But I guarantee you only the most amazing and celebrated of individuals have self-taught themselves advanced mathematics and performed at the highest level of the art. The only one I can think of the modern era is http://en.wikipedia.org/wiki/Srinivasa_Ramanujan, who is essentially legendary for what he did.

The core issue is climbing the tower of knowledge of what has gone before requires deep investment and usually a guide until you attain a deep and broad knowledge. There is so much knowledge, we must leech off of the knowledge of those who have also done the studying and have more experience. It's a pain.