Fans pick 100 books like Makers of Mathematics

I have always liked the classical geometry of triangles and circles, but Matt Parker's book helped me go way beyond that and broaden my whole outlook. And the attractively hand-drawn diagrams and zany humour just added to the whole experience. After all, how many maths authors do you know who decide to build a computer out of 10,000 dominoes, just to calculate 6 + 4? 

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.  

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 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.

It is fair to say that many people—even those who loved mathematics as students—view mathematics as having always existed. The idea that definitions and theorems that fill our school textbooks were created or discovered by human beings is something that has never crossed their mind. In fact, mathematics has a long, fascinating, and rich history, and William Dunham’s Journey Through Genius is a perfect introduction to the topic. Dunham expertly writes about the history of topics like geometry, number theory, set theory, and calculus in a way that is entertaining, understandable, and rigorous. After finishing Journey Through Genius, readers will not think about mathematics in the same way, and they will be eager to learn about the history of other mathematical topics, people, and cultures.

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).

First published in 1937, this lovely book is a true classic. In two volumes Bell brings to life 30 or so mathematicians, from Archimedes to Cantor. When first reading the book many years ago I had remembered some of the names from school and college, but only as labels to theorems or equations, and I felt taken into a delightful new realm of knowledge – I could now think of Fermat, Lagrange, Gauss, and Riemann as people. And I began to want to know more about the scientists whose names I had heard in school and college. Bell’s book had sparked a lifelong interest.

Frenkel came from the Soviet Union, where discrimination against Jews made it impossible for him to get into Moscow State University. During the oral exam they sent two graduate students to question him, pick holes in his responses, and ensure he failed. He turned to an informal network of Soviet mathematicians for help.

Like him, they were denied serious employment in the field, but after the 'cold war' against the Soviet Union, Harvard invited him to take a fellowship that later turned into a permanent job. Years later, when his old tormentor from Moscow State arrives to give a talk, he confronts the man in a lecture room with first-hand evidence of allegations against the system. Faced with a victim, the Russian mathematician's denials rang hollow. 

This book reaches beyond mathematics to anyone of independent thought in an environment where it is not permitted to step out of line or,… show more.

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.

John Urschel is an African-American mathematician specializing in graph theory, who recently completed his Ph.D. in mathematics at MIT. But he is better known for his football career, as a starting offensive lineman for the Baltimore Ravens. Six of Urschel’s papers were completed while he was still in the National Football League.

Mind and Matter is John Urschel’s memoir, co-authored with his wife Louisa Thomas. Each chapter alternates between football and mathematics, and how his success on the field translated to success in the classroom, and vice-versa. I loved how accessible the book is, for readers of all ages, and I fully agree with the author’s perspective that mathematics gives us a way of making sense of the world, and helping us see past the confusion of everyday life.