Books like Fermat's Enigma — picked by fans

A primary reason to love math is because of its usefulness. This book shows two sides of math’s applicability, since it is so ubiquitously used in various algorithms.

On the one hand, such usage can be good, because statistical inferences can make our life easier and enrich it. On the other, when these are not properly designed or monitored, it can lead to catastrophic consequences. Mathematics is a powerful force, as powerful as wind or fire, and needs to be harnessed just as carefully.

Cathy O’Neil’s message in this book spoke deeply to me, reminding me that I need to be always vigilant about the subject I love not being deployed carelessly.  

Math is so much more than algebra.

Steve Strogatz is our generation’s poet laureate of math. I could not put this book down because, although I use math daily, I was amazed at how Strogatz connects everything to everyday experience. Just one example: Hardly anyone gets told about “group theory” in high school because it’s “too advanced”—but here we find it beautifully illustrated with the problem of flipping your mattress twice a year.

This book will help you have your own ideas by opening your eyes to a world of things that just make better sense through the lens of careful analysis, the interplay of the visual and the symbolic, and (just enough) abstraction.

This classic rumination on the nature of mathematics is perhaps the most famous book ever written by a mathematician.

I’ve read it several times, and each time, it brings up another facet of the subject in some new light. Portions of what Hardy says ring eerily true, and seem to be part of the identity, the very DNA, that all mathematicians must surely share. Other parts seem so alien to be almost repugnant – such as his contention that most mathematics we classify as useful is ugly and inelegant.

I’d love to argue face-to-face with Hardy about this highly opinionated work of his. In the end, I suspect we’d find lots of common ground, since intrinsically, we both love mathematics so much.

For me, this book got the closest to the nitty-gritty of why mathematicians like me, whose job is to prove theorems, find this activity so compelling.

It’s always been the long hunt, with all the frustration as well as the occasional success, that I’ve found so addictive. Doxiadis brought out the nuances of such pursuits brilliantly – the wily Uncle Petros tells the narrator to prove a mathematical statement despite knowing it is almost surely false.

Ah, these little tricks that we mathematicians enjoy playing on unsuspecting souls (I’ve been known to do this to my students a couple of times).

It provides an engaging description of the work that went into proving a famous result, first mentioned by the French mathematician Pierre de Fermat in the margin of a book.

The question was whether a sum of two nth powers of whole numbers could be the nth power of a whole number. It is certainly true for n = 2 but was not known for any n greater than 2. Fermat thought he had a proof that this was the case but later wrote proofs when n was 3 or 4, so his earlier claim was not taken seriously.

The general result turned out to be much harder than anyone imagined, and 350 years later, its truth was implied by another conjecture that was finally proved by Andrew Wiles, as this book explains. I admire the fact that the author distills some essential points from what turned out to be… show more.

This book has haunted me for years. For what is it, exactly, that gives it such enduring popularity? After all, it was first published in 1936, yet is still in print today. In his autobiography, Hogben remarks on the importance of eye-catching illustrations but speculates that its success may instead be because the book contains – most unusually for a 'popular' work – exercises and answers, making it more suitable for self-teaching. Whatever the real answer, his book must surely have something to teach anyone – like myself – who aspires to bring mainstream mathematics to life for the general public.

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

This is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.  

In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.

My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.

The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.

I highly recommend this book as a second book on linear algebra.

Reuben Hersh is responsible for a revolution in the way we look at mathematics. His main idea is very simple: mathematics is something that is created by human beings. Isn’t that obvious, you say? Not if you believe that mathematics is there even before life itself, that it is built into the nature of reality in some way. In philosophy, this view is called Platonism. Hersh had the radical but obvious idea that if we want to understand what mathematics is we should look at what mathematicians actually do when they create mathematics. Like all great ideas it can be stated very simply but the implications are enormous. His ideas are what got me started writing my own books about math and science.