Six Maths Essentials: How to Model the World

by Terence Tao

In Six Maths Essentials, the renowned mathematician Terence Tao shows how mathematics has evolved from counting and geometry into a flexible set of tools for understanding an increasingly complex world. He moves effortlessly from children discovering infinity through play, to the numbers that underpin our online lives; from Johannes Kepler using algebra to price a barrel of wine, to curved geometries that explain why GPS works and planes don’t fly in straight lines on a map. Along the way, dice games, insurance policies and financial crises illuminate probability’s promise—and its limits—while deceptively simple rules give rise to chaos, pattern and life itself.

Six Maths Essentials, Tao’s first popular math book, provides a glimpse into the workings of his incomparable mind and how he thinks about the creativity and interconnectedness of the mathematical enterprise. Contrary to popular perception, math, he insists, isn’t magic—it's a powerful way of thinking from first principles and modelling the world that anyone can learn.

Kindle Edition

Expected publication October 27, 2026

About the author

Terence "Terry" Tao FAA FRS (simplified Chinese: 陶哲轩; traditional Chinese: 陶哲軒; pinyin: Táo Zhéxuān) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.