At the age of 19, Ramanujan found himself very poor with no job. However, this did not stop Ramanujan from trying to pursue a career in math. While trying to look for any job at this point, Ramanujan's mother had arranged a marriage for him to a 10 year old girl, at this time he was about 21 years old. In spite of luck, after marriage Ramanujan found himself talking to an official named, Ramaswamy Aiyer who was also a mathematician. Ramanujan had showed his findings for the first time to someone else who appreciated math, Aiyer was immediately impressed and wanted to help Ramanujan publish his findings. In 1911 Aiyer had finally helped him publish his first piece of work on Bernoulli numbers in the Journal of the Indian Mathematical Society. A team of people were on Ramanujan's side trying to help him succeed. By this time, Ramanujan had written a letter and had sent it off to many British mathematicians. The only one to take an interest in his letter was Godfrey Harold Hardy from the University of Cambridge. Ramanujan was now 25, and did not know that he had impressed Hardy to the extent that he did.
Finally in 1914, Ramanujan found himself traveling to England where Hardy was awaiting to work with him. it only took two years for Ramanujan to be recognized for his contributions and was given an award. Although his success finally had come through, Ramanujan's health was not in good shape. In the year of 1917, Ramanujan was diagnosed with Tuberculosis. The disease itself forced Ramanujan to receive a lot of bed rest. However, while in the hospital, Hardy and Ramanujan kept a great friendship. A ear later Ramanujan recovered enough to go back to India. In 1919, Ramanujan would pass way at the age of 32.
Contributions in Math
One of the greatest contributions that Ramanujan had dealt with was the Goldbach conjecture. The Goldbach conjecture states, the statement is "Every even integer greater that two is the sum of two primes." Even though the conjecture itself was never solved, Hardy and Ramanujan had showed that every larger integer could be written of at most 4 numbers. In addition to this discovery, Ramanujan was also trying to proof Fermat's last theorem. Fermat's Last Theorem states, "that no three positive integers \(a,b\) and \(c\) satisfy the equation \(a^n+b^n=c^n\) for any integer value of \(n\) greater than \(2\)." The neat thing that Ramanujan was able to do with this was find many near counter examples. In other words, Ramanujan was able to come up with counter examples that missed a cube by just one. One of the counterexamples include \(135^3+138^3=172^3-1\). We can see that these sort of examples will always have a \(+1\) or \(-1\) at the end which comes from \(\left(-1\right)^n\) in our generating function.