Sleight of Mind offers “75 ingenious paradoxes in mathematics, physics and philosophy” – and there are many classics here – the Monty Hall problem; the Hilbert hotel; Feynman’s sprinkler; Achilles and the Tortoise.
I was expecting a rather breezy discussion of the puzzles and paradoxes – along the lines of Julian Baggini’s popular book The Pig That Wants To Be Eaten – but it’s actually WAY more technical than I anticipated. I studied Godel’s incompleteness theorem, Arrow’s general possibility theorem and Cantor’s diagonalisation argument at university – none of them in introductory classes. I did not find Matt Cook’s treatment to be dumbed down relative to that level – it was more like being taken back to a classroom surrounded by a small number of very intimidating mathematicians…
Cook’s treatment of the problems is perfectly lucid but for those without a background in mathematics or logic it is going to require some very hard thinking.
All that said: there’s a lot to enjoy here, if you feel up to it. And if you’re studying a relevant degree this is a great resource.
An alternative for the generaly reader is Raymond Smullyan’s wonderful book of puzzles, What Is The Name Of This Book? It starts gently, one brain-teaser at a time, but by the end of the book you’ve gone deep into powerful ideas of logic and mathematics.
My NEW book The Next Fifty Things That Made the Modern Economy is NOW OUT. Details, and to order on Hive, Blackwells, Amazon or Watersones.
Bill Bryson comments, “Endlessly insightful and full of surprises — exactly what you would expect from Tim Harford.”