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Srinivasa Ramanujan was a mathematical genius who made numerous contributions in the field, namely in number theory. The importance of his research continues to be studied and inspires mathematicians today.
Synopsis
Srinivasa Ramanujan was born in southern India in 1887. After demonstrating an intuitive grasp of mathematics at a young age, he began to develop his own theories and in 1911 published his first paper in India. Two years later Ramanujan began a correspondence with British mathematician G. H. Hardy that resulted in a five-year-long mentorship for Ramanujan at Cambridge, where he published numerous papers on his work and received a B.S. for research. His early work focused on infinite series and integrals, which extended into the remainder of his career. After contracting tuberculosis, Ramanujan returned to India, where he died in 1920 at 32 years of age.
Intuition
Srinivasa Ramanujan was born on December 22, 1887, in Erode, India, a small village in the southern part of the country. Shortly after this birth, his family moved to Kumbakonam, where his father worked as a clerk in a cloth shop. Ramanujan attended the local grammar school and high school, and early on demonstrated an affinity for mathematics.
When at age 15 he obtained an out-of-date book called A Synopsis of Elementary Results in Pure and Applied Mathematics, Ramanujan set about feverishly and obsessively studying its thousands of theorems before moving on to formulate many of his own. At the end of high school, the strength of his schoolwork was such that he obtained a scholarship to the Government College in Kumbakonam.
A Blessing and a Curse
But Ramanujan’s greatest asset proved also to be his Achilles heel. He lost his scholarship to both the Government College and later at the University of Madras because his devotion to math caused him to let his other courses fall by the wayside. With little in the way of prospects, in 1909 he sought government unemployment benefits.
Yet despite these setbacks, Ramanujan continued to make strides in his mathematical work, and in 1911 published a 17-page paper on Bernoulli numbers in the Journal of the Indian Mathematical Society. Seeking the help of members of the society, in 1912 Ramanujan was able to secure a low-level post as a shipping clerk with the Madras Port Trust, where he was able to make a living while building a reputation for himself as a gifted mathematician.
Cambridge
Around this time, Ramanujan had become aware of the work of British mathematician G. H. Hardy — who himself had been something of a young genius — with whom he began a correspondence in 1913 and shared some of his work. After initially thinking his letters a hoax, Hardy became convinced of Ramanujan’s brilliance and was able to secure him both a research scholarship at the University of Madras as well as a grant from Cambridge.
The following year, Hardy convinced Ramanujan to come study with him at Cambridge. During their subsequent five-year mentorship, Hardy provided the formal framework in which Ramanujan’s innate grasp of numbers could thrive, with Ramanujan publishing upwards of 20 papers on his own and more in collaboration with Hardy. Ramanujan was awarded a bachelor of sciences for research from Cambridge in 1916 and in 1918 became a member of the Royal Society of London
Doing the Math
"[Ramanujan] made many momentous contributions to mathematics especially number theory," states George E. Andrews, an Evan Pugh Professor of Mathematics at Pennsylvania State University. "Much of his work was done jointly with his benefactor and mentor, G. H. Hardy. Together they began the powerful "circle method" to provide an exact formula for p(n), the number of integer partitions of n. (e.g. p(5)=7 where the seven partitions are 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1). The circle method has played a major role in subsequent developments in analytic number theory. Ramanujan also discovered and proved that 5 always divides p(5n+4), 7 always divides p(7n+5) and 11 always divides p(11n+6). This discovery led to extensive advances in the theory of modular forms."
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Synopsis
Srinivasa Ramanujan was born in southern India in 1887. After demonstrating an intuitive grasp of mathematics at a young age, he began to develop his own theories and in 1911 published his first paper in India. Two years later Ramanujan began a correspondence with British mathematician G. H. Hardy that resulted in a five-year-long mentorship for Ramanujan at Cambridge, where he published numerous papers on his work and received a B.S. for research. His early work focused on infinite series and integrals, which extended into the remainder of his career. After contracting tuberculosis, Ramanujan returned to India, where he died in 1920 at 32 years of age.
Intuition
Srinivasa Ramanujan was born on December 22, 1887, in Erode, India, a small village in the southern part of the country. Shortly after this birth, his family moved to Kumbakonam, where his father worked as a clerk in a cloth shop. Ramanujan attended the local grammar school and high school, and early on demonstrated an affinity for mathematics.
