In this report I have tried to avoid the obvious causes for the poor state of mathematics in Pakistan and remedies to improve it. Instead, I have attempted to highlight the causes and remedies in more general terms leaving the nitty-gritty details for later discourses.
1. MATHEMATICS AND ITS NEED
The uplift of our economy requires that we pay due attention to science and technology. For development in science and technology, a sound mathematical foundation is a pre-requisite. Therefore, it is imperative that we develop an adequate infrastructure for a mathematical culture in Pakistan.
Mathematics in Pakistan is misunderstood. This misunderstanding does not only exist at the laymen’s level, but at the academic and professional level as well. Unfortunately mathematics is regarded as an additional subject during school and university in order to move on to careers in sciences or engineering. This thinking exists even at the government level in the minds of the policy makers of science and education.
For instance, the requirements demanded by the grant donors for projects ignore the very nature of mathematics. Their utilitarian approach towards mathematics imposes such conditions for grants, which by and large cannot be met. Questions such as: What national interest is to be protected by this research project? What economic or trade benefit are to be achieved by this project? are frequently asked.
The use of impact factors and the citations count for ranking mathematicians at par with scientists in other branches of science is yet another example of misunderstanding on the part of scientists who make policies for improving science and technology in Pakistan. One of the requirements of the Higher Education Commission for the private sector institutions to get certificate of recognition from the government is to subscribe to at least 20 journals with impact factor not less than 1 in their libraries. However, there are only about five journals of mathematics amongst 1500 mathematical journals, which can meet this requirement.
There are many other such examples of misunderstanding about the nature of mathematics, which can have adverse effects on the development of the subject in Pakistan. Researchers in mathematics are being left behind as compared to the researchers working in other branches of science. The total amount received by researchers in the entire country on mathematical projects is probably far less than the amount received by a single project in any other branch of science.
We need to examine the state of mathematics in Pakistan and collect data to analyse objectively the causes of its poor state. Since 1947, no one has ever tried to come out with a seriously researched comprehensive report explaining the state of mathematics, the amount that public and private sector has been spending on mathematical research and development, and the support that has been given to the teaching and learning of mathematics.
Mathematics has always been considered as an art, language of science, and service to science and technology. This is a view of mathematics, which in my opinion, is a major cause of its decline in Pakistan.
Due to the lack of proper planning, since 1947 we only have had about 60 to 70 doctorates in mathematics in a country with 140 million people. The first Ph.D. in mathematics was produced 24 years after the birth of Pakistan. By now, only about 35 Ph.D.s in mathematics have been produced in Pakistan. Quaid-i-Azam University was hardly four years old when it produced Pakistan’s first Ph.D. in mathematics in 1971. The production of 30 doctorates in mathematics in 34 years is highly unimpressive by international standards. One can compare it with an example of a single professor of mathematics at Oxford University, namely Professor P.M.Neumann, who produced about 30 doctorates in mathematics in the same span of time.
But it is not the number only; there is more to it if one is to review the situation analytically for improvement and rectification. Out of 14 doctorate producers, only one is a local Ph.D. and only five are still active. The rest of them left Pakistan for good for greener pastures or have abandoned producing PhDs. According to the Mathematics Subject Classification 2000 (MSC-2000), the Ph.D. theses are classified in only 5 categories, namely:
MSC-2000 #16 Associative Rings and Algebras,
MSC-2000 #20 Group Theory and Generalizations,
MSC-2000 #46 Functional Analysis,
MSC-2000 #76 Fluid Mechanics, and
MSC-2000 #83 Relativity and Gravitational Theory.
Invariably the students who register themselves for Ph.D. degree in mathematics are M.Phil. degree holders from the same university.
Out of the total number of Ph.D.s produced so far, one thesis has been written on a topic in statistics, seventeen theses have been written on topics in applied mathematics and twelve theses on topics in pure mathematics.
Due to lack of incentives, inadequate support facilities and the absence of an appropriate mathematical environment, the production of doctorates in mathematics has been rather less than what it should have been otherwise.
In order to change the backward attitudes toward mathematics in Pakistan, the government has been promoting this idea of “indigenisation.” The idea is that the Ph.D’s already in the country will produce Ph.Ds locally. This is sad news for mathematics in Pakistan. Mathematics is a global activity, both in teaching and research. This is also true for other sciences.
