Mathematics Reading List – the last twenty years

David Acheson

1089 and All That (2002)

Alex Bellos

Alex’s Adventures in Numberland (2010) & Alex Through the Looking Glass (2015) auto-maths-ography

The Puzzle Ninja (2017) & Can You Solve My Problems? (2017) puzzle books

Snowflake Seashell Star (2015) & Visions of Numberland (2017) colouring books

Eugenia Cheng

How To Bake Pi (2015) aka Cakes, Custard and Category Theory

Beyond Infinity (2018)

Marcus du Sautoy

The Music of the Primes (2003)

Finding Moonshine (2007)

The Num8er My5teries: A Mathematical Odyssey Through Everyday Life (2010)

Rob Eastaway

Why do Buses Come in Threes? (1998, new edition 2020)

The Hidden Mathematics of Sport (2011)

Hannah Fry

The Mathematics of Love (2015)

The Indisputable Existence of Santa Claus (2017)

Hello World: How to be Human in the Age of the Machine (2019)

Clarissa Grandi

The Artful Maths Activity Book (2020)

Vicky Neale

Closing The Gap: The Quest To Understand Prime Numbers (2017)

Matt Parker

Things to Make and Do in the Fourth Dimension (2014)

Humble Pi: A Comedy of Maths Errors (2019)

Simon Singh

Fermat’s Last Theorem (1997)

The Code Book (1999)

The Simpsons and Their Mathematical Secrets (2013)

David Spiegelhalter

The Norm Chronicles: Stories and numbers about danger (2013)

The Art of Statistics (2019)

see also: Michael Blastland, Andrew Dilnot for other great Statistics books

Ian Stewart

Professor Stewart’s Cabinet of Mathematical Curiosities (2008)

Professor Stewart’s Hoard of Mathematical Treasures (2009)

and many more

Older books – in reverse chronological order

David Wells – The Penguin Book of Curious and Interesting …

… Mathematics (1997)                  … Numbers (1997)             … Puzzles (1992)                … Geometry (1991)

Courant, Robbins and Stewart – What Is Mathematics? (1996)


Keith Devlin – Mathematics: The New Golden Age (1988)


Berlekamp, Conway, Guy – Winning Ways (1982)

An exhaustive, 2 volume, collection of games (including cellular automata Game of Life, which Conway invented) and the maths and strategies behind them


Davis & Hersch (and Marchisotto) – The Mathematical Experience (1981, revised 1995)


Douglas R Hofstadter – Gödel, Escher, Bach: An Eternal Golden Braid (1979)


Martin Gardner – Mathematical Puzzles and Diversions

a series of books from the 1960s-1990s, in Penguin, and republished by Cambridge University Press


Darrell Huff – How To Lie With Statistics (1954)


GH Hardy – A Mathematician’s Apology (1940)

If you’re interested in the mindset of a great mathematician, it is worth skimming through

Preparation for University Maths

Vicky Neale

Why Study Mathematics?

Lara Alcock

How to Study for a Mathematics Degree

Richard Earl

Towards Higher Mathematics: A Companion

Kevin Houston

How to Think Like a Mathematician

Timothy Gowers

Mathematics: A Very Short Introduction

Books on specific numbers

For a historical slant, you could try one of many books about the development of a particular number:

zero, infinity, pi, the golden ratio, the square root of minus one, and others.


Look for these authors:

  • Robert Kaplan
  • Charles Seife
  • Brian Clegg
  • Eli Maor
  • Paul Nahin
  • Mario Livio
  • Barry Mazur

Books about problem solving

Alex Bellos

The Puzzle Ninja (2017) & Can You Solve My Problems? (2017)


Stephen Siklos

Advanced Problems in Mathematics (2016, download from StepMaths)

An excellent selection of graded problems, including hints, solutions and discussions for each. A good preparation for STEP.


George Pólya

How To Solve It (1945)

The classic work on mathematical problem solving for students and teachers

The Stanford Maths Problem Book (1974)

Similar to “Advanced Problems” above, this is an excellent collection of problems with hints and solutions. The problems are designed to test aptitude rather than achievement and will reward creativity and insight.


Thomas Povey

Professor Povey’s Puzzling Problems (2015)

A collection of interesting physics problems, with discussions of each. This is particularly useful for students considering courses in physics or engineering, where these types of questions may come up in interviews.


Raymond Smullyan

What Is The Name Of This Book? (1981)

Smullyan’s style is engaging and entertaining. These are mainly riddles, for example the lying and truth-telling Cretans of whom you can only ask one question.


Frederick Mosteller

Fifty Challenging Problems in Probability (Dover, 2000)

More than any other area of mathematics, the solutions to probability problems can seem counter intuitive and contrary to our expectations. These puzzles cover many classic and interesting situations and encourage critical thinking about chance and risk.


Anany and Maria Levitin

Algorithmic Puzzles (2011)

A collection of interesting problems that require you to find an algorithm to solve a problem, or generalise to solve a whole class of problems. Finding an algorithm is part of the exercise, proving it works in all cases may be harder! These problems would appeal to students studying the discrete/decision modules in further maths, or students studying maths with computer science.

Books for Maths Activities (not just for teachers!)

Brian Bolt

Mathematical Activities 1, 2, 3

Mathematical Jamboree

Amazing Mathematical Arcade & others


Lorraine Mottershead

Sources of Mathematical Discovery


Tony Gardiner

Mathematical Puzzling

Mathematical Challenge, and More Mathematical Challenges

Maths Challenge 1, 2 and 3

Extension Mathematics: Alpha, Beta, Gamma and Teacher’s Book


Tarquin Publications



Images of Infinity

Curve Stitching

Curves of Pursuit

Pascal’s Triangle

Can You Solve These? by David Wells