When I read
The
Mathematical Century (TMC), I wanted
to tell lots of my software colleagues and friends about it.
That's why I'm reviewing it here for *UnixReview.com*, although
it has nothing direct to say about such usual *UnixReview*
topics as network programming, project management, or `$CLASSPATH`

.

In fact, TMC not only includes no recognizable computer program, but it boasts barely a dozen mathematical formulae, most of them such familiarly classic icons as Euler's identity or the standard roots of the quadratic equation. Despite this, the content is of high rigor and illuminating for those who work with computers.

The chapter "Mathematics and the Computer" might as well be titled, "Computers as mathematicians see them", for the topics are the predictable and rather dated ones of "The Theory of Algorithms ...", "... the Game of Chess", "Chaos Theory ...", "Computer-Assisted Proofs ...", and "Fractals ..." There's nothing about, say, wavelets, symbolic algrebra, database theory, aleatory methods, or information-based complexity theory, and only a hint of proteomics and cellular automata, all of which I'm willing to argue constitute highlights of computing.

In restricting himself to only the most essential subjects, though, author Piergiorgio Odifreddi is able to write correct and lively history. He clearly and succinctly traces the important concepts behind "algorithm", for instance, properly crediting not only Turing and von Neumann, but also McCulloch, Frege, Church, Hilbert, and Post. Throughout the books, individuals are known only through their professional trophies--theorems proved, Fields medals won--with a few exceptions for notable anti-war activists. Because Odifreddi is so comfortable with TMC's wide range of domains, however, different sections of the book blend nicely to make clear the distinctive roles of such actors as Hilbert and von Neumann. This nicely complements the presentations of most "computing science" curricula, and rescues the book from the staleness its topic list otherwise suggests.

Even more interesting to most UnixReview.com readers, though, are the other four chapters of TMC. They're best understood as a collection of very careful lunchroom conversations with experts: "You want to know about X? Well, Euler or Newton or Gauss first ... and then ..." The writing is delightfully precise at a survey level. Proofs appear like the battles of pedestrian textbooks, often reduced to a mere date and heroic assemblage ("Grant received Lee's surrender ..."; "... the concept of a nonorientable surface [was] discovered in 1858 by ... Listing and ... Moebius"). Oddifreddi assumes the reader's acquaintance with the "now familiar epsilon-delta formulation" of standard calculus, but slows down to list the divisors which establish six as a perfect number. On the other hand, the leisure of the latter allows him to slip mention of Augustine of Hippo into the final chapter on "Open Problems".

I want my friends who are not specialists in mathematics to read
TMC because it so effectively conveys "what all the
fuss is about": that mathematics abounds with exciting, curious,
and, most importantly, *live* ideas, ones that turn up
constantly in computing and other areas.

TMC's flaws are slight: I found three typographical errors, I think Soviet work is slightly neglected (not on simplistic ideologic grounds: Odifreddi pauses briefly to loose warning shots at bourgeois complacencies), along with mathematical philosophy, the word "some" appears in a few sentences where it contributes nothing, and one has to anticipate that "analysis, non-standard" is in the index, rather than "non-standard analysis". Also, while I tried several different counting schemes, I was never able to come up with exactly thirty as the number of problems in the book, despite the promise of the subtitle. The Foreword obliquely warns of this, though, explaining Odifreddi's navigation between the big themes of "theories" and "problems". Freeman Dyson, a keynoter at last summer's Open Source Convention, authored the Foreword.

Read TMC and you'll understand far more deeply the reasons software language designers want to include "lambda" in their creations, and why there's so much commotion over Riemann and his zeta. That's a good payoff for the few hours you'll need to absorb this slender volume.

Vice president of Phaseit, Inc., Cameron Laird frequently reviews books for UnixReview, and co-authors the monthly "Regular Expressions" column.