## Did Srinivasa Ramanujan Have Formal Training in Mathematics?

Srinivasa Ramanujan had no formal mathematics training in his early years. He did his research in isolation, rediscovering old theorems and producing new ones. The main proof of this is the historical record of Ramanujan’s life paired with Ramanujan’s notebooks, which he mostly compiled before his more formal training later in life.^{[1]}^{[2]}

Although its true Ramanujan had no formal training, much of his story is romanticized. Ramanujan was gifted and self-taught in his early years, yet attended schools in his late teen and college years and had access to relevant mathematic texts which he studied obsessively. In his 20’s, after already working out many of his theories, he attracted attention in the academic world which eventually resulted in him receiving a Ph.D. from Cambridge, along with other formal accolades and training.

Unlike Einstein who was rumored to be a poor student (but wasn’t), Ramanujan struggled with formal schooling throughout his life due to his insistence on focusing on self-learning in mathematics rather than any other studies. Below is a quick story about Ramanujan’s background and his contributions to mathematics.

The Man Who Knew Infinity. An overview of Ramanujan’s early years.

**FACT**: One fundamental contribution to mathematics that Ramanujan developed was an infinite series for π. A further contribution is “the Circle Method.” Another insight is one of Ramanujan’s personal favorites, Mock Theta Functions. He also explored continued fractions like the “insane” 1+2+3+ … = -1/12. See Ramanujan’s notebooks for a complete listing of his often proof-less, yet typically correct, mathematical theorems in fields like Number Theory.

Ramanujan: Making sense of 1+2+3+… = -1/12 and Co.. 1+2+3+… = -1/12 (yes, that says all positive integers when added together equal -1/12). This identity was discovered by Ramanujan before it was proven to be true. This video IS the simple explanation.

## A Quick Account of Ramanujan’s Academic Background

Ramanujan was born on December 22, 1887, in South India. He began working with formal mathematics at the age of 10 at Secondary School, between borrowing books from peers and learning from college students who were lodgers at his home, he mastered several areas of mathematics. By 13 he began developing his complex mathematic theorems.^{[3]}

### Carr and Ramanujan’s Notebooks

In 1903, when he was 16, Ramanujan obtained from a friend a library copy of *A Synopsis of Elementary Results in Pure and Applied Mathematics* (Amazon), G. S. Carr’s collection of 5,000 theorems. It is really closer to 4,800, as each chapter skips some numbering. This was the book he acknowledged as the key element in inspiring his genius. Hid fondness for this volume is particularly interesting as Carr presents theories without proofs since it was meant to be a workbook, not specifically a textbook. Ramanujan apparently mirrored Carr in his enigmatic notebooks and learned math in a way very different from the way most learn. Perhaps he found some methods for solving equations still undiscovered today.

### Ramanujan Goes to College

For the next few years, Ramanujan ran away from home and bounced around schools as his focus on math detracted from other studies and resulted in him having to leave more than one school, although he is said to have spent considerable time at the Government College in Kumbakonam.

In 1906, without a degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty. He was often in poor health and on the brink of starvation, partly as a result of wartime food shortages in England, and partly as he never learned to cook the food that was dictated by his adherence to the vegetarian dictates of being a Brahmin Hindu.^{[4]}

Throughout all these years he compiled mathematic discoveries (often without proofs) in his notebooks. It is the fact that he lacks proofs, yet discovers old and new theorems which lends itself to romanticizing his spirituality and lack of formal education.

The Meaning of Ramanujan and His Lost Notebook

### Ramanujan and the Indian Mathematical Society

In late 1910 began to earn the respect of his peers after showing off his notebooks to the head of the newly created Journal of the Indian Mathematical Society in an attempt to get a paying job. He developed the relations between elliptic modular equations in 1910 and published a research paper in 1911 on Bernoulli numbers, which he had been interested in since his early years.^{[5]}

### Ramanujan, G.H. Hardy, and the Cambridge Years

In 1913 he began corresponding with British mathematicians who urged him to “spend time at Cambridge.” After an initial refusal to go to England Ramanujan received spiritual guidance in a vision.

Ramanujan spent the last years of his life working with British mathematicians including G. H. Hardy. He earned a BS (converted to a Ph.D.) at Cambridge, was published in respected journals, and in 1918 was the second Indian elected a Fellow of the Royal Society “for his investigation in Elliptic Functions and the Theory of Numbers.” On 13 October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.

The genius of Srinivasa Ramanujan

### Ramanujan’s Final Year

Ramanujan died at the age of 32 in 1920, a year after returning to India and having finally received formal training in mathematics at Cambridge. In his last year, Ramanujan continued to produce proof-less theorems that are still being decoded by math’s greatest minds today.

When that prodigious oddity of an Indian mathematician Srinivasa Ramanujan lay mortally ill at the age of thirty in a London hospital, he was visited by one of his peers, Professor G. H. Hardy of Cambridge. Wishing to divert the patient, and being at that time absorbed with number theory. Hardy remarked that he had just driven up in a taxicab numbered 1729 and that the number seemed to be rather a dull one. “Oh, no!” replied Ramanujan. “It is a very interesting number; it is actually the smallest number expressible as a sum of two cubes in two different ways.” –

Science Since Babylon(Full Text) (An anecdote, but maybe also a true story).

Srinivasa Ramanujan brilliance explained. A simple explanation of Ramanujan the self-taught genius.

**FACT**: It has been over 100 years since Ramanujan wrote his notebooks and mathematicians are still finding proofs for his equations and identities.

## Ramanujan’s Spiritual Influence

Ramanujan was deeply spiritual, described by biographers as rigorously orthodox Hindu, he was born into a Brahmin “varna” (a caste that specializes as priests, teachers, and protectors of sacred learning across generations).

He believed his mathematical prowess was a gift from the gods, claiming equations would come to him in full (with one story famously claiming they were sketched on the back of a turtle). He was said to have credited his gift to his family Goddess, Mahalakshmi of Namakkal. He looked to her for inspiration in his work and any other story says he claimed to dream of blood drops that symbolized her male consort, Narasimha. Afterward, he would receive visions of scrolls of complex mathematical content unfolding before his eyes.

SRINIVASA RAMANUJAN: The Mathematician & His Legacy. An Indian documentary about Ramanujan.

**FACT**: The family name Ramanujan means a person who contains a particle of the god Rama. The personal name Srinivasa roughly means Prosperous, more literally one who abides in wealth.^{[6]}

“An equation for me has no meaning unless it represents a thought of God.” – Srinivasa Ramanujan