100 books like Fermat's Enigma

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.

The Univalent Foundations program in foundations of mathematics launched by Voevodsky and others in the past decade and a half has contributed to a promising new paradigm unifying computation, mathematics, logic, and proof theory.

Understanding the core elements of this research program, Homotopy Type Theory, is essential for contemporary philosophers who want to engage directly with current developments in mathematics and computer science.

Corfield is a well-established name in philosophy of mathematics, and this book is the best introduction to Homotopy Type Theory for philosophers.

Working within themes and problematics that will be familiar to philosophers with a basic background in logic, Corfield covers the elementary constructions of homotopy types from a logical point of view and provides plenty of provocative suggestions for how these formal tools might reinvigorate philosophical research today.

This book is not about computing, but it is relevant in an indirect way. I love this book, since it is written in such an engaging style and illustrates with many examples that math is not a dry subject to be practiced only by mathematicians but helps everyone to solve real-world problems. The book shows how important it is to be precise in describing problems and that applying a little mathematical rigor goes a long way in solving them. Ellenberg describes mathematics as the “extension of common sense by other means.” In a similar way, I view computer science as the extension of problem-solving methods (aka “algorithms”) by other means. 

What child isn’t curious about the night sky and all the stars that live up there? Did you know that the Sun is a giant star?  This book is full of fun facts, not just about stars but about our planet. It helps to put things into perspective, so to speak. It talks about gravity and how many miles away the moon is from the earth. I think kids will learn a lot from reading this book and will even be able to impress their friends with all of their newly acquired knowledge. Did you know the earth looks green because it’s covered in 3,000,000,000,000 trees?? I love this book because learning new things is fun and this book is all about fun. I felt very smart after reading this book.

Mathematics requires accurate calculation, and students sometimes think that getting the right answer is enough. But mathematics is also about valid logical arguments, and the demand for clear communication increases through an undergraduate degree. Students, therefore, need to learn to write professionally, with attention to general issues like good grammar, and mathematics-specific issues like accuracy in notation, precision in logical language, and structure in extended arguments. Vivaldi’s book has a great many examples and exercises, and students could benefit from studying it systematically or from dipping into it occasionally and reflecting on small ways to improve.

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.