To meet the demands of industry, technology, and other sciences, mathematicians have had to invent new branches of mathematics and expand the old ones. They have built a superstructure of new ideas that people who are trained in the classical branches of the subject would hardly recognise as mathematics at all.
Applied mathematicians have been dealing with the world’s problems successfully, while pure mathematicians seem almost to have lost touch with the real world. To them, mathematics is an art and they don’t care much whether it will ever have any practical use.
By applying the concepts of mathematics to worldly problems, the applied mathematician can often brush away the obscuring details and reveal simple patterns. Celestial mechanics, for example, enables astronomers to calculate the positions of the planets at any time in the past or future. Now, this ancient branch of mathematics has suddenly become very practical for calculating the orbits of Earth satellites.
Applied mathematicians, who are interested in worldly problems, have learned to solve many of them that were almost impossible to solve twenty or thirty years ago. They have developed new statistical methods for controlling quality in high-speed industrial mass production. They have built the basis for Operations Research, which businessmen use to plan production and distribution. They have dealt with the complexities of human behaviour through ‘game theory’, which applies to military and business strategy. They have analysed the design of automatic controls for such complicated systems as factory production lines and supersonic aircraft.
Now they are ready to tackle many problems of space travel. Mathematicians have begun to turn their attention to the biological and social sciences as these sciences have started to use mathematics. The bond between mathematics and life sciences has been strengthened by a group of applied mathematics specialties, such as biometrics, psychometrics and econometrics. Now that they have electronic computers, mathematicians are solving problems that they could never solve a few years ago.
In a few minutes, they can get an answer that previously would have required months or even years of calculation. Furthermore, in designing computers and programming them to carry out instructions, mathematicians have had to develop new techniques. Computers have contributed very little to pure mathematical theory, but they have been used to test certain relationships among numbers.