Books About Mathematics
In these lists I've added links to The Internet Bookshop and to Amazon UK. They will give you all the information you need if you want to buy them or order them from your library. These sites may also tell you more about the books than given on this page.
Of course you can buy the books from these sites but please don't feel pressurised into doing so. There are lots of other on-line bookshop and your local bookshop may need your custom to survive. In most cases the links are to the British edition of the books.
1. Fermat's Last Theorem by Simon Singh
This is book an absolute must for anyone interested in mathematics. It is a best seller in Britain. It gives a history of the ideas behind the theorem from the time of Pythagoras up to the proof by Andrew Wiles, including the year when the proof appeared to be flawed. It gives an excellent insight into the way mathematical research is conducted.
You'll find a review of this book at Non-fiction Reviews: Simon Singh
2. The Man Who Loved Only Numbers by Paul Hoffman
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- This is the biography of a truly remarkable mathematician Paul Erdös (1913 - 1996). He has probably published more papers than anyone else yet he had difficulty tying up his own shoelaces. He was an extraordinarily generous and warm-hearted man who is remembered with great affection by mathematicians.
- Mathematicians have invented Erdös numbers to indicate their worth, a bit like a handicap in golf. As with handicaps the lower the number the higher is their reputation.
- Erdös collaborated with more mathematicians than anyone else and they are said to have Erdös number 1. Mathematicians who have published a paper with someone with Erdös number 1 have Erdös number 2. Those who have published papers with someone with Erdös number 2 have Erdös number 3 and so on. The highest known Erdös number of a working mathematician is 7.
- This book is a very good read.
- This is the biography of a truly remarkable mathematician Paul Erdös (1913 - 1996). He has probably published more papers than anyone else yet he had difficulty tying up his own shoelaces. He was an extraordinarily generous and warm-hearted man who is remembered with great affection by mathematicians.
3. What Is Mathematics? by Courant, Robbins and Stewart
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- This the latest version of a classic first published in 1941. It bridges the gap between school and university mathematics and gives a great insight into mathematics at the degree level. If you're thinking of studying maths at University then do read this book and find out what's coming. There's more about the book at What is Mathematics?
4. The Penguin Dictionary of Curious and Interesting Numbers by David Wells
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- This is a mine of absolutely fascinating information. Unlike most dictionaries it is arranged in number order rather than word order. Thus 6
- The Pythagoreans associated 6 with marriage and health, because it is the product of their first even and first odd numbers, which were female and male respectively
- comes before 45
- Every number greater than 45 is the sum of distinct primes greater than 11.
- A book to dip in and out of.
- This is a mine of absolutely fascinating information. Unlike most dictionaries it is arranged in number order rather than word order. Thus 6
5. An Introduction To The Theory Of Numbers by Hardy and Wright
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- This is the number theory book. It develops the theory from scratch with no preliminaries. It is very comprehensive, starting with elementary results about prime numbers and goes on to prove some difficult theorems about the distribution of primes, via Fermat's various theorems, irrationals, continued fractions, Fibonacci numbers and so on.
- You need a good level of mathematical maturity to appreciate this book but nevertheless it is the best way to learn about number theory.
- This is the number theory book. It develops the theory from scratch with no preliminaries. It is very comprehensive, starting with elementary results about prime numbers and goes on to prove some difficult theorems about the distribution of primes, via Fermat's various theorems, irrationals, continued fractions, Fibonacci numbers and so on.
6. Proofs From The Book by Martin Aigner and Günter Ziegler
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- Paul Erdös liked to talk about 'The Book' which contains the perfect proofs for mathematical theorems. Proofs From The Book contains many examples of results which use "brilliant ideas, clever insights and wonderful observations". Many of the topics were suggested by Erdös, though he died before the book could be written.
- It includes the Euclid's classic proof of the infinity of primes, Bertrand's postulate that there is a prime number between any integer and twice that integer, applications of Euler's formula, the pigeon-hole principle (if n objects are placed in r boxes, where r < n, then at least one of the boxes contains more than one object) and its use, amongst numerous other great proofs.
- Paul Erdös liked to talk about 'The Book' which contains the perfect proofs for mathematical theorems. Proofs From The Book contains many examples of results which use "brilliant ideas, clever insights and wonderful observations". Many of the topics were suggested by Erdös, though he died before the book could be written.
