Browsing the remainder table in Half Price Books a few weeks ago, I ran across David Berlinski’s Infinite Ascent: A short history of mathematics. The cover copy looked good, and a quick flip through a few pages was enough to convince me that it was worth the three bucks. At 180 pages, you’d expect it to be a pretty short read, and it might be for some. I found it tough going.

The book focuses on what the author (and others, I gather) considers “the ten most important breakthroughs in mathematics,” giving some biographical information about the people most closely associated with those discoveries, the historical context, and also an explanation of why the breakthroughs are important. At least, that’s how the first five chapters (Number, Proof, Analytic Geometry, The Calculus, and Complex Numbers) went. The next five chapters (Groups, Non-Euclidean Geometry, Sets, Incompleteness, The Present) seemed much less approachable.

I freely admit that some of my difficulty could be that I’m fairly comfortable with the topics discussed in the first five chapters, but with the exception of Sets I have no experience with or more than passing knowledge of the topics discussed in the later chapters. Somehow, though, I get the feeling that the fault is not entirely mine. I didn’t expect to gain a detailed understanding of Gödel’s incompleteness theorems by reading a short chapter, but I had hoped to learn something. Instead, I’m treated to prose like this:

The final cut–the director’s cut–now follows by means of the ventriloquism induced by Gödel numbering. This same formula just seen making an arithmetical statement in that subtle shade of fuchsia now acquires a palette of quite hysterical reds and sobbing violets, those serving to highlight the metamathematical scene presently unfolding, for while Bew(x) says something about the numbers, it also says that

x is a provable formula,

meaning that honey the number x is the number associated under the code with a provable formula, whereupon the director, lost in admiration for his own art, can mutter only that deep down it’s a movie about a movie.

That’s all pretty writing, but by the time I wade through the director’s psychedelic visions I’ve totally lost track of whatever mathematical subject we’re talking about. The first time I read that chapter, I put my lack of understanding down to having read it in bed, just before I fell asleep. The author’s point continues to elude me after a second reading. I learned more by skimming the Wikipedia article linked above than I did trying to puzzle out whatever Berlinski was trying to say.

Flipping through the book again after finishing it, I noticed that the style is pretentious throughout. The book suffers from too many inappropriate and incomprehensible metaphors, too much temporal hopping around in its short biographies, and too many paragraphs that jump off the page screaming, “Look, Ma, at how pretty I can write!” Like the director in the excerpt above, Berlinski seems lost in admiration of his own writing.

All in all, I’d say you’d be much better off reading Wikipedia articles about mathematics than trying to decipher the word splatter that Berlinski is trying to pass off as intelligent writing in Infinite Ascent. Not only is Wikipedia free, but you’ll learn a lot more and you won’t be tempted to track down the author and smack him upside the head for killing trees and wasting your time with his drivel.

Sometimes there’s a very good reason for a book to be on the remainder table.