The greatness of Srinivasa Ramanujan | UPSC

Varahasimhan is a history of science enthusiast based in Chennai

RESEARCH AT A FEVERISH PITCH

• BORN MATHEMATICIAN : Ramanujan, born on December 22, 1887 was an autodidact who specialised in pure mathematics.
• FOCAL POINT : While he excelled in mathematics, he neglected other subjects and could not complete his pre-university course.

• POVERTY AT DOORSTEP : He struggled in poverty until in 1910, a benefactor, Ramachandra Rao, district collector of Nellore, provided him monthly allowance from his own pocket so that Ramanujan could pursue research.
• SERVICE RECORDS : This would continue for a couple of years until Ramanujan managed to become a clerk at Madras Port Trust.
• PATRONS : He initiated contact with the British mathematician G.H. Hardy under whose insistence Ramanujan travelled to England in early 1914.

• RESEARCH PAPERS : His partnering with Hardy was productive: Ramanujan published more than 20 research papers between 1914 and 1919.
• DOCTORATE DEGREE : During his stay, he was awarded a doctorate and made Fellow of Royal Society.

• DEMISES : Unfortunately he lived only a year after his return succumbing to illness which was diagnosed then as tuberculosis but now revised as hepatic amoebiasis.
• RECORDS : Until he left for England in 1914, Ramanujan recorded his mathematical results, mostly equations, in his notebooks.There were three such notebooks (preserved now).
• DEEP INTUITION : One more was added when Ramanujan returned to India. Together there were about 4,000 results.The results were the culmination of research backed by deep intuition and insights.
• PROOF OF HIS RESULTS : Ramanujan did not record proofs of his results: that work would be taken up by future generations of mathematicians.

MATHEMATICAL SERIOUSNESS

• THE SERIOUSNESS OF MATHEMATICS : The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

• RAMANUJAN CONJECTURE : One such was ‘Ramanujan conjecture’ which he published in 1916 and was proved in 1973 by Pierre Deligne.
• FERMAT’S THEOREM : The conjecture inspired the development of theory of Galois representation that was employed in Andrew Wiles’ proof of Fermat’s last theorem published in 1995.

OTHER CONTRIBUTIONS

• A few significant contributions were multiple formulae to calculate pi with great accuracy to billions of digits (22/7 is only an approximation to pi)

• Modular forms and hypergeometric series (the terms in every consecutive pair in the series form rational functions).

RECENT APPLICATIONS OF RAMANUJAN’S WORK

• Ramanujan’s works and their extensions have found applications in signal processing to identify periodic information, akin to Fourier analysis.

• For Ramanujan, mathematics was art.
• For Ramanujan, his mathematics was an end in itself.

HOW DID RAMANUJAN DEVELOP HIS MATHEMATICAL ABILITIES?

• He cultivated a feeling for form, a capacity for rapid modification of his hypothesis, that were often really startling, and made him, in his own peculiar field, without a rival in his day.