Why should a journal like New Blackfriars be looking retrospectively at books about mathematics? A short answer is that mathematics, or at least the myth of mathematics, affects the way we think. I shall be looking at two books which demythologise mathematics: The Mathematical Experience and Mathematics: The Loss of Certainty by Morris Kline. These help examine the myths of proof—the myths about how mathematicians think. Part of the demythologisation process is to look at alternatives to the myths; in particular I shall look at the role of intuition, and will illustrate this with reference to Catastrophe Theory and Gödel, Escher, Bach.

The prompting for this investigation is the emergence of a new genre of books about mathematics following in the wake of Gödel, Escher, Bach, of which The Mathematical Experience is an example. It would be a fascinating aside to trace the rise of this genre from Fourteen Funny Bits of Mathematics in Avuncular Style as found on the shelves of most public libraries, alongside popularisations of pedestrian seriousness. No doubt it would mention the science-as-a-human-activity school as exemplified by Koestler’s The Sleepwalkers, or Watson’s The Double Helix, a vein continued by Catastrophe Theory. It would take a venture into catastrophe theory itself to explain the emergence of Gödel, Escher, Bach—a rogue book which won the Pulitzer Prize in 1980 for general non-fiction, a picaresque which takes in the art of fugue, Zen koans, and the Jabberwocky and leads to questions at the heart of some of the problems in the foundations of mathematics and of artificial intelligence, while remaining accessible to a child of twelve (albeit the one I know is quite bright). The audience the genre aims at seems to be not so much the interested layman, but more the new technical elite whose computer skills and mathematical awareness can be used to outflank the experience of their seniors. In my years in radar design it was interesting to watch the gradual take-over of certain departments by mathematicians in spite of the active opposition of the electronics-trained managers. In my last department over half the people there had copies of Gödel, Escher, Bach.