Ramanujan: A mathematical genius with an aura of mysticism
For many people, mathematics is a word that evokes feelings of awe. They remember the subject from their school days as a world difficult to get into, the finer points of which they never understood. They also remember that there were always a few students in class who with no apparent difficulty understood maths. They were the brightest students in class―that's the halo that mathematicians wear around their heads.
This winter solstice marks the 137th birth anniversary of one such extraordinarily bright student who possessed an uncanny ability to see beyond the apparent and transcended the boundaries of traditional knowledge in the realm of mathematics. He was Srinivasa Ramanujan, one of the world's all-time great mathematicians. Born into modest circumstances in Erode, Tamil Nadu, India on December 22, 1887, under signs in the heavens that portend great events, his horoscope, cast by his mother, predicted that he would be a wunderkind beset by great suffering.
For all latest news, follow The Daily Star's Google News channel. Ramanujan received almost no formal training in mathematics. Yet, he was so consumed by it that he was unable to focus on any other subject in college and thus, could not complete his degree.
When he was in his mid-teens, a friend introduced him to the book Synopsis of Elementary Results in Pure and Applied Mathematics. This two-volume encyclopaedic tome played an instrumental role in awakening this mathematical prodigy and set the tone for his career. Since then, Ramanujan committed all of his time to mathematics, proceeding to record his theorems without proofs in his notebooks.
As he continued to make deep discoveries of his own, he wrote to the erudite men and women of mathematics for recognition. But they ignored him because his claims seemed too incredible to be the product of someone with no formal background in mathematics.
In 1913, while working as a clerk in the accounts department of the Port Trust Office in Madras, Ramanujan dispatched a letter containing more than 100 theorems to Godfrey Hardy, a famous number theorist at Cambridge University and a Trinity College don. Initially intrigued by the "outlandishly original" theorems, Hardy eventually saw a genius in Ramanujan and invited him to Cambridge University in April 1914.
Once in Cambridge, Ramanujan produced hundreds of new equations, identities and theorems, mostly without proofs, dazzling his peers who were baffled as to the source of his exceptional abilities. Being a great exponent of exactness and proofs, Hardy was unhappy with just conjectures and wanted Ramanujan to back up his work with rigorous proofs. But Ramanujan treated proofs as mostly redundant and relied instead on intuition. Unable to convince him that proofs were the currency of mathematics, a frustrated Hardy finally concluded that Ramanujan was otherworldly, a savant who erupted into something never seen before.
John Littlewood, another brilliant Trinity don who worked closely with Hardy and Ramanujan, opined that Ramanujan ruled out conventional reasoning because his work had an aura of mysticism. Indeed, Littlewood was correct. As a devout Brahmin, Ramanujan perceived a mystic connection between mathematics and his religion. He believed his mathematical formulas came to him as visions provided by Goddess Namagiri. To him, an equation holds no meaning unless it expresses a thought of God. This way of conceptualising mathematics was anathema to Hardy's code, an atheist with a hostile attitude towards religion. This made the two an odd couple with conflicting views of religion but consonant views of mathematics.
An amusing anecdote that came to symbolise Ramanujan's genius concerns the number 1729. Hardy once came to visit Ramanujan in a cab numbered 1729, a number he claimed to be totally uninteresting. Ramanujan immediately stated that it was actually a very interesting number. It's the smallest number representable in two different ways as a sum of two cubes: 13 + 123 and 93 + 103. Such numbers are now referred to as "taxicab numbers."
Ill health had been an issue with Ramanujan since his birth. In the spring of 1917, he was diagnosed with tuberculosis. Despite being in and out of sanatorium for the rest of his stay in Cambridge, he continued to make enormously important contributions in the areas of number theory, analysis, and algebraic combinatorics.
By early 1919, Ramanujan seemed to have recovered sufficiently and returned to India. A year later, on April 26, 1920, at the young age of 32, he died of tuberculosis. Even on his deathbed, he documented a series of theorems that he claimed had been revealed to him during a dream.
After Ramanujan's death, Hardy was asked in an interview what his greatest contribution to mathematics was. He replied without hesitation that it was the discovery of Ramanujan. He even characterised their collaboration as "the one romantic incident in my life."
During his short life span, Ramanujan spawned thousands of identities, conjectures, equations, and theorems. His deep intuitive understanding of numbers and their representation as infinite series created identities that were previously unknown to the world of mathematics. Besides his published work, he left behind a priceless treasure: his three notebooks and a few scraps of paper covering around 3,900 equations.
Mathematicians around the world marvel at Ramanujan's contributions to mathematics, although the meaning of much of his work is still a mystery. They continue to strive to reach his extraordinary intellect as his insights manifest repeatedly in disparate corners of the world of mathematics. As noted by Freeman Dyson, a renowned theoretical physicist at Princeton University, Ramanujan "discovered so much, and yet left so much more in his garden for other people to discover."
The Vajrayana form of Buddhism, adherents say, provides a quicker path to enlightenment and early freedom from the wheel of incarnations. If this is really true, then Srinivasa Ramanujan, a self-taught Indian mathematical wizard, who revolutionised the field of real analysis, number theory, game theory, continued fraction, infinite series, and many more, is an example of this potent form of Buddhism.
Dr Quamrul Haider is professor emeritus at Fordham University in New York, US.
Views expressed in this article are the author's own.
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