Check out the unofficial course description for Math 55 at Harvard’s math department web site (all emphases added):
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. 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.
The most difficult undergraduate math class in the country, taught by faculty whose teaching ability is not necessarily guaranteed, designed for freshmen but requiring several years of university level math experience? I detect a distinct amount of satisfaction from whomever wrote this.
The funny thing is, according to the article I referenced earlier, dozens of Harvard freshmen sign up for the course each year — some with no intention whatsoever of staying on in the course but just wanting to say they’d enrolled in the course and watch the real math people at work.