When at age 15 he obtained an out-of-date book called A Synopsis of Elementary Results in Pure and Applied Mathematics, Ramanujan set about feverishly and obsessively studying its thousands of theorems before moving on to formulate many of his own. At the end of high school, the strength of his schoolwork was such that he obtained a scholarship to the Government College in Kumbakonam.
A Blessing and a Curse
But Ramanujan’s greatest asset proved also to be his Achilles heel. He lost his scholarship to both the Government College and later at the University of Madras because his devotion to math caused him to let his other courses fall by the wayside. With little in the way of prospects, in 1909 he sought government unemployment benefits.
Yet despite these setbacks, Ramanujan continued to make strides in his mathematical work, and in 1911 published a 17-page paper on Bernoulli numbers in the Journal of the Indian Mathematical Society. Seeking the help of members of the society, in 1912 Ramanujan was able to secure a low-level post as a shipping clerk with the Madras Port Trust, where he was able to make a living while building a reputation for himself as a gifted mathematician.
Cambridge
Around this time, Ramanujan had become aware of the work of British mathematician G. H. Hardy — who himself had been something of a young genius — with whom he began a correspondence in 1913 and shared some of his work. After initially thinking his letters a hoax, Hardy became convinced of Ramanujan’s brilliance and was able to secure him both a research scholarship at the University of Madras as well as a grant from Cambridge.
The following year, Hardy convinced Ramanujan to come study with him at Cambridge. During their subsequent five-year mentorship, Hardy provided the formal framework in which Ramanujan’s innate grasp of numbers could thrive, with Ramanujan publishing upwards of 20 papers on his own and more in collaboration with Hardy. Ramanujan was awarded a bachelor of sciences for research from Cambridge in 1916 and in 1918 became a member of the Royal Society of London
Doing the Math
"[Ramanujan] made many momentous contributions to mathematics especially number theory," states George E. Andrews, an Evan Pugh Professor of Mathematics at Pennsylvania State University. "Much of his work was done jointly with his benefactor and mentor, G. H. Hardy. Together they began the powerful "circle method" to provide an exact formula for p(n), the number of integer partitions of n. (e.g. p(5)=7 where the seven partitions are 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1). The circle method has played a major role in subsequent developments in analytic number theory. Ramanujan also discovered and proved that 5 always divides p(5n+4), 7 always divides p(7n+5) and 11 always divides p(11n+6). This discovery led to extensive advances in the theory of modular forms."
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1)Pythagoras (circa 570-495BC)
Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat beans.
2)Hypatia (cAD360-415)
Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis
Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her most valuable scientific legacy was her edited version of Euclid's The Elements, the most important Greek mathematical text, and one of the standard versions for centuries after her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs.
3)Girolamo Cardano (1501 -1576)
Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty
Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers.
4)Leonhard Euler (1707- 1783)
The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formulaeiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics.
5)Carl Friedrich Gauss (1777-1855)
Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death.
6)Georg Cantor (1845-1918)
Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns .
7)Paul Erdös (1913-1996)
Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him.
8)John Horton Conway (b1937)
The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status.
9)Grigori Perelman (b1966)
Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the cash. He had already turned down maths' most prestigious honour, the Fields Medal in 2006.
10)Terry Tao (b1975)
An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes, since the primes by then are more than 18 digits long.
Hope it helps you
Here's Ur Answer
1)Pythagoras (circa 570-495BC)
Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat beans.
2)Hypatia (cAD360-415)
Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis
Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her most valuable scientific legacy was her edited version of Euclid's The Elements, the most important Greek mathematical text, and one of the standard versions for centuries after her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs.
3)Girolamo Cardano (1501 -1576)
Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty
Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers.
4)Leonhard Euler (1707- 1783)
The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formulaeiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics.
5)Carl Friedrich Gauss (1777-1855)
Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death.
6)Georg Cantor (1845-1918)
Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns .
7)Paul Erdös (1913-1996)
Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him.
8)John Horton Conway (b1937)
The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status.
9)Grigori Perelman (b1966)
Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the cash. He had already turned down maths' most prestigious honour, the Fields Medal in 2006.
10)Terry Tao (b1975)
An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes, since the primes by then are more than 18 digits long.
Hope it helps you
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