Visions of Infinity
By Ian Stewart
The book Visions of Infinity talked about some of the very important discoveries made my mathematicians in the past. One aspect of this book that I enjoyed was the position that was taken on presenting these discoveries. This book stayed away from long, confusing proofs of mathematical discoveries. Instead of focusing on the actual mathematics of certain people, this book focused more on the thought process behind the math. Throughout the book, many different theorems and conjectures are discussed, as well as how each of these was thought about. Some of the problems that are talked about are the millennial problems. These problems offer a hefty reward of $1,000,000 if they are solved. While there have been numerous attempts to solve these problems, only one of the problems has been solved so far. Visions of Infinity covers a spectrum of topics. These topics range from simple things like prime number and the four color theorem to the Mass Gap Hypothesis.
This book does a good job of making the topics readable to an audience that is not an expert in mathematics. However, I don’t think that this book is a good read for everyone. Even though Visions of Infinity does a good job putting much of the information in simpler terms, there were a few parts that went clear over my head. I know that I am no master mathematician by any means, but I would like to think that I have more experience and a better understanding of math than the general population.
Overall I think that this is a great book to read if you are interested in the mathematical discoveries throughout history, and have at least some knowledge of upper level math. I really enjoyed reading about how each of these discoveries has progressed over time and the contributions of the many mathematicians over the years. I also liked seeing that each of these discoveries required the work of so many different people. I would recommend this book to any undergrad math student with the advice to take the time to really this book, as it is not a quick read if you want to really understand it.