Arnold on mathematics

In 1981, the Soviet mathematician V. I. Arnold wrote a little book attempting to explain catastrophe theory to a general audience. It was translated into English by R. K. Thomas and published with the title Catastrophe Theory by Springer in 1983. At the time, catastrophe theory was somewhat controversial, having its strong proponents and equally strong opponents. It seems to me that Arnold’s attitude was that catastrophe theory is a dose of low-dimensional singularity theory, obscured by a large cloud of mysticism. In the final chapter, “The Mystics of Catastrophe Theory”, he writes: The nice results of singularity theory are happily not dependent on the dark mystics of catastrophe theory. But in singularity theory, as in all mathematics, there is an element of the mysterious: mathematical objects and theories, which at first seem quite independent, turn out to be closely related. One example of such a relationship is the enigmatic (though partly understood) A, D, E-classification. It…