Tuesday 17 July 2012

Ramanujan



SRINIVASA RAMANUJAM
                               (1887-1920)

 Srinivas Ramanujam was a natural genius in mathematics. During a very short life span of 32 years, he did a vast amount of work in mathematics.
    He was born on 22nd December 1887 at Erode in a middle class family. He did his primary schooling at Kumbhakonam. His brilliance in Mathematics was apparent from his school days. In the high school he won many prizes for Mathematics. But he could not get admission in university due to his poor record in all other subjects. So he concentrated only on the study of pure Mathematics.
   In 1909 he got married to Janki Ammal. In 191 his first paper was published in the Indian Mathematical Society’s Journal. This paper was based on the study of Bernoulli’s numbers. He extensively studied G.S.Carr’s Synopsis of Elememtary Results in Pure Mathematics.
   He sent his papers to the Cambridge University in 1913. Srinivas did not have any formal college education. But he studied Mathematics from books which he borrowed from the libraries. In 1914 the University of Madras granted him a scholarship to study at the Trinity College, Cambridge. He produced many papers while studying there.
  Ramanujam was elected the fellow of the Royal Society of London. He was the first Indian to earn this honour. He got a degree of Bachelor of Science by Research.
  Although he was a genius, his outstanding work did not help him financially. But he was an acclaimed scientist world-wide.
  While in England, he fell ill in 1917. He did not recover completely  in spite of the best treatment. So he had to return back to India in 1919. This remarkable mathematician died on 26th April 1920.






SRINIVASA Ramanujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss. Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re- discovered Euler's identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant.Ramanujan received a scholarship to study at Government College in
Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself. In 1912– 1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge. Srinivasa died of illness, malnutrition, and possibly liver infection in 1920 at the age of 32.During his short lifetime, Ramanujan independently compiled
nearly 3900 results (mostly identities and equations). Most of his claims have now been proven correct, although a small number of these results were actually false and some were already known. He stated results that were both original and highly unconventional,
such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research. However, the mathematical mainstream has been rather slow in absorbing some of his major discoveries. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work. In Dec 2011, in recognition of his contribution to mathematics, the Government of India declared that Ramanujan's birthday (22 December) should be
celebrated every year as National Mathematics Day, and also declared 2012 the National Mathematical Year. Ramanujan has been described as a person with a somewhat shy and quiet disposition, a dignified man with pleasant manners. He lived a rather Spartan life while at Cambridge. Ramanujan's first Indian biographers describe him as rigorously orthodox. Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal.
He looked to her for inspiration in his work, and claimed to dream of blood drops that symbolized her male consort, Narasimha, after which he would receive visions of scrolls of complex mathematical content unfolding before his eyes. He often said, "An equation
for me has no meaning, unless it represents a thought of God." Hardy cites Ramanujan as remarking that all religions seemed equally true to him. Hardy further argued that Ramanujan's religiousness had been romanticised by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan's strict observance of vegetarianism. In mathematics, there is a distinction between having an insight and having a proof. Ramanujan's talent
suggested a plethora of formulae that could then be investigated in depth later. It is saithat Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a by-product, new directions of research were opened up.
Examples of the most interesting of these formulae include the intriguing infinite series for π. A common anecdote about Ramanujan relates to the number 1729. Hardy arrived
at Ramanujan's residence in a cab numbered 1729. Hardy commented that the number 1729 seemed to be uninteresting. Ramanujan is said to have stated on the spot that it was
actually a very interesting number mathematically, being the smallest natural number representable in two different ways as a sum of two positive cubes SRINIVASA Ramanujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to
mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss. Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re- discovered Euler's identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant.Ramanujan received a scholarship to study at Government College in
Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the
Accountant-General's office at the Madras Port Trust Office to support himself. In 1912– 1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge. Srinivasa died of illness, malnutrition, and possibly liver infection in 1920 at the age of 32.During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Most of his claims have now been proven correct, although a small number of these results were actually false and some were already known. He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research. However, the mathematical mainstream has been rather
slow in absorbing some of his major discoveries. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work. 
        In Dec 2011, in recognition of his contribution to mathematics,
the Government of India declared that Ramanujan's birthday (22 December) should be celebrated every year as National Mathematics Day, and also declared 2012 the National
Mathematical Year. Ramanujan has been described as a person with a somewhat shy and quiet disposition, a dignified man with pleasant manners. He lived a rather Spartan lifestyle at Cambridge. Ramanujan's first Indian biographers describe him as rigorouslyvorthodox. Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal.vHe looked to her for inspiration in his work, and claimed to dream of blood drops thatvsymbolised her male consort, Narasimha, after which he would receive visions of scrollsvof complex mathematical content unfolding before his eyes. He often said, "An equation for me has no meaning, unless it represents a thought of God." Hardy cites Ramanujan as remarking that all religions seemed equally true to him. Hardy further argued that Ramanujan's religiousness had been romanticized by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan's strict observance of vegetarianism. In mathematics,
there is a distinction between having an insight and having a proof. Ramanujan's talent suggested a plethora of formula that could then be investigated in depth later. It is said that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a by-product, new directions of research were opened up. Examples of the most interesting of these formula include the intriguing infinite series for π. A common anecdote about Ramanujan relates to the number 1729. Hardy arrived
at Ramanujan's residence in a cab numbered 1729. Hardy commented that the number 1729 seemed to be uninteresting. Ramanujan is said to have stated on the spot that it was actually a very interesting number mathematically, being the smallest natural number re presentable in two different ways as a sum of two positive cubes.

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