Creativity vs. Rigor

In The Man Who Knew Infinity, the conflict between creativity and mathematical rigor arises again and again. From Ramanujan's first letter on we are aware of Ramanujan's sparkling and original mathematical creativity. Many of the theorems he sent Hardy were true and original, but they lacked the rigorous proofs that mathematicians require traditionally. Hardy replied to Ramanujan's first letter that proposing the theorems was not enough and he needed to actually prove them. Hardy was a mathematician that prized rigor and proof above all else, while it was clear that Ramanujan was best when he was speculating and creating theorems that would be proved by others later. In fact, many of the theorems that Ramanujan developed but did not prove were later used or proved by other mathematicians. One question that arises is to what extent was Ramanujan helped or hindered by his encounter with Hardy...