Ramanujan(The Great Mathematician India ever produced )
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When at age 15 he obtained an out-of-date book called A Synopsis of Elementary Results in Pure and Applied Mathematics, Ramanujan set about feverishly and obsessively studying its thousands of theorems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 He lost his scholarship to both the Government College and later at the University of Madras because he was so much devoted to maths that he had failed in all other subjects.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.
Of Ramanujan's published papers — 37 in total — professor Bruce C. Berndt reveals that "a huge portion of his work was left behind in three notebooks and a 'lost' notebook. These notebooks contain approximately 4000 claims, all without proofs. Most of these claims have now been proved, and like his published work, continue to inspire modern-day mathematics."
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