On a related note, there's a good in-depth answer to the question "What is it like to understand advanced mathematics?" here: http://www.quora.com/Mathematics/

On a related note, there's a good in-depth answer to the question "What is it like to understand advanced mathematics?" here: http://www.quora.com/Mathematics/What-is-it-like-to-understand-advanced-mathematics/answers/873950 http://www.quora.com/Mathematics/What-is-it-like-to-understa... I'm not a mathematician, but was a theoretical physicist for more than a decade, and the Quora article accords well with my experience in understanding mathematics. (Fairly) readable examples of some of the points made in the above article may be found in Terry Tao and Scott Aaronson's comments about how to think intuitively in high dimensions: http://mathoverflow.net/questions/25983/intuitive-crutches-for-higher-dimensional-thinking http://mathoverflow.net/questions/25983/intuitive-crutches-f...