a four digit no: abab-baba where a>b
gives9tothepowera-b9tothepowera-b.
copyright sahalsajjad
copyright sahalsajjad
Sunday, 3 July 2011
Saturday, 2 July 2011
sreenivasa ramanujam
  This is a remarkable story of perhaps the greatest mathematician who has ever lived. What makes this story compelling is that Srinivasa Ramanujan, who was born in India in 1887 and lived to only 33, is a person largely unknown outside the world of mathematics. But his short life's work will amaze you! Without a doubt, Ramanujan was a genius, ranking with Isaac Newton, Albert Einstein, and a few other great mathematicians of the past two centuries. His story is unique in the history of scientific inquiry, yet you probably have never heard of him or what he accomplished. Here is his story. Srinivasa Ramanujan was born in 1887 near Madras, in India. India was largely a poor country, and Ramanujan's family could not afford to educate him. He had no library of books, or other resource material, and was unaware of the centuries of mathematical ideas and discoveries which had preceeded his birth. The only exposure he had to modern Western mathematics was one small, obscure book of mathematics. Nevertheless, as a small child he became fascinated with numbers and mathematical ideas, and by the age of ten, it was evident that he had great gifts. On his own, he rediscovered Euler's identity relating trigonometric functions and exponentials. Using the obscure theorems in his one small mathematics book as a starting point, he developed his ownformulas. He was able to win a scholarship to high school, but found that he was already well beyond what was being taught, and dropped out. Eventually he landed a low-paying clerk's job which didn't demand too much of his time, and began to devote himself to exploring mathematical ideas. Without any awareness of what had already been discovered by European mathematicians, he re-derived many of the previous century's discoveries completely on his own. What hundreds of other mathematicians had contributed to the field during the previous hundred years, he discovered on his own, all by himself . (Tragically, much of his short life was spent rediscovering mathematics that was already known).  Ramanujan kept a record of his ideas in a set of notebooks, and some of these ideas he sent in a letter to a respected mathematician in England, Godfrey Hardy. Hardy at first was tempted to throw away the letter, because the ideas it contained were seemingly just a collection of already well-known mathematical theorems. However, when he eventually took a closer look at Ramanujan's letter, he realized that these ideas had been developed by the young mathematician completely on his own, without any mathematical training. More importantly, he discovered that Ramanujan had included 120 theorems that were completely unknown to Western mathematicians, and Hardy had never seen anything like them. Some of them he couldn't even understand.Hardy now recognized the genius of Ramanujan, and arranged for him to come to England to study at prestigious Cambridge University. There the young mathematician was finally able to work with others and share their ideas. Ramanujan was awarded a B.A. Degree in 1916, was elected a Fellow of the Royal Society, in February, 1918, and was also elected to a Cambridge Trinity College Fellowship, in October, 1918. In these three or four short years, between 1914 and 1918, he produced an astounding number of new theorems, filling more notebooks with his work. His approach to mathematical ideas was different than other mathematicians; he discovered new theorems in a completely incomprehensible manner. Ramanujan often said that his ideas came to him in his dreams, which he then wrote down. After an intense three years of amazing work, Ramanujan sadly became ill of tuberculosis, and died, at the young age of 33. But he continued working right up until the end, and eventually left behind three volumes of his notes (and a fourth, which was only discovered in 1976), containing more than 4000 formulas, some of which had never been seen before, and which would represent a lifetime of work for any other mathematician. Frustratingly, Ramanujan did not describe his work in his notes, nor did he provide proofs for his theorems. As a result, his writings remain a fascinating but largely undeveloped source of new ideas, which mathematicians are still trying to decipher. Many of his theorems and ideas have become valuable new tools in various branches of both mathematics and physics; his description of modular functions is one of the strangest ideas ever to be proposed in mathematics, yet has been found to be useful in the study of symmetry in particle physics only recently. Unquestionably, Srinivasa Ramanujan was a most amazing mathematician, and truly a genius. The great tragedy is that he was able to devote so little of his short life to the study of new mathematics. What might he have accomplished had he lived? |
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