Srinivasa Ramanujan

Personification of genius

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 number theory, is an example of this potent form of Buddhism.

Ramanujan was born during the winter solstice, December 22, 1887, under signs in the heavens that portend great events. Out of several siblings, he was the only one who survived infancy. His horoscope, cast by his mother, predicted that he would be a genius beset by great suffering. 
Ramanujan received almost no formal training in mathematics. Yet, he was so consumed by mathematics 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 encyclopedic tome played an instrumental role in awakening his mathematical genius and set the tone for his career. Since then, Ramanujan devoted all of his time to mathematics, while continuing 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 extraordinary 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 GH 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 extraordinary 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 about the importance of proofs, a frustrated Hardy finally concluded that Ramanujan was otherworldly, a genius who erupted into something never before seen. 
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 the Goddess Namagiri. This way of conceptualising mathematics was anathema to Hardy’s code, an atheist with 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 – 1x1x1 + 12x12x12 and 9x9x9 + 10x10x10. 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 sanatoria 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. He died a year later – on April 26, 1920, at the young age of 32. The cause of his death was hepatic amoebiasis, a disease caused by liver parasites. 
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, Ramanujan spawned nearly 4,000 identities, conjectures, equations and theorems. Besides his published work, he left behind several notebooks, which have been the object of much study. In a cryptic letter written from his death bed, he outlined several never-before-heard-of mathematical functions which, decades later were proved to be true by researchers. 
Mathematicians around the world still marvel at Ramanujan’s contributions to mathematics although the meaning of much of his work is still a mystery. 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.” A fitting tribute to a mathematical genius beyond our comprehension! 

The writer is Professor of Physics at Fordham University, New York.

Srinivasa Ramanujan

Personification of genius

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 number theory, is an example of this potent form of Buddhism. Ramanujan was born during the winter solstice, December 22, 1887, under signs in the heavens that portend great events. Out of several siblings, he was the only one who survived infancy. His horoscope, cast by his mother, predicted that he would be a genius beset by great suffering. Ramanujan received almost no formal training in mathematics. Yet, he was so consumed by mathematics 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 encyclopedic tome played an instrumental role in awakening his mathematical genius and set the tone for his career. Since then, Ramanujan devoted all of his time to mathematics, while continuing 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 extraordinary 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 GH 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 extraordinary 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 about the importance of proofs, a frustrated Hardy finally concluded that Ramanujan was otherworldly, a genius who erupted into something never before seen. 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 the Goddess Namagiri. This way of conceptualising mathematics was anathema to Hardys code, an atheist with 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 Ramanujans 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. Its the smallest number representable in two different ways as a sum of two cubes 1x1x1 + 12x12x12 and 9x9x9 + 10x10x10. 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 sanatoria 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. He died a year later on April 26, 1920, at the young age of 32. The cause of his death was hepatic amoebiasis, a disease caused by liver parasites. After Ramanujans 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, Ramanujan spawned nearly 4,000 identities, conjectures, equations and theorems. Besides his published work, he left behind several notebooks, which have been the object of much study. In a cryptic letter written from his death bed, he outlined several never-before-heard-of mathematical functions which, decades later were proved to be true by researchers. Mathematicians around the world still marvel at Ramanujans contributions to mathematics although the meaning of much of his work is still a mystery. 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. A fitting tribute to a mathematical genius beyond our comprehension! The writer is Professor of Physics at Fordham University, New York.