St. John's graduate here. It looks like that list includes a lot of what we read in "lab" class mixed in with what we read in math class. Freshman math was almost entirely the study of Euclid and Nicomachus.
I got a Master's degree from St. Johns liberal arts program in my 50s, in part to complement a Master's degree in computer science from three decades earlier, together to help me be a better teacher of high school computing.
For me, the three-decade interval gave me work and life experience which prepared me to read and discuss the Great Books. (The graduate program's list is similar to the undergraduate list, if a bit shorter.) The authors and works we read at St. Johns come from a wide range of contexts with different assumptions than ours, which made them both such a challenge and a reward to study.
There are other "Great Books" programs, including The Catherine Project, https://catherineproject.org/, which give opportunities to read and discuss many of these important works.
I went to St. John's for a year and the math curriculum was the high point by far.
I didn't read the OP and can't vouch for it. the curriculum I got was almost entirely Euclid, plus a little bit of Greek stuff about arcs and sections, which I imagine was Nicomachus per the above comment, and there may have been some stuff about astronomy as well.
but reading Euclid, and doing an entire year of math that doesn't even have numbers until the very end, which was early number theory: just incredible.
I got bored, though, and the later years of the curriculum skew very hard towards European philosophers. the longer you stay there, the more you become justified in summarizing it as a philosophy degree for the sake of convenience.
That's an extremely complicated question for me. I'll talk about each of the classes and offer what thoughts I can:
Math -- without math class at St. Johns I don't think I'd have ever thought I could be a programmer, much less that I could learn it on my own from books and online self-study. I still don't know much about math-as-math, but having a class dedicated to studying proofs and formal logic in various forms and communicating that to a group has been extremely valuable to me in my professional life. So I'm somewhat of a patriot for the math program.
That said, I think the poster in this thread who argues it's "a bad way to learn math" is correct. The St. John's program was founded in 1937, and, let's face it, the world of math and science is different now. If you sat me down next to a math major and made both us do a math test, they'd massacre me.
I'm more critical of the lab program. It felt like a complicated review of high school physics, chemistry, and biology and it was the area where the "amateur" nature of the teaching often hurt, rather than enhanced, the lesson. My thoughts about "the world's moved on since 1937" are even more acute related to lab. I don't feel I was very literate in science after I graduated beyond being able to talk about the Maxwell equations or relativity with some confidence.
Language class is a mixed bag. It's meant to support seminar by giving you access to Greek (and in junior and senior year, French) so that you can dig into some of the original sources. I enjoyed and was good at it -- but it's two years of college French that may make you able to read French literature but unable to order a meal in Paris.
When it comes to the seminar class, I enthusiastically endorse the St. John's method. I don't think there is a better way to read philosophy, history, literature, politics, etc.
Unrelated to the subjects themselves: at the very least, you're spending four years with roughly the same class of <100 people, reading the same texts, doing the same intellectual work, exposing your thoughts in class, living in the same area, eating in the same dining hall. That kind of -- let's call it intimacy -- means you're going to make some pretty deep friendships and rivalries and learn some social skills about getting on in group settings.
Would I recommend it? It's not for everyone. For people who don't need their hand held and who like the idea of reading and talking about a bunch of important books that discuss a lot of important questions in life, I think it's very right. For people who want to prepare for a specific technical career, or who are very shy, or who are not intellectuals by nature, I don't think it's right at all.
