If this is the wrong forum for this, I apologize. I tried to narrow this question to the right section. I somehow ended up on a Harvard undergraduate maths webpage for incoming freshman. The first two courses I read were pretty gnarly but I have read enough posts on this website throughout the years that I have become familiar with the kinds of people who would excel in these courses out of high school. However, the third course that I read sounded unreal. I was curious if anyone has taken this course and what it was like? I can't fathom the type of people who are this advanced at mathematics by the time they are a freshman. Granted, I was never talented in maths (I always have had to work hard to do well) but I can abstract my experience far enough out that I can imagine how/why more talented people that I have met are better at solving problems. Mathwonk: If you happen to read this post, let me know if this is the kind of course you took. I have read some of your anecdotes and distinctly recall you discussing how insanely difficult your freshman math course was (using Spivak I believe). I have always been curious. http://www.math.harvard.edu/pamphlets/freshmenguide.html "This is probably the most difficult undergraduate math class in the country; a variety of advanced topics in mathematics are covered, and problem sets ask students to prove many fundamental theorems of analysis and linear algebra. Class meets three hours per week, plus one hour of section, and problem sets can take anywhere from 24 to 60 hours to complete.1 This class is usually small and taught by a well-established and prominent member of the faculty whose teaching ability can vary from year to year. A thorough knowledge of multivariable calculus and linear algebra is almost absolutely required, and any other prior knowledge can only help. Students who benefit the most from this class have taken substantial amounts of advanced mathematics and are fairly fluent in the writing of proofs. Due to the necessity of working in groups and the extensive amount of time spent working together, students usually meet some of their best friends in this class. The difficulty of this class varies with the professor, but the class often contains former members of the International Math Olympiad teams, and in any event, it is designed for people with some years of university level mathematical experience. In order to challenge all students in the class, the professor can opt to make the class very, very difficult. You should take this class if one or more of these describes you: You are fairly certain that you want to be a math concentrator and want to be challenged to your limit. You have a solid base in advanced mathematics and are very comfortable with proofs and rigorous arguments. You want math to be your most important class." 1This is what really stood out. Another Question: I have always been curious what the experience is like to be able to connect so many seemingly disconnected and generalized concepts. Are you able to follow the threads of objects and interactions and sort of watch it emerge into a connected, unified, network of inner-reality? I mean, when your mind is that advanced mathematically, is the mathematical world you experience in your mind far more interactive than the average person? Is it possible to even describe?