ordinary human activities should keep it gentle and clean," wrote G.H. Hardy (1877–1947) in A Mathematician's Apology (Hardy, 1967, p. 121). For their part, physicists often assumed that once they had learned some rough-and-dirty techniques for using such mathematics as calculus and differential equations, mathematics had nothing further to teach them.

Over the past couple of decades, work in dynamical systems (and in other fields, such as gauge theory and string theory) has resulted in a rapprochement between science and mathematics and has blurred the once-clear line between pure and applied mathematics. Scientists are seeing that mathematics is not just a dead language useful in scientific computation: it is a tool for thinking and learning about the world. Mathematicians are seeing that it is exciting, not demeaning, when the abstract creations of their imagination turn out to be relevant to understanding the real world. They both stand to gain, as do we all.


Hardy, G.H. 1967. A Mathematician's Apology. Cambridge University Press, Cambridge.

Hubbard, John H., and Beverly H. West. 1991. Differential Equations: A Dynamical Systems Approach. Part I: Ordinary Differential Equations. Springer-Verlag, New York.

Kline, Morris. 1959. Mathematics and the Physical World. Thomas Y. Crowell, New York.

Krantz, Steven. 1989. The Mathematical Intelligencer 11(4):12–16.

Lorenz, E.N. 1963. Deterministic non-periodic flows. Journal of Atmospheric Science 20:130–141.

Moser, Jürgen. 1973. Stable and Random Motions in Dynamical Systems. Princeton University Press, Princeton, N.J.

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