Except that list is ... eclectic, to put it politely. If you want to learn maths, I wouldn't recommend Aristotle, Descartes and Darwin.

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.

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.

Can you give your thoughts on the approach at St. John’s and whether you would recommend it?

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.

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.

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.

We actually read some Descartes in math-- some of the papers from which we get the term "Cartesian coordinates." What he does in those papers fascinating, but has very little to do with the way that we learn and use Cartesian coordinates.

The Great Books approach involves reading the actual historical development of a subject and seeing not only what the state of the art is but how we got from here to there.

I believe the person you're replying to understands that. The claim is that this approach is really bad way to learn math.

As someone who has learned and taught a lot of math, I agree with that claim.

It appears to be a liberal arts program. Is this substantially different, with respect to the rigor of mathematics, than most other comparable programs? They might cover more calculus (maybe at a theoretical level?) than most liberal arts programs.

I'd expect the rigor is fine, but the particulars that are learned differ.

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.

Yes, it is substantially different with respect to rigor and content than standard undergraduate mathematics programs. It covers a few historically important texts and does not teach (if those texts are any indication) most of what is usually taught in an undergraduate math degree. (A poster above writes: "Freshman math was almost entirely the study of Euclid and Nicomachus.")

So this is the books used in an undergraduate liberal arts degree (your degree is IN liberal arts). These are the math tagged books in a quirky bachelors in philosophy degree, essentially. They do not have a math degree (or any degrees aside from bachelors in liberal arts?).

I see - I understood "liberal arts program" above to mean a liberal arts college in general (typically offering a mathematics major). I agree that this reading list is better suited for something like "history of math for humanities students."

Perhaps it is a bad way to learn 'applied math'? Bertrand Russel might disagree...

Johnnie and math Ph.D. here. It's a bad, or at least slow, way to prepare for math or math-heavy graduate school as you'll need to take additional coursework elsewhere in order to be competitive. On the other hand, freshman math at St. John's (Euclid, a bit Apollonius, start into Ptolemy) was for a significant fraction of students in my year the first math class they had ever enjoyed. Euclid's Elements, despite its many inefficiencies, and faults, does not heavily rely on mastery and/or acceptance of earlier curricular material, nor is it designed in service to later curricular material that most students are in no position to anticipate or appreciate.

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.

But consider that they include Hardy's "Mendelian Proportions in a Mixed Population" but not Riemann's "On the Hypotheses Which Lie at the Foundations of Geometry."

Is it actually doing that? Like it seems to have some good stuff for early history - euclid's elements and what not, but i'm not sure what the theme is for the later books, and lots of it seems very applied, or just other sciences that use math and not really about math itself.

That said, i haven't read most of these, so maybe i am wrong.

It has been trendy in the last fifty or so years to strip historical and cultural content from math classes in favor of rote computation (as the former is easiest to test in a “standardized” setting), but I’d argue that dehumanizing mathematics makes it far harder to understand, or indeed even care about.

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.

Agreed. The book "A Mathematician's Lament" I found enlightening on this topic.

This coupled with a weird fixation on achieving a sufficiently "high" level of mathematics, typically without a strong justification for any non-grad-school-bound students. Reeks of gate-keeping. I've known multiple people who've failed to finish a degree solely because of math classes covering material that they'd almost certainly never have seen again their entire lives, even if they achieved a middling-successful career in their desired field.

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.

I know I'd prefer a population that understands how to read graphs, what rate of change means, can actually solve a word problem, etc. People are voting on complex topics like tax rates and I think you'd be amazed at how many people can not, and I mean not with a calculator or at all, calculate what 60% of 75 is.

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.

I used to TA an intro philosophy course designed for STEM types based on Aristotle’s Physics and etc., and lemme tell you the students ate that shit up.

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.

Aristotle is reasonable because (1) logic and (2) it's going to be a core part of any Great Books curriculum so it's part of the core as opposed to specifically "mathematics". But if you're going to read Aristotle and Russell with the justification "logic", you must include Goedel and Hilbert.

