Fantastic numbers and where to find them A cosmic quest from zero to infinity

Numbers explain the universe in the electrifying debut from Padilla, a theoretical physicist and YouTuber on the math channel Numberphile. Using metaphors, analogies, and carefully constructed commentary, Padilla tackles such subjects as general and special relativity, black holes, the elusive Higgs boson particle, quantum mechanics, and string theory. He includes mini-biographies of physics' key players, including "savant of symmetry" Emmy Noether, "quantum pioneer" Wolfgang Pauli, and "rock-star physicist" Richard Feynman. Naturally, there are numbers galore: googols (a one followed by 100 zeros), used to explain the "vastness of infinity"; googolplexes, "a one followed by zeroes 'until you get tired,' " per its creator; and the enormous Tree(3), based on a game that mathematicians believe can end, though it could "easily last beyond the lifetime of a human, a planet or even a galaxy." Padilla caps his survey with an intriguing discussion of infinity in which he looks at the possibility that some infinities can be bigger than others. He's a stellar guide, shifting from playful to serious with ease, and his love for his subject is infectious and his knowledge vast in a way that is fitting for the material. This one deserves wide readership. (July)

A fascinating book that guides us through the labyrinth of numbers and what they mean. Theoretical physicist Padilla, whose research focuses on the intersection of advanced mathematics, physics, and cosmology, sees the world as a collection of particles, waves, and forces described by a spectrum of numbers ranging from the vanishingly small to the unbelievably large. Dividing the book into "big numbers" and "little numbers," the author traces the history of each of his fields of study, providing sketches of the people who made the key breakthroughs. This is lively history, from the Newtonian world of movement and collisions to the mysteries of quantum mechanics, with Einstein and a host of others making appearances. Finding numbers large enough to make sense of the universe has been a constant problem. Graham's number, usually written as a mixture of numerals and esoteric symbols, was the standard for a while; Padilla describes it as a "black hole head death," too big for the human brain to handle as anything but an abstraction. Graham's number was eventually surpassed by TREE(3), the product of a self-replicating series. At the other end of the numerical scale, Padilla stares into the abyss of supertiny particles and components of atoms, confronting the randomness of the way they stick together, or don't. "It worries me to think that everything I know should never have existed: me, my family, my closest friends," he writes. "This book should never have existed and yet, somehow, you're reading it, right now, in a moment that might never have arrived." Padilla has a knack for effectively deconstructing difficult concepts, using explanations that include Usain Bolt, Lego, and Squid Game. Though parts of the book are extremely challenging, like James Gleick's Chaos and Stephen Hawking's A Brief History of Time, it is a remarkable piece of work that is well worth the effort. Astonishing in its sweep and depth, this book offers a unique way of looking at the universe. Copyright (c) Kirkus Reviews, used with permission.