Timely reminder of a mathematical genius

 

That’s Maths:In two weeks, an international mathematical conference will be held at the Viceregal Lodge in New Delhi, once the nerve-centre of the British Raj. The conference marks the 125th anniversary of the birth of Srinivasa Ramanujan, one of the greatest mathematical geniuses to emerge from India.

Ramanujan was born in 1887 into a poor Brahmin family and had limited formal education. He was consumed by a passion for mathematics, neglected all other subjects, and failed the entrance exam for the University of Madras. However, he continued his mathematical research with intensity.

In 1913, Ramanujan wrote to GH Hardy, the leading mathematician in Britain, enclosing some of his results. Hardy examined them and concluded that they “could only be written down by a mathematician of the highest class”.

Thus began one of the the most successful mathematical collaborations of all time. For five years, Ramanujan worked with Hardy in Cambridge, publishing many papers of great richness and originality. In 1918 he was elected a fellow of the Royal Society.

Ramanujan returned to India in 1919, but lived for only one more year. Shortly before his death, aged only 32, he wrote a last letter to Hardy in which he introduced 17 completely new and strange power series that he called “mock theta functions”.

In 1976, the American mathematician George Andrews was looking through some papers in the Wren Library in Cambridge and recognised the handwriting of Ramanujan. What he found is now known as the “Lost Notebook”, containing many remarkable results, including Ramanujan’s results on the mysterious mock theta functions.

Andrews’s discovery opened up a vast landscape. The results were of stunning novelty, representing what many regard as Ramanujan’s deepest work. The finding of the notebook has been compared to finding a manuscript of Beethoven’s 10th Symphony. The consequences have been profound, for pure mathematics and theoretical physics.

Ramanujan gave no clue as to how he had discovered the mock theta functions. An intrinsic meaning of them has eluded mathematicians until very recently. Sander Zwegers, a lecturer at UCD until he moved to Cologne in 2011, finally explained how they fit into a broader context. Zwegers’s 2002 PhD thesis was groundbreaking, and has led to numerous publications and international conferences.

The breakthrough in our understanding is having an impact on many areas of mathematics and physics. Ramanujan’s startlingly brilliant and innovative research paved the way for many major breakthroughs in number theory over the past century.

This is an indication of the prescience and genius of Ramanujan’s work, confirming Hardy’s description of him as having “profound and invincible originality”.

Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com

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