100 Books Like Infinite Powers

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. 

When I saw this book, translated into English in 2009, I was very skeptical. I’d never enjoyed a graphic novel, and even though I’d enjoyed math in school, I couldn’t imagine reading an entire book devoted to the history of the philosophy of mathematics.

But somehow the sheer audacity of what they had attempted made it catnip to me, and before I knew it, I’d inhaled the whole thing and felt high on the feeling that anything was possible. If this could be a graphic novel, I thought feverishly, couldn’t my old obsession, Maria Lani? If only I could find an illustrator who felt the same way….

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.

The author explains the importance of abstraction in logic, demonstrating its three main components: paths made of long chains of logic, packages made of a collection of concepts structured into a new compound unit, and pivots to build bridges to previously disconnected places.

Eugenia Cheng does an excellent job of abstracting principles of logic to better understand challenging real-world societal issues such as affirmative action and cancer screening. I found it quite compelling to understand how and why she came to her positions on various issues, through her axiom that "avoiding false negatives is more important than avoiding false positives." I appreciated the expertise by which she weaved numerous hard topics, in both mathematics and social justice, into a coherent and compelling narrative.

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 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 book is full of beautiful puzzles on a mathematical topic called pursuit evasion. Its author Paul Nahin has written tens of books in physics and mathematics.

Nahin's writing can be described as a captivating reading experience pulling readers into his world like a whirlpool. His appreciation of mathematics, physics, and the people who discover them is unmatchable. It seems like the physics of motion and the mathematics of calculus is inseparable, as can be witnessed in the book.

The calculus used in this book is heavy. Nevertheless, Nahin makes his readers fall in love with this big beast. Almost every puzzle in this book is aesthetically beautiful and gives readers a deep sense of satisfaction. My favorites include Lady in the Lake, and Lion and Man.

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.

Many people associate mathematics with calculating things or plugging numbers into formulas to get answers to a multitude of problems.

But this isn't how mathematicians view their discipline. They see mathematics as more about starting with definitions of key mathematical concepts, stating axioms about these concepts, and proving things about them. For those interested in going from calculating and plug and chug mathematics to "real" mathematics, Richard Hammack's book is a terrific place to start.

The book covers a number of topics that cut across all of pure and applied mathematics, topics such as sets, relations, and functions. But the heart of the book is focused on how mathematicians go about proving things. If one wants a glimpse of how mathematicians really work, go out and get this book immediately.  

Most of us figure doing evil, even if good results, is not ethical but without this, there would be no medicine. Martin Pernick covers the discovery of anesthesia and the ethical dilemmas this new ability to save lives by poisoning people posed. Anesthesia is a technique and techniques are amoral. How do we ensure they enhance rather than diminish us? How do we avoid seduction into a sleep during which we can be cosmetically enhanced? Is there a limit to how many drugs we give children to manage their behaviour – just because we can? Treating and stopping are not the same as not treating. Pernick doesn’t tell us how to manage this calculus, but he makes us aware modern life involves more of a calculus than we might have thought.