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Infinity and Beyond!

This was the e-mail question as asked: I was having a discussion with my "math" students today about infinity and they asked me if there were any fairly accessible books on the subject. I think they were thinking about historical context but also the meaning of infinity. Do know of anything I could recommend to them? Thanks, A.H. (Bellingham)

And, my answer: A.,I have suggested books based on my preferences...most are easily available either on ebay or as used books on-line....:

  • As a high school student, I fell in love with the author Lillian Lieber, who writes math books in comic book style complete with poetry-format, etc....and accompanied by artwork of her husband Hugh Leiber. Her book Infinity opened my eyes as a high school student to the realm of infinity, complete with neat geometrical paradoxes (that I still use in my math classes) and transfinite numbers ala Cantor. It is a fun read...and if they like it, ask them to read her other book The Education of T.C. Mits, which is a neat intro to modern mathematics (Note: "T.C. Mits" means "The Celebrated Man in the Streets")
  • Rozsa Peter's Playing with Infinity was my second book purchased on infinity, and it works since it reveals all of the interesting areas that infinity shows up in to create trouble.
  • Rudy Rucker's Infinity and the Mind. Rucker is a mathematician who writes science fiction about the fourth dimension and infinity. This book is a fun read...even served as the basis for a funeral eulogy for a WWU math professor who died many years ago... I recommend it to students all of the time.
  • Robert Kaplan and Ellen Kaplan's The Art of the Infinite. Another enjoyable read, filled with paradoxes...some history and culture...even leads into division in mathematics between the formalists and the intuitionists.
  • Eli Maor's To Infinity and Beyond: A Cultural History of the Infinite. A great author....Gets a little more into the mathematics involved, but also brings in the interplay of infinity with art, etc.
  • Leo Zippin's Uses of Infinity. A good reference book for math teachers, it was designed to use with motivated secondary and college students. Filled with neat problems and ideas.... I have made good use of it over the past 30 years!
  • David Foster's Everything and More: A Compact History of Infinity. Gets at history aspect, Zeno on up...and role of calculus...up to Cantor's resolution of types of infinity.
  • John Barrow's The Infinite Book: A Short Guide to the Boundless, Timeless, and Endless. Author has a formal style and often writes about science things....but he did a good job with this book....introduces some new ideas. For example, last chapter is on something called "infinity machines."
  • A. Gardiner's Understanding Infinity: The Mathematics of Infinite Processes. Gets at the mathematics involved (some of it higher mathematics above calculus), but has a lot of neat ideas relative to infinity's influence on number, geometry, calculus, etc.
  • Theodore Faticoni's The Mathematics of Infinity. This is the most formal of all of them as to the mathematics involved....students may not be willing to plow through it, but it has some good ideas.
  • Michel Blay's Reasoning with the Infinite. I include this one only if the students involved have a scientific bent, as it looks at infinity from the point-of-view of how infinity was used in calculus and understanding motion ala Galileo, Descartes, Leibniz, Newton, Lagrange, etc.
Next week, the remainder of my response will be provided....