I Visited the World’s Hardest Math Class

Hey y’all,

A few months ago, I visited Harvard to check out Math 55, which many call the “hardest undergraduate math course in the country.”

The lore surrounding the course runs deep. Some say that half the students drop out by the end of the first semester; others say that homework assignments can up to 60 hours per week.

This course is filed with brilliant math students from around the world—think science fair winners and olympiad medalists. Among its roster of notable alumni is none other than Bill Gates.

Having heard all this, I reached out to the Harvard Math Department to see if I could visit the class and document my experience.

…and to my surprise, they said yes.

Here are some of my biggest takeaways:

The Class Moves Fast

Math 55 covers four years of math in two semesters, and the course itself is actually two separate courses—Math 55a and Math 55b.

The official title of 55a is “Studies in Algebra and Group Theory,” and it covers “linear and abstract algebra with a bit of representation theory.”

The official title of 55b is “Studies in Real and Complex Analysis,“ and it covers “real and complex analysis with a bit of representation theory.”

What seems to make this course notoriously difficult isn’t the material itself—though it is definitely challenging—but the speed.

Succeeding in this course relies less on being a “genius” and more on having the sheer grit to keep up with the material. As former Math 55 professor Denis Auroux once said, “If you’re reasonably good at math, you love it, and you have lots of time to devote to it, then Math 55 is completely fine for you.”

This sentiment aligns with what I experienced. I talked to a student who said he had never solved a proof before enrolling yet was doing well in the course.

But how?

The Class is Collaborative

Yes, taking Math 55 is sort of a status symbol at Harvard, and some students (apparently) come to Harvard just to take the course.

But the course isn’t as cutthroat or ruthless as people make it out to be.

The course relies on collaboration—as does the field of mathematics more broadly. During my time in lecture, I noticed an open discussion between the professor and the students. They weren’t afraid to ask questions or be judged even as they were sitting among the brightest math minds at Harvard.

These students also come together to tackle the course’s infamous PSETs, which allegedly take 24-60 hours to complete.

The Rumors Are Outdated

I want you to think about that range—24-60 hours. Is the gap actually that wide?

After a few quick discussions, I discovered that most students spend around 15-20 hours per PSET, and once they throw in self-studying, they seem to spend around 30 hours a week on the course at max.

Also, the rumor that half the students drop out was true… nearly 50 years ago. But as of this academic year, only 3.3% of students have dropped out.

61 started in Math 55a, and 59 remain in Math 55b.

The dropout rate was higher in the past for two reasons:

1. The curriculum wasn’t standardized.

2. Students were less prepared.

For many years, the Math 55 professor would decide what they want to teach, but that’s been changing. Professor Harris and his colleagues have been working to standardize the syllabus to provide students with a clear roadmap of the course material.

Also, students nowadays are coming in with olympiad experience, summer camp experience, and even research experience that equips them to do well in the course. Back when college admissions was far, far less competitive, these opportunities didn’t exist, so students enrolling into Math 55 (especially in their freshman year) were jarred by the unfamiliar material.

Conclusion

Is Math 55 as challenging? Obviously.

Is it one of the hardest undergraduate math courses in the country? Probably.

But is it this ruthless, competitive course that people on the internet make it out to be? Absolutely not.

What did you think about this newsletter? What do you want to see in the future? Feel free to DM me on Instagram to let me know (@goharsguide).

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I’ll see you next week!

Best,
Gohar