Bryan Bunch

About every month or so, diagrams go around social media proving various paradoxes. From proving 2 = 3, or that certain infinite series converge to -1/12, these proofs often use fallacious logic or hidden steps to achieve their ends. Bryan Bunch’s Mathematical Fallacies and Paradoxes collects eight such examples to help broaden our understanding of both logic and math. Be wary, though, this is not for the faint heart.

Bunch’s paradoxical exploration looks at simple divide-by-zero proofs, then looks at linguistic and philosophical paradoxes, and on to geometrical oddities and ancient paradoxes (including Zeno’s paradox). Each one is a step up from the previous so as to ease the reader to the math involved. Bunch does, however, assume some level of mathematical literary on the part of the reader. Back in the day, I entertained the idea of becoming a mathematician, but my love of literature and language got the better of me. So, for me, Bunch’s collection was a little nostalgic, dusting off a few unused areas of my brain. All in all, it’s a perplexing book, but in a good way.… (altro)

How did I enjoy thee? Let me count the ways.

This book isn't for everyone, but if you like numbers, this is an incredibly fun book. It is like a field guide to animals or insects or rocks: It is a list of numbers you might encounter, and what their characteristics are. So the number four is a square, six is triangular, and so forth. All the smaller positive integers are covered, and some larger integers. After that, we get into fractions, algebraic numbers, even such things as Liouville Numbers -- numbers which are not the solution to any algebraic equation.

To me at least, those are the really fun part. Sure, it's interesting that eight is the first even cubic number, or the like -- but those sorts of things we encounter in relatively ordinary life. Liouville Numbers? I have a math degree, and I'd never heard of them.

Scattered through the book are little excursi on number theory topics. These too are quite pleasant.

And the best part is, it all takes very little mathematical knowledge. (That's perhaps the best part of number theory.) Mathematicians may be the most likely to appreciate this book, but there really is something here for everyone. Go ahead, give it a try. I suspect you'll read more of it than you expected upon opening it.… (altro)