Peter's Reviews > Everything and More: A Compact History of Infinity

Everything and More by David Foster Wallace
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's review
Jun 26, 11

bookshelves: popular-science, history, math-general, read-in-2011
Read from June 15 to 26, 2011

This book relates, or attempts to relate, how the topic of infinity was treated in different eras. These eras include ancient Greece (e.g., Zeno's paradoxes); the 17th century, when Newton and Leibniz developed calculus; and the period from the mid-19th to the early 20th century, when Georg Cantor and others developed new foundations for the concept of infinity (as well as for set theory and indeed for all of modern mathematics).

The book tries to present its complex subject matter in a conversational style, one that I gather received some unfavorable criticism. I didn't mind that style at all; in fact, I liked it, as far as it went. Rather, the stylistic aspect that bothered me was the book's brevity in covering certain topics. I think the author assumed a great deal about the reader's familiarity with some advanced concepts. It seemed like he would devote a single paragraph to a circle of ideas that, in order for the typical student to understand it in an undergrad math course, requires several pages of textbook reading, plus lecture time and homework exercises. It was unsatisfying when the book would bring up a deep topic only to gloss it over in this way (especially so for those topics I didn't already understand!).

More significantly, I tend to agree with the criticism leveled by some math professors, who panned the book for flaws in its mathematical content. I don't know foundational math well enough to assess the book at a deep level, but I did spot significant errors in a couple of passages. Perhaps the book's grasp of the philosophy was better than its grasp of the math, but my lack of confidence in the latter made me skeptical about the former, too.

Long story short, the book tries and fails at a new type of expository math writing. I give the (late, lamented) author credit for making the attempt, at least. I read someplace that there was some sort of deadline pressure and the book was not edited the way it really needed to be. This is a shame.
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