Is math 55 really the hardest undergrad math class in the world? Has anyone here taken it?
Well, nobody has taken every undergraduate math class in the world, so nobody can say. Is it harder than Stanford’s Math 51? Probably at the same level.
From friends that have taken it, it is a ton of work, and the math department claims that it is about 24-40 hours of HW per week. It’s probably closer to 20, which is still a lot. Every year the class starts out with about 60-70 students, but quickly settles into about 20.
The challenge is that the course content varies according to who is teaching it in a given year, as it is not the same professor year-to-year. This year it is being taught by Noam Elkies, who does have a reputation for knowing his stuff.
For giggles, you can look at last year’s problem sets.
http://www.math.harvard.edu/~elkies/M55a.16/index.html
http://www.math.harvard.edu/~elkies/M55b.16/index.html
I’d posit than any student who is taking/has taken Math 55 does not have time to hang out here. 
Actually, if you search back a few years ago, there are a few threads in which some posters who took Math 55 (at least for a while) and a poster who took the University of Chicago’s version of math prodigy boot camp, called “Honors Analysis,” compared assignments, texts, and teaching methods, and debated which was the more challenging course. I think I remember the Chicago poster was called furiku, or something like that, and graduated from college in 2011. The experience in both classes reflected in those threads is now about a decade old.
*phuriku
The time spent on the psets most likely isn’t exaggerated. My D’s boyfriend and roommate are taking Honors Analysis at Princeton and probably spend 20 hours+ a week on it. The boyfriend is also taking the Integrated Science Curriculum and that’s another 20-40 hours a week. He’s not getting much sleep. I met another of my D’s friends in her dorm and I think he takes Accelerated Honors Analysis and he’s from Boston and apparently took classes at Harvard in high school. If I see him again I’ll ask him about Math 55 and if he has any thoughts. My D goes to him for help if she has questions on her math psets - she’s only taking the advanced MV Calc which is still a lot of hours of homework.
By the way, based on my limited understanding Math 55 at Harvard is practically in a different universe from Stanford’s Math 51. They’re not at the same level at all.
About 400 students per year take Math 51 at Stanford. It’s pitched as a one-quarter practical course to give students an accelerated background in linear algebra and multivariable calculus so they can use them in social science, physical science, and life science classes. It is specifically non-proof-based. Students whose focus is theoretical mathematics take a different series of course.
After its first few weeks, I believe Math 55 usually boils down to 15-20 students, and fewer than that take its second semester. Most of them – and most of the people who sample the class and drop out – already have considerable background in multivariable calculus and linear algebra. Math 55 is entirely theoretical and proof-based; its informal function seems to be to get a handful of advanced freshmen through what a normal four-year college math major would entail. There probably aren’t 400 people in the country in any cohort who could take and pass Math 55.
Math 55 is a controversial course, pedagogically. Harvard has it and Chicago has something like it; I thought Stanford, MIT and Princeton didn’t, because they prefer that advanced students take more focused, less intense courses in the normal progression for the major. But it looks like since I thought that Princeton has come up with “Accelerated Honors Analysis,” which sounds a lot like Math 55. Stanford still seems not to have a course that functions as a boot camp/elite credential for math prodigies.
Math 55 has some issues.
Five of the last ten semesters (50%) have seen no women enrolled in Math 55. Over the past 5 years, less than 7% (11/163) of the students enrolled in Math 55 have been women.
The math department at Harvard has never had a tenured female professor.
Math 55 has been criticized for not taking the time to properly cover some areas of math. For example after taking math 55 you can not take the undergraduate version of complex variables (math 113). Yet many of the former 55ers feel unprepared when they try and take the graduate version of complex variables.
There is really no substitute for taking your time and learning math thoroughly.
“The most profound contributions to mathematics are often made by tortoises rather than hares.”
— William Timothy Gowers
“I tend to be slower than most mathematicians to understand an argument.”
— Stephen Smale
“It’s true that I’m not good at solving problems. For example, I would never be good in the Math Olympiad. There, speed counts and I am certainly not a speedy worker. That’s one pleasant thing in mathematics: it doesn’t matter how long it takes if the end result is a good theorem. Speed is an advantage, but it is not essential.”
— John Tate
Gowers and Smale were Fields medalists!
My bad. Obviously I’m not a Stanford student. I was simply trying (and failing) to come up with an analogy. Princeton’s 216/218 would have been a better example.
That is not the fault of Math 55, though. And the quoted statement is not quite correct; the math department currently has no female tenured professors. Although their track record of only ever having had one female tenured professor (Sophie Morel) is not a cause for celebration.
I stand corrected. Sophie Morel was there for two and half years.
From her own mouth
“As for being the only female research professor, I might not even have noticed if it had not been pointed it out to me so many times.”
She is at Princeton now. I wonder if she teaches the honors analysis class there.
JHS wrote:
Stanford does have a more advanced and theoretical/proof-based version of the 51-53 series, Math 61/62/63 (now divided into two “tracks”, one emphasizing continuous and the other discrete math):
http://exploredegrees.stanford.edu/schoolofhumanitiesandsciences/mathematics/
I have no idea how it compared to Math 55 at Harvard, but it is definitely a more theoretical and proof-based course, with probably far fewer students.
I went to Stanford over 3 decades ago; I had a fairly advanced math background in high school including Real and Complex Analysis, and when I started at Stanford I tried out the 60 series math classes. There were only about half a dozen students in the class. The professor kicked me out after the first week - he said I had way too much background, of the wrong kind. His approach seemed to be to take the absolute smartest theoretical math freshmen on campus and build their foundation from the ground up at an extremely high level, and I was probably both not quite good enough and too influenced by prior background to fit what he wanted. Again, I have no idea how this compares to Math 55, but it was way more rigorous and theoretical than what I was used to, and at a totally different level than the upper-level “more focused, less intense” math courses that I subsequently took at Stanford.
Math 55 is where Putnam contestants go to play.