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(edit: apparently these are just "books tagged mathematics", not the mathematics tutorial reading list. First and second paragraphs mostly hold) I went through

(edit: apparently these are just "books tagged mathematics", not the mathematics tutorial reading list. First and second paragraphs mostly hold) I went through a great books curriculum (not in math), and this list reminds me of my primary complaint with the whole Great Books approach. "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. This works... well enough... in Philosophy and History and the like. 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. I really like the general approach, but the cultural baggage grates and for Mathematics in particular leads to odd selections. Sometimes you feel like your reading list is being commanded from the grave by a sort of snobby Oxbridge man who, in 1980, was already transparently classist in a kind of irrelevant and borderline senile way. With respect to this list in particular, the critical points of the Grundlagenkrise are hardly covered at all despite having so many wonderful candidates for short illustrative texts that fit the Great Books tradition perfectly. Russell is predictably floating around (see paragraph 1) even though... well, yawn. 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 the topic and its importance to the modern world. I'm honestly not sure what eg Darwin is doing in this list (despite being a good candidate in 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. The Greek fetishism strikes hard in that first year; no one born after 1850 needs that much Euclid. 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.

blewboarwastake 4y ago
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/ https://www.alexanderarguelles.com/great-books/
tessierashpool 4y ago
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.
zozbot234 4y ago
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.
voldacar 4y ago
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.
- alwayslikethis 4y ago
  I think the Structure and Interpretation of Computer Programs is the closest to attaining such a reputation.
- ianai 4y ago
  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.
- thwayunion 4y ago
  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.
  - adamsmith143 4y ago
34611 4y ago
> "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?
- thwayunion 4y ago
  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.

blewboarwastake 4y ago

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/ https://www.alexanderarguelles.com/great-books/

tessierashpool 4y ago

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.

zozbot234 4y ago

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.

voldacar 4y ago

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.

alwayslikethis 4y ago
I think the Structure and Interpretation of Computer Programs is the closest to attaining such a reputation.
ianai 4y ago
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.
thwayunion 4y ago
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.
- adamsmith143 4y ago

34611 4y ago

> "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?

thwayunion 4y ago
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.