Srinivasa Ramanujan 1887 - 1920 Considered the greatest mathematician of all time. He was born into extreme poverty in India and had virtually no formal training but made incredible contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. His work was so advanced and cutting edge that no one could understand it until G.H. Hardy of Cambridge University reached out to Ramanujan and brought him to England. At the age of 31 he was awarded Fellow of the Royal Society, only the second Indian to receive the honor. He died one year later in India. (more below)
By the age of 11, Ramanujan had pretty well burned through all the math and equations he could get his hands on in his hometown of Kumbakonam in southeast India. When he was 16 a friend got him a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics, a compilation of over 5,000 theorems by G.S. Carr. This was the entryway into his genius as Ramanujan exploded with ideas from this point forward. Most of the people around him rarely understood him but were in respectful awe. He graduated from secondary school with the highest honors in mathematics and received a scholarship to study at Government Arts College. But since he was unable to focus on anything other than mathematics, he quickly lost his scholarship. He then ran away from home and later enrolled in Pachaiyappa College in Madras. Though he did exceedingly well in mathematics here - it was a repeat of before as he had no interest in any other subject and failed his Fellow of Arts exam. He left and began studying advanced mathematics independently but was so poor that he was often at the brink of starvation.
In 1910 after meeting the now 23-year-old Ramanujan, Professor Ramaswami of the Indian Mathematical Society in Madras got him a job as a researcher at the University of Madras. At about this time Ramanujan married a girl who was only ten years old and had been selected for him by his mother. Also during this period, he got very ill but thanks to free surgery volunteered by a sympathetic doctor he got better.
A short time later Ramanujan was introduced to Ramachandra Rao, secretary of the Indian Mathematical Society where he hoped to get a job as a clerk. But upon reviewing Ramanujan's work and equations Rao concluded that he was a fraud. However, after some months Rao gave Ramanujan another chance and after listening to Ramanujan discuss such advanced topics such as elliptic integrals, hypergeometric series, and his theory of divergent series, he ultimately believed in Ramanujan's brilliance. Rao gave him a job and additional financial support so that he could continue his research. A short time later he got his first work published by the Indian Mathematical Society. He posed a problem that no one could answer and so eventually Ramanujan himself answered it. At his job, Ramanujan was able to complete his work so quickly that he had plenty of time to pursue his own higher mathematics and his superiors endorsed this behavior.
With the help of his superiors, Ramanujan's work was introduced to some of England's leading mathematicians but was quickly turned down. Then G.H. Hardy of the University of Cambridge looked at 9 pages of his equations. While at first, he thought they must be fraudulent, he nevertheless could not stop thinking about them and subsequently realized that some of the equations, "defeated me completely; I had never seen anything in the least like them before." Ultimately this led to Hardy inviting Ramanujan to Cambridge but amazingly Ramanujan turned down the offer, mainly because his mother would not let him go. Eventually, though she said God told her not to hold back his natural calling and he went.
Ramanujan slowly became a star at Cambridge and soon eclipsed the work of all around him. He gave all the credit for his genius to his family goddess, Mahalakshmi of Namakkal, who he felt was channeled through him with vivid images in numbers an equations.
As for his place in the world of Mathematics, why not use Hardy's personal ratings of mathematicians. On a scale from 0 to 100, Hardy gave himself a score of 25, J. E. Littlewood 30, David Hilbert 80 and Ramanujan 100. Not too shabby!
There is a wonderful movie starring Dov Patel (Slumdog Millionaire) as Ramanujan and Jeremy Irons as Hardy called, The Man Who Knew Infinity: A Life of the Genius Ramanujan. Highly recommended!
Film Link - https://www.youtube.com/watch?v=QqRnkFXuMmo