THE NEED FOR MATHEMATICS

THE MUSLIM, 4 August 1989

The world is going through a period of major political, economic, military and technological changes. These changes present unique challenges and opportunities. Countries are becoming superpowers on the basis of their economies alone.

The world's geopolitical polarity is shifting. Old alliances are moderating on both the Soviet and US sides, new forces are emerging, overpowering military force is appearing less useful than before, and communist countries are clearly concerned about what their poor economic condition portends for their long-term power and status.

Like many other Third World Countries, Pakistan is coping with complex fiscal and technological efficiency problems, which challenge our work and market ethics and our competitive abilities.

The challenges we face today are daunting. We need, today, to deal with vast quantities of data in an efficient manner. We need to distinguish important objectives from the unimportant ones, supporting decision making in time-critical environments, converting complex situations and problems into simplified, understandable ideas and improving communications and information management. All this involves mathematics.

These changes cannot be understood nor these challenges met by relying solely on the theories of the past. Rather, we must have fresh insights, new ideas, and a deeper understanding of the way the world works. These are tasks uniquely suited for the mathematically trained mind. Yet our nation lacks a sufficient number of such minds.

We have 22 universities in Pakistan, but the total number of mathematicians in these universities is only 124. There are about 55 mathematicians in Pakistan with Ph.D. degrees. Since 1947, only 7 Ph.D's in mathematics have been produced here.

Great Britain, for instance, which has half the population of Pakistan boasts about 2,500 high class Ph.D.'s in mathematics in its universities alone. A tiny country like Singapore, whose population is 2.6 million and which has only one university, has approximately 60 mathematicians.

The condition in Pakistan is thus practically hopeless. All mathematics departments in the country are understaffed. Pakistan is devoid of mathematically skilled manpower everywhere - in DESTO, PAEC, PINSTECH, KRL, HMC, the Pakistan Armed Forces, etc.

On the other hand, the world has become more mathematical in recent years, and this change can only accelerate. Modern technology and science demand a comfortable command of discrete mathematics, statistics and mathematical modelling - and these are just the entry-level requirements.

We cannot find mathematically literate workers, when the government can no longer recruit the mathematically skilled, and when must finally rely on the scientific insights and advances of other nations, then we will have entered a sad period of technological stagnation and decline. This will result in more reliance upon foreign aid and more dependence upon the technological and scientific knowledge of others. We will spend huge amounts of foreign exchange buying necessary and important equipment and expertise.

There is also a great need to move beyond the artificial divisions of mathematics: pure versus applied; defence versus civilian; industrial versus academic; research versus teaching. WE must realize that what is good for mathematics in its broadest sense benefits every user, no matter how narrowly focussed the application may be.

There are plenty of reasons for promoting mathematics. Let us consider a few examples of the broad application of mathematics. In the 1800s, mathematicians expended a lot of energy on the wave equation - a partial differential equation arising from the physical properties of waves in a string or in fluid.

Despite the physical origin, the problem was one of pure mathematics: nobody could think of practical use of waves. In 1864, Maxwell laid down a number of equations to describe electrical phenomena. A simple manipulation of these equations produces the wave equations. This led Maxwell to predict the existence of electrical waves. In 1888, Hertz confirmed Maxwell's predictions experimentally, detecting radio waves in the laboratory. In 1896, Marconi made the first radio transmission.

The sequence of events is typical of the way in which pure mathematics becomes useful. The same sequence of events occurred in the development of atomic power; or in matrix theory of Cayley (used in engineering and economics); or in integral equations, which took about 30 years to develop, from the point where Courant and Hilbert developed them into a useful mathematical tool the point where they became useful in quantum theory.

Nobody could have realized at the time of Galois that group theory turn out to be needed later in almost every branch science. This means that all mathematics, however unimportant it may seem now, should be encouraged on the off chance that it will be needed later.

Overall, mathematics is becoming even more essential to our defence, to our industrial competitiveness, and to our nation's academic research. The role of mathematics in the future of Pakistan's economy and government will be central, crucial and in escapable. Mathematics will be one of the skills that separates service careers from those requiring imagination, creativity and originality.

Supporting and improving mathematics can no longer be merely a slogan, goal or platitude. It must now become an essential objective of any industry, scientific organization, government, or academic institution that expects to remain competitive in the future.

We simply must ensure that adequate support for mathematics research is an accepted norm, that our standards for pre-college education are equal to our capabilities and needs, and that the standard of mathematics and teaching of mathematics at these levels is improved. The decline must stop now, and we each have a role to play.

In the past, our governments and the private sector have taken a limited and narrow approach to mathematics. If the work in question is not 'mission oriented', if it does not increase profits, if it does not have an obvious application, then it is not worthy of support.

Mathematical research benefits everyone, because it creates a fertile field of ideas from which we can draw solutions to our problems. Mathematics education is the only hope that we have to continue our work; if there is not a sufficient mathematically educated labour pool in the future, then our work today is for naught. Despite the restrictions we believe may limit our actions, we must ensure the future of mathematics in Pakistan.

Responsibility for promoting and improving mathematics in Pakistan rests primarily with academics. If mathematics is to be properly supported by society, then mathematicians must not forget their obligations. Universities must go beyond measuring success only in terms of grants or publications, and researchers must recognise their larger obligations.

If we cannot convince our greatest minds to tackle the vital problems of education, government and business, then society will invest elsewhere, and everyone will be the loser in the long run.

Mathematics also suffers from a public relations problem. Pakistani researchers solve problems and advance theory on every frontier, but general public (and often the government) does not appreciate these achievements. If academics cannot convince the public that they are doing useful work and solving problems that directly or indirectly affect everyone, them their other efforts will be in vain.