies and earned a scholarship to continue his education at Pachaiyappa's College in Madras. However, due to his family's financial struggles, Ramanujan was unable to accept the scholarship and was forced to return home.

Despite this setback, Ramanujan continued to pursue his passion for mathematics. He read books on the subject and corresponded with other mathematicians, sharing his ideas and insights with them. In 1909, he began to publish his own research in the *Journal of the Indian Mathematical Society*. His work caught the attention of prominent mathematicians and scholars, who recognized his exceptional abilities and invited him to collaborate on research projects.

During this period, some of the people Ramanujan worked with tried to reach out to British University professors, but with no response. One day, however, G.H. Hardy, a renowned mathematician at the University of Cambridge, received some of Ramanujan's work in the post, and it got his attention. Hardy showed the work to his colleagues and realised that the author was a genius.

In 1913, Ramanujan was invited to work with Hardy, who was impressed by Ramanujan's work and recognized his potential as a mathematician. He arranged for Ramanujan to travel to Cambridge to work with him and other mathematicians at the university.

## Ramunujan's Contributions to Mathematics

Ramanujan spent several years at Cambridge, working on various mathematical problems and collaborating with other mathematicians. He made significant contributions to the study of the partition function, modular forms, and the distribution of prime numbers, among other areas. His work was characterized by a deep understanding of mathematical concepts and a remarkable ability to find patterns and connections in seemingly unrelated areas.

Ramanujan's work was highly influential and had a lasting impact on mathematics. He was awarded a Bachelor of Science degree by the University of Cambridge in 1916, and his contributions to the field were recognized by numerous awards and honours.

## Ramanujan's Most Notable Achievements

Ramanujan most notable achievements include:

- Developing the
**Ramanujan prime**, a special class of prime numbers that are named after him. - Finding a formula for the number of primes less than a given number, known as the
**prime-counting function**. - Developing a new method for evaluating infinite series that is now known as the
**Ramanujan summation**. - Making significant contributions to the study of modular forms and elliptic functions, including the
**Ramanujan theta function**. - Discovering and proving numerous identities and theorems, including the
**Ramanujan-Soldner constant**, the**Ramanujan-Hardy-Littlewood conjectures**, and the**Ramanujan-Göllnitz-Gordon identities**.

## A Life Cut Short

Despite his many accomplishments, Ramanujan's life was cut short due to poor health. He contracted tuberculosis and was forced to return to India in 1919. He died on April 26, 1920, at the tender age of 32, leaving behind a legacy that continues to inspire and influence mathematicians and researchers today.

Sadly, no one knows what breakthroughs and impact Ramanujan might have achieved had things been different.

*The Man Who Knew Infinity* (2015)

An excellent movie was released in 2015. featuring Dev Patel as Srinivasa Ramanujan. The story is about the short life and academic career of the pioneer Indian mathematician, Srinivasa Ramanujan, and his friendship with his mentor, Professor G.H. Hardy.

The story is set in the 1910s and shows Srinivasa Ramanujan as a man of boundless intelligence that even the abject poverty of his home in Madras, India, cannot crush. Eventually, his stellar intelligence in mathematics and his boundless confidence in both attract the attention of the noted British mathematics professor, G.H. Hardy, who invites him to further develop his computations at Trinity College at Cambridge.

Forced to leave his young wife, Janaki, behind, Ramanujan finds himself in a land where both his largely intuitive mathematical theories and his cultural values run headlong into both the stringent academic requirements of his school and mentor and the prejudiced realities of a Britain heading into World War One. Facing this with a family back home determined to keep him from his wife and his own declining health, Ramanujan joins Hardy in a mutual struggle that would define Ramanujan as one of India's greatest modern scholars who broke more than one barrier in his world.

Why not watch the movie—here is a link to the DVD:

## The Legacy of Ramanujan

Ramanujan's contributions to mathematics have been recognized and celebrated by the scientific community around the world. He is remembered for his exceptional talent, dedication to mathematics, and significant contributions to the field despite facing numerous challenges and setbacks. His work has inspired many other mathematicians and researchers and has had a lasting impact on the field of mathematics.

## Sources and Further Reading

- Srinivasa Ramanujan – Biography, Facts and Pictures

Lived 1887 - 1920. Srinivasa Ramanujan was a largely self-taught pure mathematician. Hindered by poverty and ill-health, his highly original work has considerably enriched number theory. - Meet a Mathematician – Ramanujan | wild.maths.org
- Papers of Srinivasa Ramanujan (1887-1920), mathematician | Trinity College Cambridge

The papers of Srinivasa Ramanujan, Add.Ms.a.94, are available to view through AtoM. - Who Was Ramanujan? | Stephen Wolfram Writings

Story of Srinivasa Ramanujan, from his early self-study of math to the pivotal letter that opened up opportunities for writing important theorems and papers. - Srinivasa Ramanujan | Biography, Contributions, & Facts | Britannica

Srinivasa Ramanujan, (born December 22, 1887, Erode, India—died April 26, 1920, Kumbakonam), Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function. - Srinivasa Ramanujan (1887 - 1920) – Biography | MacTutor History of Mathematics

*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

**© 2022 Mr Singh**