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ADDICTIONS: February 25,2001

A passion for numbers

Kalyanalakshmy Bhanumurthy

Genius, passion and near-obsession seem inextricably linked. Be it music, mountaineering or mathematics. Numbers pervade our entire world and beyond, into realms of Time and Space. One might agree with the mathematician who said, "God made the integers and man made the rest". For persons whose relationship to numbers is basic to their lives, numbers constantly open up new vistas of knowledge. For them, mathematics was work and play. It was fun and fascination. At moments, it was anguish. They could not live without it, any more than they could without air.

Srinivasa Ramanujan was born on December 22, 1887, an answer to fervent prayers and therefore, a special child from the beginning. His mother was very ambitious for him, propelling him at every turn into achievement. She had total conviction about his genius and lived to see its fulfilment. The quiet child, sitting on the banks of the Cauvery would gaze at the stars at twilight and wonder about cosmic distances. Otherwise, he would sit on the pyol of his house in Kumbakonam, helping other children with their problems in arithmetic, or continue writing number patterns that floated into his mind. His "slate pencil" would be whittled down to half an inch in the course of an hour. His imagination had an easy flow.

By the time he was ten, his gift for numbers became apparent to his teachers. He was given a scholarship from the early years of school. His skills in making the school time-table juggling around with class periods, workloads and teachers' preferences were put to full use. For the youngsters, it was as easy as spinning a top.

The passion for mathematics was combined with indifference to other subjects. When he failed in English, his scholarship was withdrawn. In the face of what he deemed to be a humiliation, he ran away to Madras, where he tried to complete his college education. This time, it was Biology which crushed. The dissection of frogs, a requirement of the course, filled him with aversion. Predictably, he failed in the examination.

There were many who recognised his exceptional talent. Among these were Ramaswami Iyer, Seshu Iyer and Ramachandra Rao. Rao supported him for more than a year, but Ramanujan found it irksome to be living on his philanthropy. Fortunately in 1912, he was offered a clerical post at the Port Trust, on a salary of Rs. 30 a month. Narayana Iyer of the Port Trust supported his mathematical work and made paper available for his equations. A significant fringe benefit!

Around this time, he started publishing papers in the Journal of the Indian Mathematical Society. Ramanujan also wrote a letter to G.H. Hardy, a fellow of Trinity College, Cambridge. That letter, now a historic document, was the turning point in his career. For Hardy, the one great happiness in life was research in maths. His friendly association shines in the annals of mathematics. Hardy had developed a scale of mathematical ability on which he could place the mathematicians he knew. He assigned himself a modest 25, and Littlewood a 30. To the eminent David Hilbert, he assigned an 80 and to Ramanujan, he gave a 100.

Ramanujan sometimes worked for 30 hours at a stretch and then slept for 20. His erratic routines played havoc with his health and equanimity, despite Hardy's nurturing him with great sensitivity. At one time, when his application for a fellowship from Trinity was turned down, he lay down on a railway track near London, luckily to be saved. Battling with tuberculosis, food shortages of war time and uncongenial sanatoria, Ramanujan decided to return to India in 1919. He was given a hero's welcome.

His health continued to cause concern and he knew he was racing against time. With his wife devotedly nursing him, he moved from one house to another in Kodumudi, Kumbakonam and Madras, still restless. He kept his precious notebooks next to his pillow. He worked on Theta Functions and made the discovery of Mock Theta Functions, a creative surge that was to be his flicker. He worked on his ideas to the end, which came on April 26, 1920. Kanigel, one of the Ramanujan's biographers gave him the apt epithet, "the man who knew Infinity".

Andrew Wiles, who solved Fermat's Last Theorem, has, in contemporary times, blazed a trail of glory. Andrew Wiles was born 66 years after Ramanujan, and in another continent. He also had a passion for numbers and he grew up near a river. But the comparison ends there. Ramanujan was like a tumultuous cataract now splashing, now flooding, now eddying, uneven in flow and unpredictable in movement. Wiles was serene as the river Cam itself.

Andrew Wiles was born in Cambridge on April 11, 1953, son of the local pastor. By the time he was ten, he showed a marked interest in solving mathematical puzzles, conundrums and riddles. One day, in the local library of Milton Road, ten-year-old Andrew came upon a book, The Last Problem by E.T. Bell. There was no solution at the end of the book. It caught his fancy and from that moment, he had a special relationship with the problem stated and left unsolved by Fermat.

As a research student in Cambridge, Wiles was already identified as one of the most promising in the discipline. His chosen topic of research was the theory of Elliptic Curves, a study which later proved invaluable. Later, he studied the history of attempted solutions to the problem, including those of Euler and Kummer. He realised that mathematics was not "a careful march down a well cleared highway, but a journey into a strange wilderness."

After his doctoral work, he moved to Princeton, New Jersey where he is a professor. He worked in solitude. Intense thinking, endless calculations! Maybe a new insight when he was relaxing. He would spend hours in his study, going down to the lake for an occasional walk. A break he enjoyed was story telling with his children. After seven years of relentless pursuit, Wiles had arrived at what seemed to be the solution. At the end of his third lecture at the Newton Institute in Cambridge, on June 23, 1993, Wiles announced his proof of the FLT. The atmosphere was charged and the 200 strong gathering of mathematicians gave him a standing ovation. It was a historic moment.

The drama did not end there. When Wiles' proofs were ready by experts in the following year, a flaw was discovered. Andrew Wiles was brought back to earth with a thud. Was his exultation premature? He went back to the isolation of his attic and wrested with the problem. On September 19, 1994, he had an incredible revelation about combining two methods. In his own words, "It was so indescribably beautiful, so simple and so elegant." This exciting insight led him to complete the proof. His wife, Nada had a birthday in October and he gave her the best present she could ever receive: the completed manuscript.

For this intellectual triumph, Wiles was on the headlines of newspapers round the world. He received the Wolfskehl prize at Gottingen in 1997. He signed in the "Golden Book" in Fermat's town of Beaumont. Others honours and awards followed and he was feted everywhere he went.

Knowledge has no frontiers. The notebooks of Ramanujan continue to be a source of inspiration and research everywhere. His vast vision led him to state that "the Universe is a product of Zero and Infinity." Wiles' extraordinary work will doubtless create new vistas of study. Ramanujan and Wiles were two giants in the world of mathematics, so different from each other, but sharing the passion for numbers.

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