|Hardy (l) and Ramanujan (r).|
While in school Ramanujan spent more time on his own mathematics than on what he had to learn for his mathematics exams. As a result he was not drilled in doing proofs but doing mathematical research became natural to him.
Many schools include a research project as part of the graduation requirements for their mathematics majors. But most students are at a loss to create their own research questions, leaving this task to their advisors. It would be better if the student came up with their own research question that involved significant mathematical investigation and the creation of original mathematics. This is a daunting task: most graduate students are unable to do this, and rely on their advisors to frame a suitable area for investigation. The task is further complicated by the fact that many questions relating to undergraduate mathematics have “already been solved,” while many of the unsolved questions require so much specialized background to understand or so much existing research to review that the preparation needed to tackle the problem is itself a major project. - Jeff Suzuki in "But How Do I Do Mathematical Research?” on MAA website.
... the intensity of his interest in mathematics led him to pay scant attention to the other subjects in which he was obliged to show some facility. ... On each occasion, his interest in his own mathematical researches was so all consuming that he neglected his more quotidian studies, with the result that he failed his examinations and lost his scholarships. p118 ...no wonder he doesn't understand how to do a proof! p125 - The Indian Clerk
Ramanujan got -kicked out- of all schools he attended. Not fit for mathematics.
In the early 1900s, long before internet, good math books were rare in India or too expensive for Ramanujan. He learned his math from an encyclopedia type of collection of formulas and theorems. He must have re-invented the math that was not in that book because when he came to England he knew more or as much as Hardy, the leading Number Theorist of that time, but -in a different way-.
Long before Ramanujan arrived in England he was called the Indian genius. What is a 'genius' anyway? Newton was a 'genius'... Why didn't Newton share his invention of Calculus for such a long time? I suppose because ( knowledge ) power corrupts. Thank God Leibniz ( and others... ) independently invented Calculus around the same time. Science is for humanity not for the individual ( company ).
Ramanujan told ( to Eric and Alice Neville while they were interviewing him in Madras ) that his inventions were sent to him by the Goddess Namagiri in his sleep. Goddess?!, Red Alert! Stop.
There are two options here. Ramanujan's story about the Goddess Namagiri is true, or Ramanujan must have found a powerful method to do mathematical research of which he had no intention of sharing, like Newton, who used his then secret, Calculus to come with all sorts of amazing results. To declare someone a genius is giving up the search for his methods. How did Ramanujan do it? It's not in Ramanujan's notebooks let alone in Leavitt's book. Yet I tend to believe that if we want to come any closer to the Source of mathematics it is through Ramanujan.