100 books like Cornell University, Cornell Studies in Classical Philology, No. III. The Cult of Asklepios

This book is a perfect story. It has a beginning, a middle, and a satisfying ending. I love it because I’m guilty of overthinking many things.

I also love books that take you on a journey. As an armchair traveler, the best adventures make me leave my chair, taking me somewhere far away, at least until dinner. 

Rarely have I opted to read a book twice, but the love story between Catherine and Heathcliff is so well written and so emotionally charged it drew me in and made me forget I was alone and single. Of course, I had to re-read it.

The first time I read this book was in school, but later, when I dreamed of having a true love, or learning about true love, this book seemed to be the case study of the type of love I was searching for. I knew in my heart, that someday, something similar could possibly be mine.

My grandparents were Irish, which explains why Celtic mythology speaks to me. I hadn’t heard of Dream Angus (aka Aengus) until I read this book, by which time it was too late to quiz my ancestors on this impish Eros, golden-haired bearer of dreams. It was said that sometimes he kissed lovers and, when they parted, the kisses turned into songbirds who followed them home, serenading them with love songs. The author intersperses his telling of the legend with contemporary stories set in Scotland where one of the characters is especially influenced by an aspect of Dream Angus’s personality, sometimes good, sometimes quite the opposite. Angus lives on in a lullaby recorded, among others, by Barbara Dickson. It’s both haunting and sweet, just as love can be.

To some, lucid dreaming (realising you’re in a dream while still dreaming), might come naturally. But if it hasn’t, and you’re willing to spend three weeks practising the techniques, the benefits are well worth it. These include: learning to banish nightmares; developing one’s powers of choice and control; healing and restoring aspects of one’s personality that are limiting personal growth. I used to keep a dream journal, mainly to check whether any dream had been predictive, but lucid dreaming is a completely different ball game, aimed at transforming one’s everyday life. As a writer, I am particularly interested in the benefit of boosting creativity. This is a book for really serious dreamers.

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.

For decades, the most famous opening chord in rock and roll was an unsolved problem, since no one could reproduce it. But in 2004, Jason Brown, a professor at Dalhousie University, used mathematics to recreate the opening chord of the Beatles hit song, “A Hard Day’s Night”. I remember when newspapers around the world reported on Jason’s findings, as I was at Dalhousie at the time, as one of Jason’s Ph.D. students.

Jason’s Beatles story serves as the final chapter in this wonderful book, a collection of short vignettes about how mathematics relates to every aspect of our lives, including garbage pickup routes, grocery shopping, political polling, and social networks. The book’s thesis is that as we understand mathematics better, our lives become more meaningful. I couldn’t agree 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 remarkable book is authored by Francis Su, the past president of the Mathematical Association of America. The author describes human flourishing as follows: “a wholeness of being and doing, of realizing one’s potential and helping others do the same, of acting with honour and treating others with dignity.” He explains how human beings, of all ages and ability levels, can experience flourishing through the doing of mathematics.

In each of the final twelve chapters, the author explores a trait of mathematics, how it relates to our journey as humans, and how the development of each trait enables us to flourish: Exploration, Meaning, Play, Beauty, Permanence, Truth, Struggle, Power, Justice, Freedom, Community, Love. As a mathematical researcher and educator, I have experienced these traits first-hand, and recommend this book to anyone and everyone.

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.

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.