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.

I went through a great books curriculum (not in math), and... what a strange list. It reminds me of my primary complaint with the whole Great Books approach: it's mired in fairly a ridiculous fetishism of the Greek classics, the Enlightenment era, the American founding, and the Anglo view of the western world. This works... well enough... in Philosophy and History and the like. But it a much larger problem in Mathematics where the field is essentially unrecognizable from the way it would've been taught in 1920 or whatever.

I really like the general ethos approach, but the cultural baggage grates and for Mathematics in particular leads to odd selections and a sort of out-of-touch-Oxbridge-retiree-who-was-already-a-touch-senile-in-1982 understanding of the history of ideas, tbh.

The Grundlagenkrise is hardly covered at all, despite having so many wonderful candidates for short illustrative texts that fit the Great Books tradition perfectly (none of which were authored by Russell, although a preference for Russell over Goedel is hardly surprising given my first paragraph). And the emphasis on Physics and Natural Philosophy over the development of the science of computing is a shocking oversight given the sheer accessibility of Turing's work. I'm honestly not sure what eg Darwin is doing in this list (despite being a good candidate any great books curriculum).

Also, significantly more coverage of the development of arithemtic in the Arab world and simultaneous developments of various things in both the Indian subcontinent and in the far east.

Where is the development of probability theory? Texts from Riemann, Boole, Laplace, Fermat, Galois, and especially Euler seem more important than Bacon or certainly Franklin.

Etc.

this is not intended as any kind of rebuttal, but the Santa Fe campus of St. John's has an Asian classics graduate degree which brings in some missing material from the Indian subcontinent (and elsewhere, of course, but you specifically mentioned India).

I don't recall if it addresses math in particular, however. my guess is no. the grad school is kind of eager about granting people excuses to skip math, and I get the impression that they have to be, because otherwise they'd go out of business.

anyway, if you did both that degree and the undergraduate degree, you could claim a more credible, globe-spanning Great Books education, although it would still have plenty of caveats and flaws.

You're right that pre-20th c. math works were quite weird from a modern standpoint. The huge development of mathematical abstraction (and, to some extent, computation) since then has meant that many and perhaps most of the topics that research mathematicians were interested in back in the 19th c. would now be considered boring and sometimes trivial.

Computing is not yet old enough for us to know which books on computing are great books.

Also the point of reading Euclid is not really to learn geometry but rather to investigate and examine the oldest, most primordial expression of the idea that math should be formalized using a few axioms.

Logic goes back. Could have stuff from Babbage, too. I definitely feel SJ would appreciate an old school style math proof exposition even perhaps between mathematicians. (Forgetting any specifics as it’s been way too long.) Notably, NM does have solid math departments to invite for lectures.

I always got the impression SJ is more about an “originalism” towards knowledge. But of course they’re going to have to pick and choose. Maybe it’s time for them to revisit math and add computing.

Edit-read the math curriculum. They threw Darwin, Feynman, and Einstein into there as electives. Seems a little of a catch-all. Also they could add Shannon entropy.

It is a living field, of course, but I do think there are certain texts that we know we would include from Turing, Von Neumann, Goedel, Church, Shannon, Backus, Hoare, Dijkstra, and I guess something about Perceptrons is now mandatory but IDK what text I'd choose. Beyond those texts things become hazier, but that's already at least a semester of undergraduate reading.

> Also the point of reading Euclid is not really to learn geometry but rather to investigate and examine the oldest, most primordial expression of the idea that math should be formalized using a few axioms.

Yeah, Euclid is important. It should be studied carefully in any Great Books program. But there's a lot of other important stuff to talk about and the extreme emphasis on Euclidean constructions is IMO a bit of a shibboleth.

