There is no best mathematician, just like there is no best politician, musician or writer. Each has a unique set of abilities and aspirations that cannot be neatly lined up on a linear scale.
For instance, the mystical vegetarian sage Pythagoras became the most famous Greek mathematician because of a theorem that he proved about right-angled triangles. Yet, he was a much more fascinating character than just that. He was a leader of a community that worshipped numbers for their spiritual qualities and elevated the concept of numbers to be the essence of the world.
The same could be said about the Indian mathematician Ramanujan. His story, complete with dramatized tales of receiving theorems in dreams from a goddess, is far more interesting than just his mathematical achievements.
