Srinivasa Ramanujan

Ramanujan
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Ramanujan

Srinivasa Aiyangar Ramanujan (Tamil pronunciation: srInivAsa aiyangAr rAmAnujan) (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. A child prodigy, he was largely self-taught in mathematics and never attended a university.

Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as π, prime numbers and partition function. Often, his formulas were stated without proof and were only later proven to be true.

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Life

Born in Erode, Tamil Nadu, India, by the age of twelve Ramanujan had mastered trigonometry so completely that he was inventing sophisticated theorems that astonished his teachers. In 1898 he entered the Town High School in Kumbakonam. He published several papers in Indian mathematical journals and later got the interests of leading European mathematicians in his work. A 1913 letter to G. H. Hardy contained a long list of theorems without proof. After some initial scepticism, Hardy replied and invited Ramanujan to England. As an orthodox Brahmin, Ramanujan consulted the astrological data for his journey, because his mother was horrified that he would lose his caste by traveling to foreign shores.

A fruitful collaboration, which Hardy described as "the one romantic incident in my life", soon developed. Hardy said of some of Ramanujan's formulas, which he could not understand, that "a single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true, for if they were not true, no one would have had the imagination to invent them." Hardy, a prominent mathematician in his own right stated in an interview by Paul Erdos, when asked what his greatest contribution to mathematics was, unhesitatingly replied that it was the discovery of Ramanujan.

Plagued by health problems all his life, Ramanujan's condition worsened in England, perhaps exacerbated the scarcity of vegetarian food during the First World War. He was also diagnosed with tuberculosis (Henderson, 1996) and a severe vitamin deficiency, though a 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver. This is also supported by the fact that Ramanujan spent time in Madras, a coastal city where the disease was widespread. It was a difficult to diagnose disease, but once diagnosed, was readily curable. (Berndt, 1998) He returned to India in 1919 and died soon after in Kumbakonam. His wife S. Janaki Ammal lived outside Chennai (formerly Madras) until her death in 1994. Janaki had been nine when they were married, a fairly common practice in India at the time. (Henderson, 1996)

The Ramanujan conjecture and its role

Although there are numerous statements that could bear the name Ramanujan conjecture, there is one in particular that was very influential on later work. That Ramanujan conjecture is an assertion on the size of the coefficients of the tau-function, a typical cusp form in the theory of modular forms. It was finally proved as a consequence of the proof of the Weil conjectures; the reduction step is complicated.

See also

Further Reading

  • Collected Papers of Srinivasa Ramanujan ISBN 0821820761
  • The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel ISBN 0671750615

References

  • An overview of Ramanujan's notebooks by Bruce C. Berndt, in Charlemagne and His Heritage: 1200 Years of Civilization and Science in Europe, Volume 2: Mathematical Arts, P. L. Butzer, H. Th. Jongen, and W. Oberschelp, editors, Brepols, Turnhout, 1998, pp. 119-146, (22 pg. pdf file (http://www.math.uiuc.edu/~berndt/articles/aachen.pdf))
  • Modern Mathematicians, Harry Henderson, Facts on File Inc., 1996

External links


de:Srinivasa Aiyangar Ramanujan eo:Srinivasa Aiyangar RAMANUJAN fr:Srinivasa Ramanujan is:Srinivasa Ramanujan nl:Srinivasa Aaiyangar Ramanujan ja:シュリニヴァーサ・ラマヌジャン fi:Ramanujan sv:Srinivasa Aaiyangar Ramanujan



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