For better or for worse, we are both the beneficiaries and the victims of a technological age. Every year brings new discoveries, new inventions and new technological advances, with resultant changes in the patterns of society and our modes of life. Indeed, there have been more scientific advances since 1900 than in all preceding centuries, and more advances in the last ten years than in any preceding decade. Nowadays, to be entirely innocent of science, to have no appreciation of the scientific temper, is to be increasingly out of touch with our times. Characteristically, as sciences advance they continue to become increasingly mathematical.

Let us content ourselves with just one example. Meteorology was as unscientific as it was unmathematical until it became possible to make quantitative measurements of atmospheric pressure. Until then weather forecasting was limited—with correspondingly limited success—to applications of such rough generalized observations as: red sky in the moming, shepherd's warning; red sky at night, shepherd's delight. With the invention of the barometer, the science of meteorology was born. Now that we are aware of upper air jet streams and have upper atmosphere photographs from satellites—with more mathematical physics to exploit more data—we have more success in weather prediction.

We hope that this preamble will entice readers to soldier on in pursuit of the role of mathematics in science, and that they will sense the mystery of it, the power and the glory: that the world is comprehensible; that with the hieroglyphics of mathematics, with pen and paper, we can hitch a pair of scales to a star and weigh the moon.