What are the “great books” of mathematics?


I was looking at the web sites of a few colleges the other day which use a “Great Books” curriculum. This is an approach to a core curriculum in which students work their way through a listing of the great books from the past, across a variety of disciplines. Here’s an example from Thomas Aquinas College, a highly-regarded Catholic liberal arts college in Santa Paula, California. St. John’s College is probably the best-known example; I remember getting a mailer from them when I was a senior in high school, and I was fascinated by the idea of attending a Great Books university at the time.  There are also a few public universities which offer a great books curriculum as an option within the larger curricular structure of the university, for example as part of an honors program. 

Apparently Mortimer Adler is credited with coining the concept of the Great Books, and he gives three criteria for a book to be a Great Book (taken from the Wikipedia article): 

  • the book has contemporary significance; that is, it has relevance to the problems and issues of our times;
  • the book is inexhaustible; it can be read again and again with benefit;
  • the book is relevant to a large number of the great ideas and great issues that have occupied the minds of thinking individuals for the last 25 centuries.
I am fairly interested in this concept of the Great Books for the same reason I am interested in the concept of having no textbooks whatsoever, or free textbooks, or cheap textbooks from a better time — Great Books appear to provide an affordable, strongly intellectual alternative to overpriced, bloated modern textbooks which have an increasingly low signal-to-noise ratio in their contents. But one of the things I’ve seen lacking in a lot of the “Great Books” universities’ curricula is mathematical content. St. John’s College has students reading Euclid’s Elements as well as Descartes’ Geometry and Discourse on Method, Pascal’s Conic Sections, Newton’s Principia Mathematica (!), some philosophical essays by Leibniz (does that count as math?), Dedekind’s Essay on the Theory of Numbers, and several papers by Einstein in which students are required to work through the math. But St. John’s appears to be by a very great margin the most mathematically-inclined of the Great Books crowd; most such universities have students reading the Elements and that’s it.  
What do you think are the Great Books of mathematics? If you were to build a mathematics major around a Great Books framework, what would you include and at what level (freshman, etc.) would you have students encounter them? I think articles and monographs could be considered “great books” as well. 

10 Comments

Filed under Education, Higher ed, Math, Teaching, Textbook-free, Textbooks

10 responses to “What are the “great books” of mathematics?

  1. I’m not sure that I have any other suggestions for the “great books” but I keep meaning to read a few of the more modern popular press books about e, i, etc.

    So to facilitate that, I’ve set up a moodle site at http://moodle.teachingcollegemath.com (my web domain) and I’m thinking about facilitating some book discussion groups this summer (because I don’t have enough to do).

    If anyone would like to join, you can start by creating a login for yourself on the site. (plus, I need some guniea pig students to see if I’ve got it set up properly)
    🙂 Maria

  2. Chris Storm

    I recently got a copy of the book Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. I have not finished it yet, but I feel pretty confident putting it out for this list.

  3. so i clicked the moodle link.
    you’ve got to register.
    okay; i’m feeling less technophobic
    today than usual; what the heck;
    i’ll try it.
    so i fill in the form & get the e-mail
    but still can’t log in. and keep trying
    for a few minutes but finally give up.
    so now yet another random net entity
    knows, not only my e-mail but
    one of my passwords and has
    provided me with no service but
    to remind me how ghastly
    this high-tech future you keep
    trying to sell everybody really is.
    thanks for nothing, maria h. andersen.

  4. If it makes you feel better, moodle SQL databases use a MD5 encryption, so not even I, the administrator of the database, knows your password.

    I’ll take a look at it this weekend and see if I can’t figure out why you can’t log in.

    m

  5. wow. that was fast. you must have figured out
    these newfangled “feed” things everybody’s
    always going on about, hunh. well, thanks
    for being a good sport about my rantage …
    to the point of taking more blame than
    i meant to’ve assigned to you! (i mostly
    blame moodle itself [for what is after all
    a pretty petty frustration …])

  6. Minor technical point: MD5 isn’t an encryption process, but rather a cryptographic hash function.

    Not-so-minor technical point: MD5 was broken a couple of years ago, at least partially, so that most people are migrating to a more secure function like SHA-1. Backstory here.

    I’m a little surprised that Moodle still uses MD5. You’d think it’d be easy to change the hashing algorithm since it’s open-source.

  7. Even though it’s more about the philosophy of mathematics (and of the mathematician), I would put “A Mathematician’s Apology” in this category.

  8. You also could fit “A Course of Pure Mathematics” on there then.

  9. amca01

    Certainly Euclid, Archimedes, Descartes and Newton would all make the grade as “great books”. Also Gauss’ “Disquisitiones Arithmeticae”, Boole’s “Laws of Thought”, papers of Riemann, Russell-Whitehead “Principia Mathematica” (even though it’s unreadable, it’s still a great book), Goedel “On formally undecidable propositions of Principia Mathematica and related systems”, and Turing “On Computable Numbers, with an Application to the Entscheidungsproblem”. (You’ll recognize a slight personal bias here.) I’ll probably think of others…