Math Mutation Classics
Since 2007 Erik Seligman is regularly posting math related podcasts. His texts are made available at his Math Mutation blogsite that he maintains since 2011 sometimes with some illustration and with extra references. Seligman has a B.A. in Mathematics and a M.S. in computer science. The topics are (as the subtitle of the book says) "Exploring interesting, fun and weird corners in mathematics", although some subjects are not really, or only remotely related to mathematics. As a computer scientist, he works as a Formal Verification Architect at Intel Corporation. Also that shows in his subjects that are sometimes more computer science than mathematics. But is not computer science, like many other sciences, some kind of applied mathematics.
In this book he has collected 214 of these texts. Some are a bit polished, some are summarizing more than one of the originals podcasts that were closely related. They are grouped into 13 chapters with 8 to 12 podcasts where the texts are collected with related subjects. The references are listed in a separate part of the book collected per podcast. They are often links to Wikipedia pages or other sites. I wonder why this is done in this way. I think it would have been more appropriate if the references were added at the end of the text of the podcast. Of course the many links are easier to deal with in an electronic version of the book like the original website. However, the podcasts and the corresponding blogs that were included in this book were removed from the website for copyright reasons. Publishing this book is just a way to make money out of it, but also it is a way to reach a wider readership. If the book had not appeared, I would probably never have heard about Math Mutation. An index of three pages at the end of the book is helpful to find some topics treated in the 183 pages of dense print, although a more extensive index would have been better to retrieve for example Borges, or John Cage, and many other proper names that are hidden in the haystack. The original website didn't have a search facility either. Again, an electronic version allows to search for any string you like.
It is of course impossible to go in this review through all the subjects discussed in the book. Some "classic" topics in popularizing mathematics books of course do also pop up here (Benford's law, Monty Hall problem, Hilbert's hotel, Flatland, Penrose tiling, fractals, etc.) but many are really original topics. For example Flatland by E. Abbott is discussed in a chapter on dimensions, but we also find there some thoughts about the physics of a 2D world, and we meet the less known Sphereland, a sequel that Abbot wrote, and Planiverse by A.K. Dewdney, which is a world on the surface of a sphere. Furthermore projection of a 4D object in a 3D space, fractal dimensions, the 11D world of string theory, etc.
Cosmology and the theory of our universe has of course mathematical foundations, but the chapter on the mathematical mind, although it starts with autistic savants like e.g. Daniel Tammit is related to how our brain handles mathematics, but it also has some texts that are more remote from mathematics e.g. when it comes down to make the (English) language less ambiguous or more easy to pronounce or avoid the use the verb "to be" because it has too many overlays. In such topics, the mathematics are only echoing remotely behind the computer scientist's interest.
So, Seligman looks beyond the strict boundaries of mathematics, but his topics are very well chosen and he looks at them unable to deny his mathematics and computer science roots. The leitmotifs of the chapters include geometry, infinity, dimensions, skepticism, arts, politics, finance, paradoxes, the mind, life, and some others. Thus the variety is very diverse. I do not think it is required or even the best way to read the sections by chapter. Reading them in a random order is I believe more entertaining than binge-reading them by chapter.
I think this is a wonderful collection of columns that will be appealing to any reader. You will learn about SCIgen (a system to automatically generate computer science papers); psychochronometry (why time seems to run faster as you grow older); the library of Jorge Luis Borges; Max Tegmark's mathematical universes; Gabriel's horn (which has an infinite surface, yet finite volume); the gnarliness of Kurt Vonnegut's Slaughterhouse Five; how to resolve the ship of Theseus paradox; Greg Fox's Carmen of the Spheres (electronic music based on the movement of the planets, realizing a true Music of the Spheres); and there are many, many more gems to find here. The whole collection it warmly recommended.