This post is inquiring about the process of how one obtains high level math knowledge .How does one produce papers such as this at 24-27 yrs old? http://books.google.com/books?id=c8...&sa=X&ei=8qXkUZWxEeH9iwLx2YFQ&ved=0CGsQ6AEwCA I remember taking calculus at 17 or so and reading some books on math but nothing, including my homework even approached anything like this. Is it just 5 years of constant study or do these people learn everything really fast while in HS and enter college with graduate level of knowledge? How does one go about writing mathematics in this type of rigor? how does one make the jump from just fooling around to producing serious, PHD quality, respectable math like the example given? There seems to be a huge chasm between high-level math in papers versus what is contained in most college courses and textbooks.