What do you think?
Rate this book
Six Maths Essentials: How to Model the World
The ‘Mozart of mathematics’ (New York Times) takes us on a tour of the core ideas of mathematical thinking
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.
Playful and wise, this is the best entry point for understanding how mathematics works. Contrary to popular perception, maths, Tao insists, isn’t magic—it's a powerful way of thinking from first principles and modelling the world that anyone can learn.
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.
Playful and wise, this is the best entry point for understanding how mathematics works. Contrary to popular perception, maths, Tao insists, isn’t magic—it's a powerful way of thinking from first principles and modelling the world that anyone can learn.
89 pages, Kindle Edition
Published October 27, 2026
About the author
Terence Tao
52 books268 followersTerence "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.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 1 of 1 review
October 28, 2026
This is a book in the 'compact collection of science/maths essays' category beloved of publishers because they can charge hardback prices for fewer than 80 pages of text - but don't let that put you off, because it's excellent.
Terence Tao introduces six areas of mathematics: numbers, algebra, geometry, probability, analysis and dynamics. Each of these is descriptive rather than practical (there are only a couple of school-level equations in sight), done in a way that gets to the heart of 'what's the point of this subject' with precision and a good level of storytelling.
It's a shame in a way that analysis and dynamics form the final third of the book (apart from a short epilogue), because they don't work as well as the other sections. For the first four, practically everyone will have a vague idea of what they are and what they do - but Tao is then able to open our eyes to their wonders and power. Because Tao has to stay away from any detail of what's going on in the final two sections they feel more vague and woffly.
My other small moan is that the probability section is weak on Bayes - bearing in mind Tao's focus on what the point of each of these various mathematical disciplines is, he doesn't mention that one of the main benefits of Bayesian probability is being able to translate from what is measured to what we actually want to know.
However, the excellent service this book provides is to give us insights into what mathematics is and why it is so important. Many people struggled with maths at school and can't see the point of anything more than basic arithmetic. Here we take a dive into the mathematical toolkit and, without resorting to the grunt work that many find it difficult to get their head around, makes it clear what gems these mechanisms are to gain an understanding of the world around us - as well as inspiring curiosity.
Terence Tao introduces six areas of mathematics: numbers, algebra, geometry, probability, analysis and dynamics. Each of these is descriptive rather than practical (there are only a couple of school-level equations in sight), done in a way that gets to the heart of 'what's the point of this subject' with precision and a good level of storytelling.
It's a shame in a way that analysis and dynamics form the final third of the book (apart from a short epilogue), because they don't work as well as the other sections. For the first four, practically everyone will have a vague idea of what they are and what they do - but Tao is then able to open our eyes to their wonders and power. Because Tao has to stay away from any detail of what's going on in the final two sections they feel more vague and woffly.
My other small moan is that the probability section is weak on Bayes - bearing in mind Tao's focus on what the point of each of these various mathematical disciplines is, he doesn't mention that one of the main benefits of Bayesian probability is being able to translate from what is measured to what we actually want to know.
However, the excellent service this book provides is to give us insights into what mathematics is and why it is so important. Many people struggled with maths at school and can't see the point of anything more than basic arithmetic. Here we take a dive into the mathematical toolkit and, without resorting to the grunt work that many find it difficult to get their head around, makes it clear what gems these mechanisms are to gain an understanding of the world around us - as well as inspiring curiosity.
Displaying 1 - 1 of 1 review