Once Upon a Number
Once Upon a Number is nominally a book about the intersection of mathematics and storytelling - two subjects that don't, intuitively, seem to have much to do with each other. From the cover blurb, it seemed as if Paulos was trying to present a kind of "mathematics of stories" — something I found rather implausible, since creating a working formal model of general storytelling seems to me to most likely be equivalent to constructing general artificial intelligence.
Fortunately, that's not what this book is. In fact, it doesn't really seem to argue any central point at all, it's more of an exploration than a presentation. It's structured as a small collection of essays, mostly concerned with how math itself can contain stories, and how stories can contain math.
The ﬁrst essay shows the relationship between informal anecdotal stories and statistics - in essence, how statistics emerge from such stories (and how much detail statistics must necessarily disregard). Paulos argues that humans have a kind of intuitive sense of statistics arising from the pattern-matching nature of our minds, although this intuition can unfortunately rather easily fall prey to trickery. The second focuses on interpretation and representation of the external world - again, with some focus on how the human tendency to look for patterns can sometimes lead os to ﬁnd spurious ones (such as the "Bible Codes"). The third essay contrasts intensional and extensional logics, and while that discussion was certainly interesting, I particularly enjoyed the "chapter appendix" that contained an extended speculation about humour and formal systems (that, curiously, mirrored my own initial reflection that creating a "mathematics of stories" would be equivalent to making general AI - at least insofar that these are humourous stories). The fourth essay gives an extended exposé on information theory and complexity (the Kolmogorov variety, not the one usually studied in algorithmics and theory of computation), and the ﬁﬅh and ﬁnal gives some speculation about how we can "bridge the gap" between stories and statistics.
Overall, I enjoyed it. In particular, the humour and wordplay worked really well - and while the general public might probably be surprised to ﬁnd so much of it in a mathematics book, some of the funniest people I have ever known have been mathematicians.
Its greatest ﬂaw was Paulos' tendency to ramble. It sometimes uses mathematical terminology before introducing and explaining it. I'd usually not even notice this - but then, I studied theoretical computer science, and I already know what, for example, Bayes' theorem and intensional logic are. My girlfriend, who's currently reading it too (and who studies law, not theoretical computer science), did notice, and would occasionally have to go back and re-read passages once she got to the relevant explanation a few pages later.
But I can forgive rambling given a fascinating subject and an ability to present it with wit and humour. Recommended.