But first, for sheer entertainment, just a cool (geometry-impinged) illusion:
on to the books:
I'm forever amazed at the number of wonderful math-related books available for the non-professional, like myself! ...Have been looking through (…or looking forward to) several recently, and give all the following a thumbs-up (…apologies that some of these are older works you may well be long-ago familiar with):
"To Infinity and Beyond" -- Eli Maor's work from 1987 may be the best intro to infinity I've yet come across (how I missed it all these years I don't know!); a rich, varied, and comprehensive introduction to an endlessly fascinating topic. A review of it here:
"The Universal Computer" -- from Martin Davis, 2000; perhaps the best and most readable summary of the historical persons and events that brought us computers as we know them today. A great read and chronology. A review here:
"A Tour of the Calculus" -- David Berlinski's 1995 volume which I started when it came out almost 2 decades ago, but never got through… having recently read and enjoyed his "One, Two, Three" I decided to give "Tour" another try, and I must've grown accustomed to his quirky, unconventional writing style, because I'm finding it much more delightful (although still ponderous at points) this go-around; certainly the most unique, outside-the-box volume on calculus out there (even for a non-textbook).
Interestingly, I've now read Gregory Chaitin's short new volume on math and biology, "Proving Darwin," and it begins by mentioning that it was inspired in part by yet another "delightfully polemical book" from Berlinski, "The Devil's Delusion." Chaitin's book is a bit choppy but still, to me, a wonderful read that I may say more about after a second reading (although if you haven't cared for Chaitin's writings/ideas in the past, you might not care for this pithy volume).
Finally, tangential to math, I'm a long-time Douglas Hofstadter fan, though didn't much care for his last book, "I Am a Strange Loop" (see Martin Gardner's review here: http://tinyurl.com/7skxw7g), so have been waiting to see what he would do next. Apparently, he has a new volume coming in the fall entitled "Surfaces and Essences," relating the importance of analogy to human thinking.
Also, a reminder that Steven Strogatz's book "The Joy of x: A Guided Tour of Math From One to Infinity" is also due out in the fall.
So much good stuff coming our way!! (...and I'm still awaiting the paperback version of Daniel Kahneman's "Thinking Fast and Slow"!)
Lastly, speaking of math books, 'Wild About Math' blog did its latest podcast with Vicki Kearn, an editor at Princeton University Press, which consistently puts forth some of the best popular math books out there (give it a listen):