100 books like Man Must Measure

David Hilbert was the most important mathematician at the dawn of the 20th century. In 1900, he gave the mathematical community its homework for the next 100 years setting out the list of open problems that had to be solved by 2000. While to the rest of the mathematicians, he may have appeared as their professor, he was also the class clown. As colorful and funny as he was brilliant, you cannot but come away loving this great mathematical genius.

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.

The Scientific American columns of Martin Gardner ran for 24 years and were read by amateurs, semi-amateurs, professionals, and major mathematicians (Conway, Knuth, Diaconis...). It was the interaction with this audience (recorded in addenda) which gave these essays their special quality and will give the interested outsider a real feel for what interests mathematicians. The collected columns are being reissued by the AMA and CUP but my view that anything by Martin Gardner is worth reading is reflected in my personal library.

More mathematicians than you might expect have had eventful lives (and most of the others are grateful that they did not). Fourier, one of my mathematical heroes was twice in danger of the guillotine, played a substantial role in Napoleon’s Egyptian campaign, is known as one of the Fathers of Egyptology, and was the first person to write about the ‘green-house effect’. To mathematicians and physicists this is all secondary to his work on heat conduction and, of course, the Fourier series. Herevel is an excellent guide to a remarkable life. (Herevel also had a non-standard career — the ‘Herevel tip’ was instrumental in early successes against Enigma.)

We love all of David Macauley’s books. He uses hand-drawn black-and-white illustrations to describe the enormous effort and complicated processes involved in building some of the most magnificent structures in the world, from cathedrals to castles to pyramids. Cathedral was his first, and we think the best. Although intended for young readers, there are many builders, engineers, and architects that find wonder in Macauley’s work. 

I laughed out loud as I joined this family of twelve children on cramped car trips, through childhood pranks, adolescent rebellion, and through the daily joys and growing pains of a loud and loving family. My dad is one of eleven children and reading this book reminds me of many of his stories about growing up. I especially related to the clatter of dinner time conversation centered around morse code or math games. We never did morse code but we’ve played plenty of math games and word riddles.

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.

This is a beautiful book filled with glossy color photos, that would be a lovely gift for any girl or woman interested in mathematics, or really, any human.

Inside the book are the “rebel women” who have specialized in mathematics (and yes it seems you still need to be a rebel to succeed in this male-dominated field). I learned so much about the mathematics the women studied and created, as well as the ways they battled for recognition to be able to contribute to mathematics.

The book is filled with powerful and creative mathematics produced by inspirational women.

Leaving me equally tickled as it did in awe, Flatland is easily one of my favorite books of all time.

Delving into concepts quite difficult to think about, let alone explain in such a delightful way, it expanded my mind into not only a better understanding of ‘dimensions’ but also the possibility, and even, the probability, that there is much more in existence than our rather limited little human brains can comprehend.

As weird as it is wonderful, I found myself stopping at various points to either laugh or to try to explain to someone else (to their annoyance I’m sure!) the profound details it explained to me. And when it was all over I was left humbled, and pondered what greater beings there may be all around me, that I simply cannot see.

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.