Making of a Mathematical Genius

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A Synopsis of Elementary Results in Pure and Applied Mathematics (1880, revised in 1886), by George Shoobridge Carr; a less than ideal book on Mathematics became the reason for Ramanujan to become what we know the great Ramanujan for, an unparalleled mathematical genius. The story goes that he encountered this book sometimes in 1903 when he was 15 years old. The book was not an orderly procession of theorems and had tidy proofs. This led Ramanujan to jump in and make connections on his own. However, since the proofs included were mostly one-liners, Ramanujan was (mis) led to get a false impression of the rigor required in mathematics.

Despite being a prodigy in mathematics, Ramanujan did not have a great start in his early career. He quickly lost the scholarship that he had secured while entering the college in 1904, by failing in non-mathematical subjects. Another try at college in Madras (now Chennai) also ended poorly when he failed his First Arts examination. It was around this time that he began his famous notebooks.

Ramanujan once convinced that his growth in Mathematics lies in the West, had started writing letters of introduction to professors at the University of Cambridge. His first two letters went unanswered, but his third—of January 16, 1913, to G.H. Hardy met the desired results. Ramanujan in his letter had included nine pages of mathematics. Some of these results were known to Professor Hardy but others took him by complete surprise. Soon a correspondence began between the two that culminated in Ramanujan joining to study under Hardy in 1914.

Ramanujan’s discoveries have influenced several areas of mathematics, but he is probably most famous for his contributions to number theory and infinite series, among them fascinating formulas that can be used to calculate digits of pi in unusual ways. His famous notebooks, among other things include 17 ways to represent 1/pi as an infinite series.

There is yet another interesting anecdote on how Ramanujan lived and breathed Mathematics. His mentor, Professor Hardy once took a cab to visit Ramanujan. When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No, it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1^3 + 12^3 = 9^3 + 10^3”. This number is what the world now knows as the Hardy-Ramanujan number, and is the smallest numbers that can be expressed as sum of two cubes in n different ways. This is also dubbed as taxicab numbers.

Hardy had come up with a scale of mathematical ability that went from 0 to 100. He put himself at 25. David Hilbert, the great German mathematician, was at 80. Ramanujan was 100. When the genius passed away in 1920 at an early age of 32, Ramanujan left behind three notebooks and a sheaf of papers (the “lost notebook”). These notebooks contained thousands of results that are still inspiring mathematical work.

Today, on 22 December, which is the 125th birth anniversary of the great Mathematician and is therefore our National Mathematics Day, I pray rich tributes to the great Ramanujan; who is unquestioningly one of the many reasons to make we Indians feel proud of our heritage. Today, I also reaffirm my commitment to continue writing however, mediocre it may appear to me or the world around me. Who knows, someday my writing may become instrumental to someone in realising their true potential.