what can we learn from Srinivasa Ramanujan?
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Answers
Self-taught and hence, self-reliable
Ramanujan was always ahead of the formal education that was taught during his time. His passion for numbers, therefore, not only took him ahead of everyone else his age, but also in a completely different direction. He was 11 when he imbibed all the mathematical knowledge of two college students that were lodging in his home. At 13, he grasped advanced trigonometry and began devising theories of his own. When he was 16, he chanced upon GS Carr’s collection of 5,000 theorems presented without proofs – a challenge that was irresistible to our prodigy. He thoroughly studied them and devised his own ways of arriving at results. His mastery of mathematical applications was completely independent of existing models because most often, he was never aware of current theories.
Surpassing rivals
Ramanujan was turned down by many British mathematicians for his lack of formal education. But it was this very trait that gave him an edge over every mathematician at the time. His crude methods didn’t follow conventional mathematical models and hence left many confounded. But his curious ways of functioning were what shaped his originality and made him unique. He would rapidly modify his hypotheses in a manner that was often startling for its acuity, and would arrive at his results “by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account,” as stated by his colleague, GH Hardy, the Cambridge professor who recognised his talent. This accounted for the fact that Ramanujan “never met his equal” and has been compared to legendary mathematicians such as Euler and Jacobi.
Failure is dwarfed by passion
Although he did exceptionally well in school, Ramanujan’s scholarship program at the Government Arts college was a shipwreck. He failed his Fellow of Arts exams two years in a row as his indulgence was only in mathematics. Subjects such as English, Philosophy, and Sanskrit could not hold his interest, and therefore took a backseat. So, the twenty-year old opted to drop out and pursue independent research in mathematics. Stricken by poverty and sometimes by starvation, he found ways to make meagre sums of money to sustain his life.
It was only when he met V Ramaswamy Iyer, Founder of the Indian Mathematical Society, that he gained recognition in the mathematical circle. Soon, he accepted the job of a clerk in Madras Port Trust and spent his spare time working on theorems. In 1912, he published a seven-page paper on Bernoulli numbers, which immediately put him in the spotlight. Professors at the University of Madras were astounded at his mathematical abilities, and with the help of Professor Ramaswamy, many strings were pulled before Ramanujan was accepted as a Research scholar at the University.
Gaining wide recognition takes patience and effort
The professors at the university tried to present Ramanujan’s work to British mathematicians, who, although acknowledging his potential, weren’t keen on taking him under their wing. Some mathematicians that Ramanujan wrote to returned his letters without any response. Ramanujan, in his letters, tended to present theories and results without their derivations and proofs. This gave many the impression that this mathematician, who was previously unheard of, was a fraud. In fact, even GH Hardy, who would later develop a long association with Ramanujan, first came to the same conclusion. His first letter (which became posthumously historic) contained 120 theorems, some of which were already postulated and some, evident breakthroughs, were all presented without proofs. After continual correspondence with Hardy, Ramanujan left for England, where he spent five years at Cambridge – years that were instrumental in building his recognition.
Work that inspires future innovations
Ramanujan’s contributions to mathematics, however eccentrically they may have been produced, influenced future mathematical research. His habit of not presenting proofs inspired many papers as mathematicians strived to decipher his methods. Hardy himself produced many papers exploring Ramanujan’s theories. Some of his work like the Ramanujan Prime and the Ramanujan Theta Function, with their unconventional results, have fuelled future research. His work on composite numbers has been the most notable as it opened the doors to a whole new line of theories. Even after all these years, Ramanujan’s work holds value and is still making contributions. Mathematician Ken Ono recently made a discovery about elliptical curves, incited by Ramanujan’s comments in his notebook.
Ramanujan lived a short life, but he did so richly among the numbers he loved so very much. His colleague at the Cambridge University, JE Littlewood, remarked that “every positive integer was one of his personal friends,” a remark that effectively summarises his ingenuity and personality in a few simple words.