Perhaps I don't understand what "The information presented is for illustration purposes only and may not reflect the current reading list" means, and why one would link that page anyway.
Word problems are the last edifice of natural philosophy in the high school mathematics curriculum and there’s constant pressure to remove those as well.
If "thinking mathematically" is the actual, vital part of that education, for most students, I have some doubts that a classics-based approach is any worse than the modern kind. Maybe better, except for a small slice of students who will continue to engage with advanced mathematics after they finish undergrad and do need the modern version.
So maybe it's not a bad thing that people graduate from College are required to take a few algebra and stats classes when they're ostensibly running the show at large corporations and in various levels of Government.
Kinda had to gently remind them that the physics they knew wouldn’t help them with ontological problems like “what is an object?” but once they got over that hurdle everything was pretty much fine.
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 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.
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.
As someone who has learned and taught a lot of math, I agree with that claim.
On the third hand, reading Newton is a really bad way to learn calculus; the college uses a lab manual which more closely resembles a modern calculus course.
I doubt the distinction matters at all for the vast majority of grads, especially ones who don't intend to become mathematicians. Learning how to math is probably more important than the specific material, outside a handful of things. You can pick up the rest as-needed, and for the vast majority of people, "the rest" that is in fact ever needed for the entire rest of their lives, will be very little. Especially if they're pursuing a classics-based liberal arts degree.
I doubt many of their grads are planning to become actual computer-scientists or mathematicians or mech. engineers or any of that. Lawyer, maybe doctor, maybe writer, maybe an ordinary computer programmer, that sort of thing. As long as you're not afraid of math, you'll be fine in any of those not having had a typical PDE class or whatever.
That said, i haven't read most of these, so maybe i am wrong.
Agree on Descartes and Darwin, but they're both sort of canonical in Great Books reading lists. Honestly not sure why Descartes is considered so important to the history of ideas, particularly in Mathematics where there are so many other very worthy minds and texts to study, but shrugs.