Recommended mathematics reading

Now, I know mathematicians don't like reading but if you want to take a degree in Maths, it might be nice to have a book to talk about in your interview. And the physicists have got a list, so we ought to have one too. Here's the collated recommendations from various threads on the site. I give multiple recommendations for the same book to give a feel for popularity.


Recommended here and here. An introduction to chaotic dynamics. Doesn't contain that many actual sums, but lots of pretty pictures, and a good overview of the role of chaos. Quite a popularist style.

  • Chaos by James Gleick

Quite Physicsy, but a good read, yet again quite biographical, some have said that it gets hard work to read quite soon after opening! MrMathsGenius. NB: I've seen this dissed a couple of times on the threads that provide the source for this page. Mr Dactyl


Recommended here. Interesting exploration into the different types of codes and CYPHERS used throughout history. Is a very good GENERAL MATHS BOOK, covering elements of basic number theory, physics (potential of photon money!), statistics (frequency Analysis) and computing. I found it interesting but view it more as an encyclopedia for reference rather than a comprehensive account. Says MrMathsGenius.

Recommended here.

Recommended here.

History of Mathematics

Recommended here.

Am currently reading this. This is definitely one of the better books on the subject. A chronological biography of the concept of infinity, from Greeks to present day. Says MrMathsGenius.

Recommended here.


An excellent account of one of the 20th Century's most prolific mathematicians.

Yet another biographical book, but well worth the read! Not that much maths in it, but looks interesting. MrMathsGenius.

Book about Ramanujan, yet again more biographical, but still worth a look.

Mathematical Physics

Recommended here.

A book about string theory, but most of the book is about relativity and quantum mechanics etc, says Speleo.

Sequel to the above. Focuses more on new research. Both books are very interesting.

Mathematical Philosophy

Recommended here.

Recommended here and here. Beginning to look decidedly old-fashioned, and Hardy makes some points which are clearly wrong about the role of mathematics in society. When he talks about the subject itself, he is powerful. This is a classic, and widely read. Try to find the version with introduction by CP Snow.

A good introduction to the philosophy of maths, presents an overview of the history and current positions in the field. Likely to be of less interest to those interested in straight maths, though.

Mathematical Problems

Recommended hereherehereherehereherehereherehereherehere and here. So basically, everyone reads this. You won't stand out at all. An enjoyable read all the same and "you must read this story" according to Cambridge's Faculty of Maths.

  • The Millenium Problems by Keith Devlin

Recommended here and here.

Strongly recommended here.

Recommended here.

Recommended here.

Recommended here.

About the Riemann hypothesis and other various topics in number theory. Recommended, says Speleo. And hereherehere and here.

Recommended here.


  • Godel, Escher, Bach by Douglas Hofstadter

A book about formal logic, Godel's Incompleteness theorems, and about 400 tedious pages on neuroscience and music. It's very interesting in parts, the dialogues especially are wonderful, but about half the book has nothing to do with maths and is tedious beyond belief, says Speleo. And here and here.

Readable Textbooks

Recommended here.

Recommended here.

Definitely not very heavy, but nonetheless, an interesting/relaxing read about imaginary numbers and a vast array of other topics:

A very clear and readable text useful for introducing some university level concepts to the top end of the A level cohort. The book starts off easy and gradually progresses onto some very interesting mathematics such as multivariable calculus and a study of the gamma function.


  • The Emperor's New Mind by Roger Penrose

Recommended here.

  • The Mathematical Universe by William Dunham

Recommended here.

  • The Wonders of Numbers by Clifford Pickover

Recommended here.

  • From Here to Infinity by Ian Stewart

Recommended here.

  • The Art of the Infinite: Our Lost Language of Numbers by Robert Kaplan

Recommended here.

  • What is Mathematics? by Richard Courant, Herbert Robbins and Ian Stewart

Recommended here and here.

  • Flatterland by Ian Stewart

Fantastic take on a 19th century book about different geometries, starts by explaining 4d by exploring the way our 3d world would look to a 2d or 1d person! Recommended here.

  • The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger

Recommended here. An entertaining book, and certainly one for younger people looking for some interesting, yet accessible, mathematics.

  • Art of the Infinite by Kaplan

More mainstream, targeted at expanding mathematical awareness. Certainly a good read for those who have perhaps gained Mathmophobia! MrMathsGenius. And here.

  • Imagining Numbers: Particularly the Square Root of Minus Fifteen by Barry Mazur

Good(ish). Mazur takes the scenic route to complex numbers, via a deep exploration of their history and a brief tour of the science of the imagination. No challenging maths, but a readable book. Recommended here.


  • A Very Short Introduction to Mathematics by Timothy Gowers

Tiny, incredibly dense book written by a Fields Medallist. Provides a great jumping off point for further independent reading around maths, and a glimpse of the character of 'real maths'. User:Mr Dactyl

Linear Algebra Step by Step by Singh. It has complete solutions to all the problems in the book and also has fresh problems on the book's website at

Real(Hard) Maths

These books are not about mathematics but rather contain mathematics for you to do.They are not standard undergraduate books but rather contain topics not covered in a typical undergraduate and often graduate program.Very different from all other math books here.Butbeware,not all of them are easy!

Vladimir Arnol'd was one one of the greatest mathematicians of the previous century but more importantly he is one of the greatest mathematics teachers ever! This is evident in his writings three of which have been included here.However a simple search will reveal a lot more.In this book he proves that a general fifth degree equation does not have a formula for its roots(i.e. is not solvable by radicals).He does so by considering the monodromy group of the riemann surface of all possible candidate multi-valued function to obtain a contradiction! This is a mouthful isn't it.But the most remarkable thing is that this book is based on lectures given to 16 year olds.Read this book and solve the problems to learn about groups,fundamental group,riemann surface and a lot more.

A great book with a collection of accessible topics and interesting but difficult problems.

Another masterpiece by Arnold.This book explains how advanced mathematics explains complicated natural phenomenon.For example when you stir a cup of tea what is the shape that the surface assumes.

This is a remarkable book that gives you a glimpse into vast and beautiful world of contemporary mathematics research.Some of the 30 lectures require you to know basic calculus others don't.This is a great book if you are keen to see what "real" mathematics looks like.

This book is a collection of annoyingly elusive and difficult problems in mathematics.It does not require you to know any advanced mathematics but the problems are HARD! These problems require you to think outside the box there is no technique or skill involved just thinking.When you do solve one of them it feels GREAT!

This book is possibly the hardest book on the list.Maybe it does not belong here.Just for the masochists among you who think they can tackle a book that would be difficult for the best of the best undergraduate students in the top universities can try this one.

This book has a lot of advanced content.But this book is perhaps much easier than most of the books in this sections.The problems are easier the proofs are more accessible.Only problem is that it sometimes requires a lot more prerequisites than the other books here.Even if you dont know anything more that differential calculus you can still read more than two-thirds of this book and enjoy it as well.The other third unfortunately requires you to know some undergraduate concepts.

This is the best book to prepare for an undergraduate maths degree.Everything you have seen in GCSE will reappear in this book in completely different form.I cannot express how helpful reading this book will be if you want to do well in a maths degree.It will teach you how to think like a mathematician.This is also the easiest book in this section.While you are at it check out some other stuff by Stillwell as well specially Geometry of surfaces and Classical Topology and Combinatorial Group Theory.

Other Reading Lists

  • Cambridge is here.
  • Balliol '04 here.