This book has been both exciting and frustrating to read. This book took me about two and a half months to get through, partially the fault of the book and partially the fault that I moved across the world while reading this book. As a preemptive note, I would not recommend this book to anyone who has not covered topics like college calculus, sequences and series, or do not have some familiarity with logic and proofs. I am no means an expert on any of those topics, but I felt having a base knowledge of these topics greatly enhanced and eased (ironic because of how difficult I found this book to digest) my experience.
Wallace does a fantastic job being the kid in the school yard explaining his borderline unhealthy obsession with everyone, but that kid is all grown up and has a off-hand, smart-ass attitude about certain things. As a means of format, aligning with the know-it-all attitude, this book is littered with footnotes that are IYI – In case You’re Interested – that add valuable insight into the topic as a whole, but contain abstractions and explanations that may not be accessible for some readers. Unfortunately, this means you spend a lot of time jumping from the footnote at the bottom of the page, to the last place on the page you struggle to find (which is okay since you’re still digesting the footnote or paragraph you just left or both).
Part of the appeal of the book is the equal parts math and history. DFW walks you through history and explains the challenges faced by society and mathematicians when dealing with the concepts such as 0 in the case of the Ancient Greeks and ∞ and its implications in the case of modern mathematicians. Topics like Zeno’s Paradox, set theory, calculus, and great detail about Georg Cantor are examined and explained in a very accessible way.
This book was indeed a challenge to read — the level of abstraction needed to comprehend the simplifications of immensely complex theories that DFW presents is very heavy and is cause for you to re-read many paragraphs (even acknowledged by DFW preemptively with notes like “Okay, deep breathe”, “Be prepared to read this more than once”, etc.), subsequently slashing my reading pace to a sails pace. It took a lunch break and an hour and a half to read the last 25 pages — there was a lot of pausing to think.
But at the end of the day, or the end of a page, you always felt like you learned something and always had a laugh with DFW’s off-hand and sarcastic tone sometime. Some of the footnotes were apologies for not addressing a topic sooner or openly addressing his editor’s notes, almost like he wrote the book and came back the next day to fill in all the extra things he forgot to say or expand on.
For anyone who appreciates mathematics in it’s pure form, enjoys expanding your horizons and stretching your brain, and enjoys (and follows) entertaining tangential thoughts and fragments of information and sarcastic tones, this book is worth reading.