An illustrated tour of the structures and patterns we call "math"
The only numbers in this book are the page numbers.
Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject.
Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world.
The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
Beckman, a math prodigy who captained the New York City Math team at age 13, debuts with a playful paean to the pleasures of studying higher math. Arguing "that everything plants, love, music, everything can (in theory) be understood in terms of math," he uses analogies, puzzles, and formal logic but no equations to tackle intriguing questions from various fields. For example, from topology, "geometry's looser and trippier cousin," he asks when two shapes can be considered the same, producing the surprising answer that it's when one can be transformed "into the other by stretching and squeezing, without any ripping or gluing." Another question revolves around infinities namely, are some larger than others? Moving on to dimensions, he considers why structures with more than three, though nonexistent, are both theoretically possible and intellectually useful for mathematicians. Beckman's conviction that math provides the tools to understand everything gets its best showing when he tackles abstract algebra, explaining, among a blizzard of examples, how modeling, where "math connects to the real world," can theoretically predict the outcomes of systems like economics. Readers with an abundance of curiosity and the time to puzzle over Beckman's many examples, riddles, and questions, will make many fascinating discoveries.