The Awe-Inspiring Work Of Srinivasa Ramanujan

The Awe-Inspiring Work Of Srinivasa Ramanujan

By Lillie Therieau 

Anyone can enjoy and learn mathematics, however, some folks are just born with the math gene. That was the case when Srinivasa Ramanujan was born in India in the late 19th century. At a very young age, it became clear that he was a child prodigy. He would eventually grow up to change the landscape of mathematical thinking.

An Unlikely Path For A Mathematical Genius 

Srinivasa Ramanujan was born in 1887 in the Madras Presidency of British-occupied India, now Tamil Nadu, India. His father was a clerk at a sari shop and his mother was a housewife. Ramanujan spent his young childhood bouncing between his paternal and maternal grandparents alongside his mother. As such, he was very close with his mother, who taught him to follow strict Brahmin (the priest class of Hindu India) traditions. By his 11th birthday, he was already recognized as a mathematical prodigy. By 14, he was teaching math classes at his local high school. 

When he graduated from high school, Ramanujan received many scholarships and awards. He went to several colleges but ended up failing out of each and losing his scholarship because he only bothered to do the work in his math classes. This led to a period of extreme poverty for Ramanujan, as he lived without a degree or job, researching mathematics on his own. 

However, after a meeting with Ramaswamy Aiyer, the head and founder of the Indian Mathematical Society Ramanujan, began garnering recognition in Indian math circles. Ramaswamy Aiyer referred and introduced Ramanujan to many of his prestigious colleagues, which eventually led to a paid research position at Madras University. Ramanujan and his new wife, Janaki, would no longer have to live in poverty. 

Photo of Srinivasa Ramanujan, sitting, wearing a dark suit and tie.

Photo of Srinivasa Ramanujan, Image: Wikipedia

Ramanujan’s Battle To Be Recognized 

Ramanujan was presenting theorems and proofs that were completely stunning to most mathematicians working at the time. He was able to think through old problems that had stumped thinkers for centuries with a kind of nimble creativity that was shocking to academics. 

His work was so new and pioneering that many mathematicians dismissed it outright as a fraud. Others refused to believe it could be true because they did not have the knowledge to check his work themselves. 

His lack of formal training in writing didn’t help in this regard. It was a detriment to the publication of his mathematical work, as he often had trouble explaining the concepts underpinning his process. Many British mathematicians ignored him altogether, believing that his lack of formal higher education meant he would never be taken seriously in academia.

His rejection by many leading mathematicians would be a source of humiliation for them later on when it became clear that he really did possess a unique genius, moving mathematics forwards by leaps and bounds. 

Ramanujan’s Work At Cambridge And His Untimely Death

However, one British mathematician recognized the true potential of his work. Ramanujan was writing to many mathematicians at the beginning of the 1910s. G.H Hardy, a mathematician at Cambridge University, was the first one who wrote back. He reportedly said that Ramanujan’s theorems defeated him. He had never seen anything like them and could hardly comprehend how someone would be able to come up with them. 

Hardy immediately invited Ramanujan to Cambridge, but he initially refused. He was still a deeply religious man, and his mother believed that traveling abroad would violate his Brahmin upbringing. However, a few months later his mother had a prophetic dream featuring their family deity, Namagiri, where she was told to let Ramanujan go to England. 

He arrived on a ship in April of 1914 and was driven to Cambridge, where he would spend the next five years of his life. He worked closely with Hardy, although the two often clashed. Hardy was an atheist, devoted to what he saw as the pure science of mathematics. Ramanujan was deeply religious, and his work was often guided by intuition, dreams, and spirituality. Moreover, Hardy wanted to help Ramanujan with his writing and formal analysis skills, which was a point of contention in their relationship.

In 1916, he was awarded the equivalent of a Ph.D. in mathematical research. Over the next few years, he was elected to the London Mathematical Society, the Royal Society, and a Fellow of Trinity College. In each of these roles, he was one of the first Indians to be admitted and the youngest member in history. 

However, Ramanujan’s health was failing him. He was diagnosed with tuberculosis in 1919 and sent to a sanitorium. He returned home in 1919 and died in 1920 at the young age of 32. 

Today he’s recognized as one of the greatest mathematicians of all time. In 2011, the Indian government designated Ramanujan’s birthday as National Mathematics Day. He’s been immortalized in several books and documentaries, and his house in Kumabokanam is now a museum. 

Ramanujan’s Mathematical Contributions

Ramanujan’s work spanned several fields of mathematics, including highly composite numbers, hypergeometric theories, elliptic integrals, divergent theories, and more. He filled four notebooks, with almost 1,000 pages of his work. 

He did not record the ways that he came to his answers, instead only notating results without proofs. Although some believed that this meant he could not prove his work, it was simply because paper was very expensive and he did most of his work on slate before transferring the results to his notebook. The lack of proofs inspired generations of mathematicians to try and figure out how he came to his answers. 

Although most of his work is beyond the scope of my understanding, Ramanujan's magic square is a wonderful example of the playful side of his work. 

The square is formed by four rows and four columns of numbers. In a typical magic square, the sum of all rows, columns, and diagonals is the same. (In this case 139.) However, Ramanujan’s magic square has a few extra alignments totaling 139, including the four center squares, the four corner squares, and the sum of the two center squares in the top row, the bottom row, and the left and right-hand columns.  

Try it yourself and be amazed by the symmetry of this wonderful magic square! 

The Inspiring Lives of Famous Mathematicians 

This article is the second in our series exploring the lives and achievements of famous mathematicians throughout history. (The first was the French mathematician, Sophie Germain!) 

Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.

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