4 ms·

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 underst

by tgv 4y ago

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.

ticviking 4y ago
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.
- spekcular 4y ago
  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.
  - viscanti 4y ago
    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.
    - spekcular 4y ago
      Yes, it is substantially different with respect to 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.")
      - uxp100 4y ago
        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?).
        spekcular 4y ago
        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."
    - yamtaddle 4y ago
      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.
  - korse 4y ago
    Perhaps it is a bad way to learn 'applied math'? Bertrand Russel might disagree...
  - ancilla 4y ago
    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.
- macrolocal 4y ago
  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."
- bawolff 4y ago
  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.
thebooktocome 4y ago
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.
- aik 4y ago
  Agreed. The book "A Mathematician's Lament" I found enlightening on this topic.
- yamtaddle 4y ago
  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.
  - adamsmith143 4y ago
    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.
  - thebooktocome 4y ago
skottk 4y ago
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.
a_techwriter_00 4y ago
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.
- voisin 4y ago
  Can you give your thoughts on the approach at St. John’s and whether you would recommend it?
  - tessierashpool 4y ago
    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.
  - gshubert17 4y ago
    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/ https://catherineproject.org/, which give opportunities to read and discuss many of these important works.
  - a_techwriter_00 4y ago
thwayunion 4y ago
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.

by tgv 4y ago

ticviking 4y ago

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.

spekcular 4y ago
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.
- viscanti 4y ago
  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.
  - spekcular 4y ago
    Yes, it is substantially different with respect to 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.")
    - uxp100 4y ago
      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?).
      - spekcular 4y ago
        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."
  - yamtaddle 4y ago
    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.
- korse 4y ago
  Perhaps it is a bad way to learn 'applied math'? Bertrand Russel might disagree...
- ancilla 4y ago
  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.
macrolocal 4y ago
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."
bawolff 4y ago
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.

thebooktocome 4y ago

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.

aik 4y ago
Agreed. The book "A Mathematician's Lament" I found enlightening on this topic.
yamtaddle 4y ago
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.
- adamsmith143 4y ago
  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.
- thebooktocome 4y ago

skottk 4y ago

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.

a_techwriter_00 4y ago

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.

voisin 4y ago
Can you give your thoughts on the approach at St. John’s and whether you would recommend it?
- tessierashpool 4y ago
  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.
- gshubert17 4y ago
  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/ https://catherineproject.org/, which give opportunities to read and discuss many of these important works.
- a_techwriter_00 4y ago

thwayunion 4y ago

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.