David Berlinski
Infinite Ascent:
A Short History of Mathematics.
Modern Library, 224 pages, $21.95

The relevant library shelves in the Courant Institute of Mathematical Sciences hold no fewer than eighteen different general histories of mathematics in English. The author setting out to write yet another such book must therefore have an angle (so to speak), some original approach to the topic. What is David Berlinski’s angle? “Short” doesn’t cut it: Dirk Struik cornered that market fifty years ago with his Concise History of Mathematics. A philosophical point of view like Morris Kline’s adds interest, but Berlinski seems not to be in thrall to any strong philosophical conviction. So what’s his angle?

He has two. The first is structural. While the narrative of Infinite Ascent proceeds more or less chronologically, each period is...

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