Math Without Numbers

Paperback, 224 pages

Published by Dutton.

ISBN:: 978-1-5247-4556-1

(5 reviews)

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 …

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.

4 editions

The Weaver Reads reviewed Math Without Numbers by Milo Beckman

Goodreads Review of Math Without Numbers

4 stars

This book leans toward the simple, and it left me wanting more for it, but it’s still a well done attempt at pulling those resistant to mathematics to its beauty and elegance. The chapter breaks down into four major sections: essentially topology, analysis, algebra, and applied mathematics, with an interlude that questions the foundations of mathematics as a discipline. The most interesting section was certainly on algebra, as this is where the most complexity (of the book, not the field) lay.

The whole project is profoundly platonic, and I’m not entirely convinced by the “foundations” section, but it is true that mathematics does seem to WORK, and I’m sure that’s worth something.

The book concludes with an argument that the universe is made of math, via the standard model. It could be! But it also seems so narrowly human to conclude that.

What do I know? I’m just a layman …

This book leans toward the simple, and it left me wanting more for it, but it’s still a well done attempt at pulling those resistant to mathematics to its beauty and elegance. The chapter breaks down into four major sections: essentially topology, analysis, algebra, and applied mathematics, with an interlude that questions the foundations of mathematics as a discipline. The most interesting section was certainly on algebra, as this is where the most complexity (of the book, not the field) lay.

The whole project is profoundly platonic, and I’m not entirely convinced by the “foundations” section, but it is true that mathematics does seem to WORK, and I’m sure that’s worth something.

The book concludes with an argument that the universe is made of math, via the standard model. It could be! But it also seems so narrowly human to conclude that.

What do I know? I’m just a layman who became curious about math through sci fi and philosophy.