Math 55

Math 55 is a two-semester long first-year undergraduate mathematics course at Harvard University, founded by Lynn Loomis and Shlomo Sternberg. The official titles of the course are Honors Abstract Algebra (Math 55a) and Honors Real and Complex Analysis (Math 55b). Previously, the official title was Honors Advanced Calculus and Linear Algebra. Some claim it is the most difficult undergraduate math course in the United States.

The Harvard University Department of Mathematics claims that "This [Math 55] is probably the most difficult undergraduate math class in the country". Formerly, students would begin the year in Math 25 (which was created in 1983 as a lower-level Math 55) and, after three weeks of point-set topology and special topics (for instance, in 1994, p-adic analysis was taught by Wilfried Schmid), students would take a quiz. As of 2012, students may choose to enroll in either Math 25 or Math 55 but are advised to "shop" both courses and have five weeks to decide on one. Depending on the professor teaching the class, the diagnostic exam may still be given after three weeks to help students with their decision.

In 1994, 89 students took the test given after three weeks: students scoring more than 50% on the quiz could enroll in Wilfried Schmid's Math 55 (15 students), students scoring between 10 and 50% could stay in Benedict Gross's Math 25 (55 students), and students scoring less than 10% were advised to enroll in a lower-level course such as Math 21, multivariate calculus (19 students).

In 1970, this demanding course covered almost four years worth of mathematics classes in two semesters, and therefore drew only the most dedicated students. In the class of 1970, only 20 of the 75 students who began the class finished it due to its difficulty. Similar drop-out rates were true for the class of 1976: "Seventy started it, 20 finished it, and only 10 understood it." and for the class of 2009: "[...] we had 51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester after the fifth Monday," said Scott Duke Kominers.

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