The prior post noted John Allen Paulos as recipient of a math communicators award for 2013. In 2001, that very same award went to Keith Devlin, and the more I read from Dr. Devlin, the more I'm blown away by his talents/insights… Keith is as close as it gets to being a "rock star" in popular mathematics (...he even sounds a bit like Paul McCartney!). If I was a Devlin fan before, I'm a near Devlin groupie now after reading two more of his volumes this month.
His latest book, "Introduction to Mathematical Thinking" is possibly the best 92-page, slim math book with a blue cover, and a 4-word title, written by someone with the initials "K.D." I've ever read ;-) …no, seriously it is a fabulous book that packs more into 92 pages than most books twice that long. But having said that, it is NOT an easy read (AND there's hardly any actual MATH in it! much more logic and set theory) -- it was the basis for the recent MOOC course, of the same title, Keith taught in the fall, and I can understand why most of the 1000s of students who signed up dropped out of the course… I'm sure the material in this book is NOT what they were expecting.
I'm not quite finished with it… but when I am, I will need to start all over and read through it again… much more s-l-l-l-l-owly and carefully. The slimness of the volume disguises the density of the ideas. Again, if you're happier just 'doing' math and feel no need to 'understand' what underlies it, this volume WON'T be for you, but if you want to pull the curtain back and try to grasp what is happening behind the process that delivers math's whiz-bang results, read and savor these 92 pages.
Below is a recent, and excellent podcast interview with Devlin specifically on his experience with his first-ever MOOC course -- for anyone interested in MOOCs, this is must-listening, so set aside the hour required to hear Keith out. If you're not interested in MOOCs you can skip it… but if you're concerned about the future of education at all, you should be interested in MOOCs!:
The other Devlin book I just finished (stumbled upon in a used book shop) is an older work (1997), "Goodbye Descartes" which I'm tempted to call the richest work of Devlin's I've read -- chockfull of interesting discussion of logic, philosophy, linguistics, cognition, artificial intelligence… covers a LOT of ground. Once again, NOT necessarily much "mathematics," just a great deal of thought-provoking material related to the cognitive processes that impinge on mathematics.
The book ends with a subject Devlin christens "soft mathematics" -- I'd never heard of the concept before, so I'm not clear if it has gained much traction since he introduced it (and I'm not myself convinced of its utility), but you can never sell Keith short. The idea is that, just as there are 'hard' sciences (physics, astronomy, engineering…) and 'soft' sciences (sociology, psychology, economics….) we need a different sort of (soft) mathematics to study various human problems. If you don't want to wade through "Goodbye Descartes" (but you should ;-) you can read a synopsis of this particular idea from the below older Devlin column:
an excerpt from it:
"There is little or nothing [in soft mathematics] that looks like, or is, traditional mathematics. There may not even be any mathematical symbols tossed around -- though in many cases there are. Soft mathematics is not mathematics as that discipline is generally thought of, and it remains an open question whether at some time in the future our conception of what constitutes mathematics will change to incorporate such activities…He then goes on to use Paul Grice's analysis of everyday conversations as an example of soft mathematics.
"What is clear, however, is that the mathematical way of thinking is such a powerful one that, when applied in a soft manner, it has on occasion led to considerable advances in our understanding of various phenomena in the messy, and decidedly non-mathematical social realm of people. One of the best examples I have come across was in the field of linguistics…"
Anyway, while I found the notion of "soft mathematics" mildly interesting, I found the 10 chapters that preceded it FAR moreso!
I might say more about one or both these books at some point in the future (they contain so much grist for discussion), and also may have some more Devlin material coming up shortly... but, that's all for today.
...And Merry Christmas everyone!!!