What are the "great books" of mathematics?

April 23, 2008, 8:27 am

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. 
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