**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.