Reading

This class does not exactly have a textbook. There is a variety of readings and depths to which we will read them. Assigned reading will be a backbone for our collaborations, and suggest topics and directions for our own research.

Main Texts

There is one book we will all read though, to give us a common experience from which to branch out:

  • Yearning for the Impossible by John Stillwell.

To support this we have two more works from Stillwell officially mentioned and prepared.

  • Mathematics and its History
  • Roads to Infinity

Stillwell excels at combining good storytelling and technical details and his first book shares the perspective of using the impossible as a lens through which to view math. Mathematics and its History will be useful because it provides so much detail, both technical and historical. It deals with many of the same topics as Yearning so we will be able to refer to it as we seek greater depth. Roads to Infinity is also a very good book, but we will only be considering the beginning of it here. It will guide us to learn about infinity and set theory, two important and interesting topics that are not touched on in the other books. If you’re interested in infinity(ies) and/or the theoretical capabilities and limits of mathematical systems (like computers) you may want to read it cover to cover a few times.

Besides marking ourselves as big fans of Stillwell, two other works will be part of our shared Pantheon:

The Cult of Pythagoras by Alberto Martinez

This recent title explodes anything you might think you know about mathematical history. Essentially math teachers (included among these are some of the most famous mathematical researchers through history) care more for a good story than honest historiography. In place of history, we have myth making. This is a great introduction to the idea that finding out more about math is a lot more like being Alice in Alice in Wonderland than it would seem. Just like everywhere else, the historical development of math respects rather little logic or order, but is usually cleaned up in generational cycles to pretend otherwise.

The Mathematical Experience by Philip Davis and Reuben Hersh

This book changed my life when I was in college. It is just the thing to broaden one’s horizons and get some real discussion on the big picture and little details of what math is, what its for, where it comes from, and so on. It is, as a book from 1980, also interesting to read for what is outdated and what isn’t. It doesn’t need to be read beginning to end and is made of lots of little, diverse chapters. A great book to pick up for a bit here and there. 

Other Math Texts

The texts above are only jumping off points for continued reading and research across a variety of mathematical texts. Some of these are similarly minded pop math books, math textbooks, classical math writing, journal articles, blogs, and yes, even Wikipedia. Some examples:

  • The Crest of the Peacock by George Gheverghese Joseph
  • Mathematics in Ancient Iraq: A Social History by Eleanor Robsen
  • A Book of Abstract Algebra by Charles Pinter

This is not a complete list, and in general, the idea is—especially as we are in a 300-level course—for you to take a few steps on your own instead of being spoon-fed the entire time. Use the readings we have, the works they cite, and the topics addressed to begin to read more widely in the subject. Our schedule will contain some direct opportunities for this, but you need not wait for them. Find interests and pursue them. Use this course and our meetings as an excuse to actually learn something.

Other Texts

We will also likely find our way to read non-mathematics and non-mathematics history, mostly to give us critical tools to analyze the development of math as a science and technology, and more generally to broaden our perspective beyond the discipline of math. Seeing connections through multiple perspectives and disciplines adds needed depth to any understanding of the world. Works whose focus is not directly math too can give us some good ideas about where we might try to make our marks with these ideas.

Some examples include

  • The Structure of Scientific Revolutions by Thomas Kuhn
  • Users as Agents of Technological Change: The Social Construction of the Automobile in the Rural United States by Ronald Kline and Trevor Pinch
  • Things that Make Us Smart by Donald Norman
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