David Berlinski

Traces the history of mathematics over the course of 2,500 years, profiling ten important developments and figures, including Pythagoras, Euclid, Descartes, Leibniz, and Cantor.

A Short History of Mathematics

Infinite Ascent

Chris Aldrich

I'm not really quite sure for whom this book was written, but it was assuredly not meant for me. 

Though I appreciate his attempt (and more so the publisher's fortitude) to include some very simple equations and even the occasional proof, I have a feeling they're likely lost on much of his readership due to general presentational style and didactic modality. Those who are seeing this material for the first time may enjoy some of the flowery language and impassioned approach to mathematics, but are likely completely lost from a mathematical standpoint. Most generally serious mathematical students who have likely seen two or more of his general subjects would otherwise appreciate this type of exposition are likely put off by the poor writing style and lack of what could have been a tad more math and a far better historical presentation. In trying to reach too many audiences, I have a feeling he's lost them all.

The text is an all-too-quick survey of some of the larger concepts in mathematical history with only brief excursions into the mathematicians' personalities and backgrounds. While trying to cover the history, the personalities, the philosophies, and even some of the math simultaneously he gives short shrift to all four.

Many concepts, particularly early on are all too quickly glossed over and often not even in complete or coherent thoughts. Berlinski often uses the ellipses (the grammatical ones, not the mathematical ones) not only to poor effect, but he actually goes so far as to pat himself on the back for it. 

His overall coverage of the history and characters involved is scant at best in comparison to various other books in this category. Most egregiously I get the feeling that in general he's parroting back much of what is already written in the generic mathematical literature without providing any particularly interesting perspective of his own. Worse yet, there are no discernible references to other works for those wishing to delve deeper. If there were at least a clear thread tying all of the generally disparate chapters together into a more cogent whole representing the current state of mathematics, I would have felt more fulfilled and felt that the author had made an interesting and original contribution to the broad general literature, but alas, even this was wholly missing. 

Many of his historical sketches aren't as well put together, thorough or well-referenced as an average Wikipedia article on any of these subjects. In some cases, particularly relating to early mathematicians as Pythagoras and Euclid, despite saying explicitly that very little exists about their actual lives, he proceeds swiftly to wax far more poetic about them than the historical record could possibly allow. 

In sum, I'd recommend the interested reader to spend some time reading Euclid's elements, or delving into Galois' back story directly instead of reading this treatise. At best, I had hoped that Berlinski might do for mathematics what Simon Singh did for physics in Big Bang, but he seems to have fallen far too short; perhaps in his second draft he'll do better.

Infinite Ascent A Short History of Mathematics

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