7. Ian Stewart
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- Ian, who is professor of mathematics at Warwick University, has written over 60 books on mathematics and related subjects. They vary from course books to theories about the universe. He writes exceedingly well and I like his sense of humour, perhaps because he introduced me to mathematical humour many years ago. For a sample read Hilbert's Hotel, which was published in December 1998's edition of New Scientist magazine, and is a wonderful story about infinity or you could try There are an infinite number of even primes.
- You should enjoy any of his books, including his recent Flatterland.
- Ian, who is professor of mathematics at Warwick University, has written over 60 books on mathematics and related subjects. They vary from course books to theories about the universe. He writes exceedingly well and I like his sense of humour, perhaps because he introduced me to mathematical humour many years ago. For a sample read Hilbert's Hotel, which was published in December 1998's edition of New Scientist magazine, and is a wonderful story about infinity or you could try There are an infinite number of even primes.
8. A Mathematician's Apology by G. H. Hardy
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- I can do no better than reproduce the review on the Internet Bookshop site:
- G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. 'Generations of readers, both in and out of mathematics, have read Apology as one of the most eloquent descriptions in our language of the pleasure and power of mathematical invention'. The New Yorker 'Great mathematicians rarely write about themselves or about their work, and few of them would have the literary gift to compose an essay of such charm, candour and insight ... a manifesto for mathematics itself'. The Guardian 'Hardy's book is carefully reasoned, beautifully written and very stimulating; ... it can profitably be read by anyone'. New Scientist.
- I can do no better than reproduce the review on the Internet Bookshop site:
9. Martin Gardner
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- Martin Gardner didn't study mathematics at University yet he must be the best known writer on mathematics for the general public. He wrote a monthly column in Scientific American for nearly thirty years and these columns, and the books based on them, influenced many students in the world of mathematics. That included me as well as Ian Stewart who went on to write his own columns in Scientific American.
- The books cover a wide variety of what is known as recreational mathematics, from hexaflexagons to flatland encompassing lots of puzzles. You are bound to find an interesting topic in any of his books.
- Martin Gardner's column in Scientific American was succeeded by Douglas Hofstadter. I can't resist writing about a competition he devised (which I previously had wrongly ascribed to Martin Gardner). To win the competition you had to submit the largest number of entries as indicated by a number on a postcard. The prize, however, was $1,000,000 divided by the total number of entries. Douglas Hofstadter convinced Scientific American that they wouldn't have to actually pay anyone and indeed that's what happened. You need to think carefully about the sort of strategy that's required if you want to win. The more you think about it the more intriguing it becomes.
- This is a most unusual competition and you can read more about it at The Largest Number Game and Hofstadter’s Games and in Douglas Hofstadter's book Metamagical Themas: Internet Bookshop, Amazon.
- Martin Gardner didn't study mathematics at University yet he must be the best known writer on mathematics for the general public. He wrote a monthly column in Scientific American for nearly thirty years and these columns, and the books based on them, influenced many students in the world of mathematics. That included me as well as Ian Stewart who went on to write his own columns in Scientific American.
10. A History of Mathematics by Victor J Katz
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- This isn't a cheap book so maybe you can borrow it from a library. I was lucky enough to be sent a copy for review. It looks at various mathematical topics in chronological order using modern notation as far as possible. This is great because one can appreciate the mathematical ideas without stumbling over strange notation. It is a very effective book because it allows one to see clearly how mathematical ideas developed and the fascinating approaches different mathematicians used for the same problems.
- The topics covered are vast, ranging from Early Greek mathematics to modern mathematics such as the four-colour theorem, set theory, topology and Turing Machines, via discussion of the importance of infinitesimals and fluxions in the development of calculus.
- There are lots of biographies included in sidebars, so as not to distract from the mathematics.
- This isn't a cheap book so maybe you can borrow it from a library. I was lucky enough to be sent a copy for review. It looks at various mathematical topics in chronological order using modern notation as far as possible. This is great because one can appreciate the mathematical ideas without stumbling over strange notation. It is a very effective book because it allows one to see clearly how mathematical ideas developed and the fascinating approaches different mathematicians used for the same problems.