I don't think the point of any great books program is to finish and say "You have now read everything of relevance, no need to read anymore." The curricula are broad and general so that if you have particular interests in a field you are now equipped to read all of the texts you mentioned on your own. If there was a specific "Great Mathematics Books" curriculum perhaps all the ones you mentioned would indeed be required.

I don't see a huge emphasis on Euclidean constructions, at least not in this particular curriculum. Euclid is just one book among several math books here. However I do think one issue with studying math from a great books perspective is that the level of prerequisite knowledge it takes to even read a lot of texts considered great would take many years of focused study to develop. I don't see Grothendieck in this list for instance. An intelligent child can read Euclid and follow along perfectly, because there isn't really any prerequisite knowledge needed.

I think the Structure and Interpretation of Computer Programs is the closest to attaining such a reputation.

> "Great Books" is mired in fairly a ridiculous fetishism of the Greek classics, the Enlightenment era, the American founding, and the Anglo view of the western world.

The webpage clearly states that the list is of foundational books of greco-roman civilization. And SJC is an american university. What do you expect?

Also, fetishism? Greek classics are the foundation of european civilization. That's like going to a christian seminary and whining about their fetishism of the bible.

> But it's a much larger problem in Mathematics where the field is essentially unrecognizable from the way it would've been taught in 1920 or whatever.

The foundation of european mathematics goes back to the ancient greeks. It's a foundational books list.

> Russell is predictably floating around (see paragraph 1) even though... well, yawn.

Are you serious?

Yeah, yeah, Evropean, we get it. You know that even SJC grads eye-roll at that stuff, right? One of them even does in this comment section.

Anyways. Even then -- typical Great Books curricula still sample from a tiny subset of literature that fits the mold of "greco-roman civilization". It was chosen by a very particular set of people at a very particular point in time. Some choices work more or less well enough. Others not so much.

The choices for what to emphasize in Natural Philosophy and Mathematics are mostly bad imo. They reflect what a 1920s humanist might conceive of as a Great Book in those fields. Which is to say, mostly weird and sort of mired in a very particular 1850s Oxbridge sensibility that most people don't even realize is being read into the whole project.

And here's the issue: those guys had well-informed opinions on what to emphasize in Philosophy and History. We can agree to disagree, or not, whatever. But in Mathematics and Science, they were barely following the plot or even already ossified in their own lifetimes. And that was a century ago. The choices there aren't a matter of opinion. They are just... bad.

>> > Russell... yawn

> Are you serious?

First of all, the text listed is his Introduction to Mathematical Philosophy. It's literally a 1920s textbook on Mathematical Philosophy. It is what it is. Doesn't really belong in a Great Books curriculum, imo, but the indignation at the idea that it's a yawnfest (too verbose) is kinda weird. It's... a textbook. Yawn.

Second, the indignation at Russell being a yawnfest in general made me LOL. Principia Mathematica is WAY less readable than the yellow pages.

Third, if you're including Russell as part of your coverage of Foundations -- but also excluding Goedel and Church and Turing and Hilbert -- then you're doing it horribly wrong! Russell is the foil in this plot, and a horribly pedantic and boring one at that. Not that a Great Books curriculum would ever treat Russell as a foil ;-)

Fourth, to the stuff you probably assumed was being included from Russell: I also found Russell's History boring and at some moments annoyingly preachy/opinionated for a History. Even his more red meat-y opinion stuff is... important for understanding the development of a certain strand of modern intellectualism. That's not meant to be dismissive; I'm in that strand!!! But let's just say not what I'd spend my best years pouring over.

The section on Russel is brief, and is read as complement to Lobochevsky and background for the Goedel readings.

Interesting; good to know. I don't see either Lobochevsky or Goedel in the lists.

I found this guy in a random recommended on youtube[1], he is working on a great books curriculum type course that incorporates literature from cultures from the Middle-east, India, Far-east, etc. The complete reading list is in his homepage.

[1] https://www.alexanderarguelles.com/great-books/