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<p>That is according to the Harvard math department and would be hard to prove (no pun intended)! MIT has 18.100B and 18.100C where the content is of the same level of difficulty as Math 55 at Harvard (and the drop-out rate just as high). It is also not unusual for MIT freshmen to take graduate level math classes which would be significantly harder than Math 55. </p>
<p>I would argue that 18.S34, an intense math problem solving seminar that MIT freshmen take and which is considered the ultimate bootcamp for the Putnam Mathematics Competition is inherently tougher from a competitive level standpoint. Most students are IMO and USAMO finalists. In the past decade, MIT students has taken around 40% of the Putnam Fellow Awards (top 5) as well as 40% of the Honorable Mentions (top 50).</p>