## 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__

Pentominoes

Tangrams

Images of Infinity

Curve Stitching

Curves of Pursuit

Pascal’s Triangle

Can You Solve These? by David Wells