When I was a teenager, I used to read a lot of popular science and math books. Of course, by “popular”, I just mean books meant for a nonspecialist audience (like a kid without a degree). A lot of those books inspired me to actually go on to study mathematics at university. Here are five of my favourites. Some of them are old now but because of the timeless nature of mathematics, they are not out of date.
1. Ian Stewart’s “Does God Play Dice”
Chaos, or sensitive dependence on initial conditions, is a profound idea in science that goes against the classic Newtonian reductionism and is the concept that one cannot necessarily predict the outcome of complex systems. Ian Stewart explains chaos in his book “Does God Play Dice”. The ideas in this book are a constant influence in my life to this day.
2. William Dunham, “The Mathematical Universe”
I read this book in my final year of high school (and I still remember the day a math teacher commenting that he liked the book also). This book takes an A-Z tour on various mathematical topics. It is more classical than some of the other books here, covering topics such as angle trisection and the foundations of probability. I like that each chapter is short and readable, isn’t shy about including mathematical details and equations, and yet contains a good amount of historical storytelling as well.
3. Simon Singh’s “The Code Book”
If there were one introduction to cryptography I would recommend, it would be Singh’s book. It covers everything from the Caesar cipher to public key cryptography. Of course, being twenty years old, it does not delve into the latest developments and the possible replacement of the standard public key schemes with postquantum schemes, but it is a highly entertaining read nonetheless.
4. Steven Levy’s “Crypto”
While Singh’s book above covers all of cryptography, Levy’s book concentrates on the disruptive events following the introduction of public-key cryptography, a truly wonderful and inventive idea without which we could not have encrypted communications on the internet today.
Levy’s book focuses on characters and conflicts, and is a cohesive story that would make a great movie.
5. Simon Singh’s “Fermat’s Enigma”
Another book by Simon Singh? That’s because he’s one of my favourite popular math writers. Fermat’s Last Theorem, the statement that there are no nontrivial integer solutions to $x^n + y^n = z^n$ when $n\geq 3$ is an integer is one of the most famous problems in all of mathematics.
Fermat’s Last Theorem is also one of those problems that is an inspiring story, because it is one of those occasions where a single individual (Andrew Wiles) works away in complete isolation to take down a behemoth. Of course, he did have some help in the end.
Before Andrew Wiles though, there was significant partial progress towards a solution to this fiendish problem, and also many wrong turns. The story of Fermat’s Last Theorem and its eventual solution is one of the coolest stories in mathematics, and Simon Singh does a perfect job of telling it!