The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathematical concepts, particularly those that have found application in current scientific research.The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Richard D. Anderson of Louisiana State University, George E. Carrier of Harvard University, Hirsh G. Cohen of the International Business Machines Corporation, Richard C. DiPrima of Rensselaer Polytechnic InstituteRobion C. Kirby of the University of California at Berkeley, William H. Kruskal of the University of Chicago, and George D. Mostow of Yale University.

Table of Contents:

Preface

Mathematics Today / Lynn Arthur Steen

Part One
Mathematics-Our Invisible Culture / Allen L. Hammond

Part Two
Number Theory / Ian Richards
Groups and Symmetry / Jonathan Alperin
The Geometry of the Universe / Roger Penrose
The Mathematics of Meteorology / Philip Thompson
The Four Color Problem / Kenneth Appel and
Wolfgang Haken

Part Three
Combinatorial Scheduling Theory / Ronald Graham
Statistical Analysis of Experimental Data / David S. Moore
What is a Computation? / Martin Davis
Mathematics as a Tool for Economic
Understanding / Jacob Schwartz
Mathematical Aspects of Popu lation
Biology / Frank C. Hoppensteadt

Part Four
The Relevance of Mathematics / Felix E. Browder
and Saunders Mac Lane