Paradoxes: Guiding Forces in Mathematical Exploration

From simple classifications to detailed explanations behind paradoxes in all fields of mathematics - geometry, calculus, statistics and infinity - this novel has something for everyone. Impressively balancing the line between breadth and depth of content, it is a must-read for anyone who has any semblance of interest in numbers. Hamza makes a compelling case for mathematical paradoxes to become an essential part of any education system, a sentiment that I, as a high school graduate would have deeply appreciated. Had students been introduced to calculus using Zeno’s paradoxes, mensuration using Gabriel’s horn or statistics using Simpson’s paradox rather than diving straight into the mere numerics, perhaps maths wouldn’t be as unjustifiably hated a subject as it is now. Hopefully, the future has such changes in store! For any reader considering giving this novel a read, I must honestly warn you that it requires an immense amount of focus and concentration. While a base level of education in maths helps in comprehension, at times, complicated concepts and mathematicians’ names are thrown at you repeatedly without much elaboration, requiring you to constantly read some parts again and again to absorb all the information. I would have preferred better explanations at some points, even if it made for a longer read. Moreover, there was a lack of structure/important links at crucial moments, driving the point home a little less powerfully than it had the potential for. Several reads reinforce the profoundness/absurdity of some of the more complicated paradoxes but that clarity at some points was definitely missing. Personally, the chapter on infinity was my absolute favourite, as I found that to be the most mind-boggling and profound segment of the novel. However, the usefulness and application of the others must not be ignored - the statistics chapter is a great reminder that much of the “data/facts” we consume are incredibly prone to manipulation while the chapter on geometrical paradoxes served as a discussion on a topic far more intuitive as the rest as we can see physical shapes/figures on a day to day basis. Overall, an educational and insightful read, Paradoxes is a novel I would recommend to anyone even remotely academic, no matter their field of study, whether philosophy, mathematics, science or even the humanities. - Oishee Banerjee

Overall a great intro to the world of paradoxes and especially its relevance to mathematics education--its importance being emphasized throughout the beginning of the book. I recommend it to anyone curious about mathematical philosophy and especially late middle schoolers and high schoolers for a much-needed bird's eye view of what they're learning in math class in relation to how they think critically and of the world around them. The book is not hard to read and follow along for those just brushing the surface of mathematics, because only basic calculus concepts like derivatives and integrals are mentioned and explained briefly. The writing is detailed and pleasantly enthusiastic--simple explanations to some of the most complex paradoxes are very appreciated and admirable. Although this book does not do a hard in-depth look into paradoxes--for example including pages upon pages of detailing out a single paradox, it does a fantastic job of a recap.

This book of paradoxes both appeals to the avid mathematician as well as any interested youth who seek to gain a heightened sense of meaning to the numbers on the pages in school. By leveraging models and graphs as well as historical arguments, this book crafts an narrative for why paradoxes are crucial to understanding the finer details of high level math as well as the backbone for more general math. As a college student, this book brought aspects of math from many fields giving me a taste of what I will experience in upcoming courses. I would recommend this book to someone between the ages of 15 to college aged and older. It was a very good read.