Saturday, 22 December 2012

The genius who continues to inspire research even after his death

He was Indian who loved numbers so much that he spent all his life doing them. He lived and died young but his contribution is so enormous that mankind still remembers him as a genius.
Born in a orthodox Brahmin family, he quickly took to mathematics like a duck to water. His progress in mathematics was so rapid that his teachers did not know what to do with him. On his part, this genius lost interest in all other subjects except mathematics.
He is none other than Srinivasa Ramanujam. He  was born on December 22, 1887 in his maternal grandfather’s house in Erode. After his birth, he spent his childhood in a house in Sarangapani Street in Kumbokanam.
His father was  K. Srinivasa Iyengar, a clerk in a sari shop and his  mother, Komalatammal, was a housewife who occasionally sang at a local temple.    
Little Ramanujum went to Kangayan Primary School just across his house on Sarangapani Street in Kumbokanam. This house is now a museum.  Ramanujam was a brilliant child but the teachers then did not know how to deal with him. Both his teachers and his parents soon realised that Ramanujam was no ordinary child.
Ramanujam’s tryst with mathematics began when he was just ten years old. He read a book on Advanced Trignometry by Sidney Luxton Loney (1860-1939) and mastered it (S. L. Loney, a British mathematician, has written several books on trigonometry, including the one called Plane trigonometry).
His interest in trignomeotry led him to discover his own theorems. Moreover, he discovered Euler’s identity independently. At school he was brilliant in mathematics. By 17, he had conducted his own research on Bernoulli numbers (The Bernoulli numbers were discovered by a Swiss mathematician Jakob Bernoulli, after whom they are named. Bernolli is a sequence of  rational numbers in relation to the number theory) and Euler-Mascheroni Constant (The Bernoulli numbers appear in the Taylor series expansions of the tangent and hyperbolic tangent functions, in formulas for the sum of powers of the first positive integers, in the Euler- Mascheroni formula and in expressions for certain values of the Riemann Zeta functions-this is a function of complex variables that analytically continues the sum of  the infinite series).
When still in school, one of his teachers (others say it was a friend) in 1903 gave him a library book on maths by a British mathematician George  Shoobridge Carr with 5,000 equations, hoping that this would satiate the child prodigy’s appetite for numbers.  
The book, called Synopsis of Pure Mathematics (1880), opened a Pandora’s Box for the teenaged Ramanujam.
Ramanujam learnt about religion, Shastras and Puranas from his mother with whom he was close. He also learnt singing from her.
He passed his primary school examinations in 1897 with Arithematic, English, Tamil and geography as his subjects. He then joined the higher secondary school (Town High School) where he came across mathematics.
By 1904, Ramanajum began his own research. He began filling notebooks with his own equations and sums.
None understood them and he did not understand who others could not understand his equations. His interest in mathematics was so deep that he neglected other subjects. His college asked him to leave.
Meanwhile, his mother had arranged his marriage with nine-year-old Janaki. He married on July 14, 1909.  He then decided to go to Madras which then was the biggest city in south. He hoped that someone in this city would be able to understand and appreciate his equations. He took his notebooks with him.   
Even in Madras, none could understand the equations or make head and tail about them. Ramanujam then took to writing letters to mathematicians and one of them reached G. H. Hardy in Cambridge, England.
It was left to Hardy (1887-1947 ) to recognize this genius and call him to England. Now began one of mankind’s most famous collaborations-Ramanujam the genius and Hardy the reformer came up with a formula on integer partitions known as the Hardy–Ramanujan asymptotic formula.
This formula has been applied in physics to find quantum partition functions of atomic nuclei (first used by Niels Bohr) and to derive thermodynamic functions of non-interacting Bose-Einstein systems.
Unfortunately, this collaboration was cut short when Ramanujam contacted liver infection in 1919 and died in Kumbokanam in 1920, aged 32. By then, Ramanujam had left enough of his mathematical genius for generations to pore over. His wife, Janaki shifted to Bombay but returned to Madras in 1950 where she lived till she died in 1984.
He has to his credit over 3900 independently compiled equations and results and some of them are Ramanujan prime and the Ramanujan theta functions. These results have continued to inspire further research.
If Ramanujan's 1916 paper on modular forms created a sensation in the Western world, his last letter to Hardy, written literally from his deathbed in 1920,  on the functions of  “mock theta,” is now creating waves.
Mathematicians have ignored Ramanujan's theory of mock theta as he had not given any specific definition of it. However, he has  listed 17 protypical examples of these new functions. As there was no theory on these functions, the mock theta theory was largely ignored.
It was only in 2002 that the unifying conceptual framework of mock theta was discovered  by  Sanders Pieter Zwegers, a Dutch mathematician, in his doctoral theses. He made a connection between Maass forms (This is a function on the upper half plane that transforms like amodular form but need not be holomorphic. They were first studied by Hans Maass, a German mathematician, in 1949) and Ramanujam’s mock theta function in 2002.
Ramanujam was born on December 22 and the blog takes a bow to this great mathematician who has continued to inspire awe and admiration not only among the mathematical community but all of mankind.

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