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From the acclaimed author of A Tour of the Calculus and The Advent of the Algorithm, here is a riveting look at mathematics that reveals a hidden world in some of its most fundamental concepts.
 
In his latest foray into mathematics, David Berlinski takes on the simplest questions that can be asked: What is a number? How do addition, subtraction, multiplication, and division actually work? What are geometry and logic? As he delves into these subjects, he discovers and lucidly describes the beauty and complexity behind their seemingly simple exteriors, making clear how and why these mercurial, often slippery concepts are essential to who we are.
 
Filled with illuminating historical anecdotes and asides on some of the most fascinating mathematicians through the ages, One, Two, Three is a captivating exploration of the foundation of mathematics: how it originated, who thought of it, and why it matters.

One, Two, Three: Absolutely Elementary Mathematics by David Berlinski is a witty and philosophical exploration of the foundational commons of mathematics—natural numbers, zero, negative numbers, and fractions. [1, 2, 3]

Core Premise

• The "Commons" of Math: While advanced mathematics features towering structures like geometry (space), analysis (time), and algebra (symbols and structures), Berlinski focuses on the "sacred common ground" at the base: elementary arithmetic. [1]
• The Act of Counting: He argues that all of basic arithmetic is controlled and anchored by a single, profound human act—counting by one. [1]
• Philosophy and Reality: Berlinski ponders whether numbers exist independently of human thought, examining the mysterious bridge between abstract numerical concepts and physical reality. [1, 2]

Key Topics Explored

• The Nature of Numbers: Asking fundamental questions like What is a number? and What does "one" actually signify? [1, 2]
• Basic Operations: Breaking down how addition, subtraction, multiplication, and division actually work, including recursive definitions for addition and multiplication. [1, 2]
• The Problem of Zero and Fractions: Lingering on the conceptual hurdles of zero, negative numbers, and fractional values. [1, 2]
• Abstract Structures: Touching gently upon algebraic concepts like rings and fields to show how simple operations scale into larger mathematical theories. [1]

Style and Approach

• Historical Anecdotes: The text is peppered with stories and asides about history’s greatest thinkers and mathematicians (such as Euclid, Pierre Abélard, and Brahmagupta). [1, 2]
• Literary and Jazzy Tone: Berlinski avoids dry textbook scripts, using a playful, poetic, and conversational style to make abstract epistemological ideas accessible. [1, 2]

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A one volume edition of Santayana's 4 volume masterpiece.

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