Much ado about, well, nothing.

Cambridge mathematician Barrow (*Pi in the Sky , 1992, etc.) has established a reputation as a lucid explicator of difficult numerical and cosmological problems. Here he turns to some of the most difficult of all, at least insofar as lesser minds can grasp: nothingness. His narrative begins, simply enough, with the development of the idea of zero in several mathematical traditions, including the Mayan, Babylonian, and Indian. These independent inventions, which early generations of scholars took to be proof of cultural contacts in antiquity, developed naturally, Barrow maintains, out of positional or place-value numbering systems. “Once a positional system is introduced,” he writes, “it is only a matter of time before a zero symbol follows.” Zero is altogether too simple for the world because, as the author points out, it cannot encompass the relative degrees of nothingness that more recent physics have postulated; for that, we need “other null mathematical entities” that embrace the concept of a set that has no numbers within it, and here and hereafter Barrow’s lightly borne argument takes a somewhat more technical turn, leading into still more difficult concepts of quantum physics, many having to do with the origin and ultimate end of the universe. His depiction of that inevitable end, when everything slides gently into the vacuum that nature supposedly abhors and when new laws of physics override the ones we know, is intriguing—and quite beautiful. Still, readers with little background in mathematics will have their work cut out for them in following the author’s analysis—an effort that the author amply repays.*

*Elegant, learned, and far more accessible than much scientific discourse.*