**The Nothing That Is: A Natural History of Zero **

*By Robert Kaplan*

Oxford University Press

225 pages, $22Oxford University Press

225 pages, $22

**Zero: The Biography of a Dangerous Idea **

*By Charles Seife Viking*

248 pages, $24.95248 pages, $24.95

One may be the loneliest number, but zero gets no respect. It's the place-holder that can't hold its own. Impotent in addition and subtraction, overly simple when multiplied, and a total freak when it comes to division, zero might be love in tennis but it gets no love itself. Robert Kaplan's *The Nothing That Is* and Charles Seife's *Zero: The Biography of a Dangerous Idea* examine the history of the number as they try to make zero more of a hero. Their approaches from opposite sides of the number line yield very different results.

Kaplan, a Harvard University mathematics professor who founded the Math Circle, a public program dedicated to the enjoyment of pure math, puts a positive spin on the natural history of zero. He traces the number and the concept of nothing from ancient times through contemporary calculus, and even into literary notions from the likes of Henry James and Sylvia Plath. Although the facts are a little cloudy regarding zero's formative years in Greece and India, Kaplan pieces together as much as possible in a tale he calls part adventure story and part mystery. *The Nothing That Is* might not be the most riveting example of either storytelling genre, but it still makes for an impressive introductory lecture from a seasoned professor.

Kaplan assures his readers that if they've had high-school geometry and algebra, nothing in the book should confuse them. They might even find some friends—the all-for-naught narrative features appearances by some of the greatest names and principles in mathematics. Descartes' plain, Fibonacci's sequence, and l'Hôpital's Rule are far more accessible here than they seemed when scrawled on the high-school blackboard.

That ease is largely due to Kaplan's conversational writing style and eclectic academic background. In addition to teaching math at Harvard, he has also taught classes in philosophy, Greek, German, Sanskrit, and "inspired guessing." Such diversity shows in the number of personal anecdotes, literary allusions, and powerful analogies Kaplan brings to the equation. He celebrates math as an artistic achievement and has fun with his subject. While discussing how 12th-century mathematicians in India were slow to treat zero as a real number, he makes a compelling case with some very unexpected imagery:

What does it take for an immigrant to the Republic of Numbers to gain citizenship? Think of the situation with words and with ideas. New words are always frisking about us like puppies—one month people go "ballistic" and the next "postal"—but few settle in companionably over the years and fewer still reach that venerable state where we can't imagine never having been able to whistle them up, there at our bidding. And ideas, large and small: where was flower power 50 years ago—and where is it now? With what fear, fascination and loathing Freudian doctrine slowly took hold and became the canon—and how quickly it all fell apart: who now have complexes, or cathect their libidos onto father-figures? But the Republic of Numbers is vastly more conservative than those of language or ideas: Swiss in its reluctance to accept new members, Mafiesque in never letting them go, once sworn in.

In passages like this, Robert Kaplan's prose is almost as infectious as his love for his subject. If more math books were written with such enthusiasm, there might be more math majors in our colleges.

If, on the other hand, more math books were written in the style of the first half of Charles Seife's *Zero: The Biography of a Dangerous Idea*, there might be more made-for-TV movies about good numbers gone bad. From the title of his book on through Chapter 5, "Infinite Zero and Infidel Mathematicians," Seife focuses on the sensationalistic side of math—if there really is such a thing. Even given the recent Y2K hysteria, it's hard to imagine math as much of a threat. When Seife throws around violent terms such as "danger" and "destruction" when speaking of arithmetic, it's hard not to roll your eyes.

A correspondent for *New Scientist* magazine who holds master's degrees in both math and journalism, Seife has the background but not the foresight to approach this subject responsibly. The first half of his debut book dwells on the gory, inconsequential historical details surrounding zero's origins rather than on the concept itself. Even though he covers a lot of the material Kaplan addresses, Seife focuses on the sensational, as when ancient thinkers were killed as enemies of their states. This violent imagery even enters in his discussion of Greek philosophers' influence on Western thought:

The Greek universe, created by Pythagoras, Aristotle, and Ptolemy, survived long after the collapse of Greek civilization. In that universe there is no such thing as nothing. There is no zero. Because of this, the West could not accept zero for nearly two millennia. The consequences were dire. Zero's absence would stunt the growth of mathematics, stifle innovation in science, and incidentally, make a mess of the calendar. Before they could accept zero, philosophers in the West would have to destroy their universe.

In the second half of the book, Seife moves away from such claims and focuses instead on a handful of influential zeroes in the scientific world. He addresses the mysteries of modern science in his explanations of black holes, wormholes (which might allow for time travel), and other zero-related phenomena, such as the difficulty of attaining absolute zero—the temperature at which all of the atoms in an object and the atoms of light surrounding it cease motion. The science-centered chapters are far more interesting than those in the first half of the book.

Seife's sudden shift in tone and subject matter makes it seem as though he wrote the first part of *Zero* in the hopes of some sort of Y2K calamity to cash in on. When the world went on as usual at the stroke of midnight on Dec. 31, one imagines Seife might have sat down and worked on this competent overview of zero in the physics world. This theory would certainly play to the author's own mathematical background, which includes research in probability theory, artificial intelligence, signal processing, and the visualization of multidimensional spaces. Unfortunately, what he lacks in comprehensive knowledge of subjects beyond math, he tries to make up for with little insight and excessive buzz words.

In both books, the authors approach zero from their own points of interest, and the success of their work depends on the depth and breadth of their knowledge base. This shouldn't come as much of a surprise to anyone. After all, whenever you try to add to zero, you only wind up with what you've already put in.