PAUPER QUEEN OF SCIENCES

THE MUSLIM, 7th June 1991

Twentieth century has seen an unprecedented growth of mathematics. According to the estimate, there are more than 1500 mathematical research journals publishing some 25000 research papers every year. In 1968, the Jahrbuck uban die Fortschritte du Mathematik, listed just 12 categories of mathematical research. In Mathematical Reviews for 1985, there are about 85. Today's mathematics contains numerous abstract theories and its most abstract theories are currently finding new applications to fundamental questions in Physics, Chemistry, Biology, Computing and Engineering.

However, mathematics is one of the many fields that has not been able to attract adequate and sufficient attention of our governments. Abrupt changes of governments and consequent changes in government policies in Pakistan have resulted in ad hoc governance and policies which have proved detrimental to science in Pakistan in general and mathematics in particular. Politically weak and unstable governments, out of fear of being ousted anytime, have not been able to address themselves to any other question but how to stay in power as long as they want.

The spending on science and technology in Pakistan, for instance, does not even come near the 1% of GNP suggested by UNESCO as the minimum for healthy science and technology. One can imagine what faction of our GNP is spent on mathematics alone; keeping in mind that it is not considered at par with applied sciences such as 'Nuclear Physics'. In fact, as compared to other basic sciences, mathematics is given third rate attention.

This attitude has stemmed from the misconception that mathematics is about calculations and symbols. As Ian Stewart has said: One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology. Its apparent delight in lengthy calculations, these tend to obscure its real nature. Mathematics, in fact, is about ideas. It is about the way that different ideas relate to each other.

The other extreme is the attitude of quakers who have an industrial approach towards mathematics which makes it less useful in their opinion. (For example, Ministry of Science Technology does not include mathematical sub-classifications as part of the Ministry's scholarship schemes).

Mathematics in Pakistan especially, unlike in other developed countries, is given less importance and attention than it deserves in fact. Keeping in mind the potential we have, we are not sufficiently productive in mathematics. (We, of course, are not basing our assertion on hitherto sporadic efforts). Pakistanis share in mathematics in the world is negligible and is pushed still further into the background because of the fast growth of new mathematical ideas.

Although today, Pakistan constitutes about 1/50^th of the population of the world, the size of the mathematical community in Pakistan is very small. An indication of the scarcity of mathematicians in Pakistan is fact that while Pakistan's 23 universities contain less than 60 Ph.Ds in mathematics, Britain, whose population is about 1/4 less than Pakistan's, has approximately 2500 mathematicians in some 80 universities. Moreover, the average production of research papers per year is 1/12^th of what it should have been.

The largest department of mathematics in the country has only 14 mathematicians. Considering the number of the student studying for M.Sc. and M.Phil. In mathematics, the number of courses that are being offered to these students and the number of M.Phil. and Ph.D. students that need supervision, there should be at least 25 mathematicians per department. This means, in the 19^th mathematics departments in the 23 universities in Pakistan, we need to have a total of at least 475 mathematicians. At the moment we have hardly 1/8^th of this minimum.

If half of the total number of mathematicians (with Ph.D. degrees) in Pakistan had produced one Ph.D. every three years since 1980, by now we would have had produced about 90 Ph.Ds in mathematics. Whereas, the fact is that only 7 Ph.Ds in mathematics have been produced in 45 years. There are many reasons for having produced so few Ph.Ds. The most prominent one is that there is apparently not enough motivation for students to go ahead and obtain a Ph.D. Even for those who desire to do so, they do not want to do it locally. Similarly mathematicians who can supervise Ph.D. students lack incentive to take Ph.D. students.

Mathematical talent, undoubtedly, exists in Pakistan. What are lacking are governments to marshal and nurture these talents. Indeed, the principal solution to the existing lot of mathematicians is the adoption of a major national commitment by the governments to acquire and enhance mathematical knowledge.

Pakistan should adopt a long-term policy on mathematics with a perceptive plan of say ten years horizon. Once have perceptive plan and set ourselves a national target, then we can adopt practically measures, short, medium and long term, to achieve our goal. Generous patronage to mathematics is of utmost importance in this respect.

Spending on mathematics is negligible by any standards. A fair fraction of our GNP should be devoted to increasing the pool of mathematical manpower. In the first instance, without spending much extra, we can fill in the vacant positions in the mathematics departments all over the country. In the 19 mathematics departments of the 23 universities in Pakistan, less than 1/3^rd of the positions are filled. There are many highly qualified mathematicians waiting for their promotions. Their promotions will not only reduce the anxiety, which is one of the major causes of brain drain, but also create vacancies for young blood. It will also produce a more congenial atmosphere, which is sadly lacking at the campuses.

The government and universities together should also create an environment conducive to the development of mathematical teaching and research. One important fact of this conducive environment is an adequate support system for teaching and research. This includes workshops, libraries, computers and channels for communication between mathematicians, such as electronical, telefax, telephone and telex.

The lack of this support system for research is an important contribution towards the mathematical brain drain in Pakistan. There is not a single university in Pakistan which has essential amenities available to its faculty members and senior research students.

Worse still, existing support systems in Pakistan are very often white elephants spending more money on administration rather than on the purpose for which they were created. Professional and learned societies and academies are also essential for the healthy development of science. For instance in the UK and in France, it were the academies which made the most significant contribution to the development of mathematics. 

However, in Pakistan, the existence of a Science Foundation, University Grants Commission and Pakistan Academy of Sciences have become an end rather than the means. More active and meaningful between these organizations and universities should be established. Isolation of mathematicians, especially from local and regional mathematical happenings, is one of the most destructive factors in the flowering of mathematics in Pakistan. Internal fast mathematical communication with regional groups, like the one which exists between ASEAN, is vital for the survival of the indigenous mathematical community.

Contact with each other must be frequent with exchange of results and ideas. Our Academy, the Commission and the Foundation can play an effective role in arranging specialized mini conferences (not melas), workshops, meetings and more importantly at regular intervals.

It is also necessary for mathematicians to remain in touch with international mathematicians so that they may not become producers of 'bad mathematics'. 'Mathematics is bad if it is trivial, over elaborated or lacks any definite mathematical purpose or direction", as is said by Ian Stewart. It is this type of mathematics which is generated if a mathematician is working in isolation without any solid background and incentive. Mathematics, like other sciences, is a collaborated activity and the research of each individual interacts with those of others.

Science is actively created abroad. Mathematics is no exception. Our universities should ensure that their mathematical enterprise maintain contact with international mathematical community through various means. For one thing, mathematicians should be able to have funds available from their respective institutions for travelling abroad and within the country. The hassle and red tape involved in getting 'permission' for such travel should be abolished.

An adequate mathematical policy is necessary to enable the country, its government and institutions to provide the resources, mathematical knowledge and manpower serving the developing needs of the country. This is especially so when the development of science and technology is increasingly dependent on mathematics which itself is going through rapid changes. Not only do we need to increase mathematical manpower, but also to modernize the curriculum, make examinations more aptitude oriented rather than depending on marks/grades, ensure timely promotion of teachers, patronize mathematical societies so that they can be used to organize special programmes to promote mathematical culture and bridge the gap between the government and the mathematical community. Our universities, the Science Foundation, the Academy of Sciences and the University Grants Commission can play a significant role in the creation of an indigenous mathematical capacity that will usher in a technologically modern Pakistan.