We do not have enough Ph.Ds in Pakistan. The result will be that only that branch of mathematics will be researched and taught that these few Ph.Ds specialize in. Moreover, Pakistani universities and institutes do not have the proper infrastructure to provide up to date research information required by potential Ph.Ds. We already depend on the international community for textbooks and research materials. Then why stop our youngsters from going abroad and doing Ph.Ds there? If nothing else, at least they will get the exposure they need to understand the global essence of mathematics in the modern world.
Most of our researchers merely want to produce research papers per se, and not to understand deeper the subject that they are supposed to like and excel in. Their concern lies in relief from economic pressures, and not the abstract non-linear remedies that can bring economic relief in some incomprehensively distant future. In order to overcome their economic difficulties, the easy way out for them is to accept too many teaching assignments without considering its adverse effects on their social life, health, prestige, research, quality of teaching, and the fact that they are not adequately paid despite sacrificing all this.
Research is difficult and at times quite frustrating. Since teaching has become more lucrative economically than doing research, the former has become more attractive than the latter. Thus, there is already a danger of shift in focus from research to teaching in our universities. Of greater concern are the reasons for this shift. This generates another problem as a consequence. The hard reality is that the universities, which cannot afford to pay adequately for lecturing or research, have become less attractive places to work in.
It was thought by the Ministry of Science and Technology that giving money to a few natural scientists as ‘research productivity allowance’ can solve the problem. But this, rather than solving the problem, is likely to aggravate it as the allowance is linked with ‘productivity’. The criterion that is used to judge a scientist's ‘productivity’ is grossly defective and above all is rejected by the majority of scientists. Only a very small number of scientists have received this ‘productivity allowance’ in the first place and secondly, the majority from amongst those who have received it are unhappy about the category that they are classified in.
3. NEW INSTITUTIONS
Given the kind of salaries that faculty members are getting in relation to the cost of living in the country, it is not surprising that many of them are busy earning extra money. The plain fact is that lecturing and doing research in the country’s universities simply do not pay money while teaching extra outside of the universities does. It is thus not surprising either that many of our best academics and researchers are sitting abroad.
We have only a handful of PhDs in mathematics. New institutions, especially the private ones, offer handsome salaries. Due to economic pressures it is almost irresistable to decline an attractive salary offer. Mathematicians migrate from one institution to another leaving behind a vacuum, thus adversely effecting one institution at the cost of improving another. Something has to be done to stop this. The need of the time is to take care of the old institutions, which are dying due to lack of funds and cannot afford to stop this transmigration.
Prescribed books and questions from these books in the examinations make it ‘reasonable’ for the teachers and students both to confine themselves to the study of a few selected chapters. It will be counter-productive for the teachers/lecturers to teach/lecture the way they should otherwise. On the other hand it will be counter-productive for the pupils/students to learn/understand mathematics the way they should.
This is a major obstruction in any effort to improve the standard of lecturing/teaching especially mathematics. Our examination system needs radical changes. Foremost change is that the questions asked in the examinations should not be confined to a particular book and they should not be the ones already seen by the examinees. This change will be a big change. It will make it incumbent on both teachers/lecturers and pupils/students to read good books and learn mathematics. Their efforts naturally will be to improve the understanding of mathematical concepts and mathematical knowledge. No doubt the curriculum needs to be improved as the time passes. But this can be done in the due course naturally.
It will certainly encourage those who are adequately qualified but are not considered worthy of ‘productivity allowance’ can easily earn more money by simply taking a teaching assignment at a private institute or a private university. There are still many who will find it better to leave the country and work abroad, earning much more money without their ‘research productivity’ being judged by a defective ‘formula’.
There is a need, therefore, on the part of policy makers to realize that academicians in our universities need and deserve a reasonable salary matching with their qualification that would allow them to live a comfortable life with dignity according to their status.
Meanwhile, the academic community needs to think collectively, sacrificing their own immediate personal benefits for the long-term benefit of the community. Accepting teaching assignments at private universities is only a timely remedy and those who support the policy of ‘research productivity’ should also think above personal advantages. They all must join hands to work for a better research and teaching environment at public universities with a handsome increase in basic salaries irrespective of whether one is a natural scientist or a social scientist, and this should not be linked with ‘productivity’.
6. PRODUCTION OF DOCTORS
There have been a few sporadic personal endeavours for producing doctorates. Most of the qualified personals have not utilised their expertise in producing Ph.Ds. The intake of scholars for Ph.D. degree has been mainly from amongst the M.Phil. degree holders. Abandonment of scholarships for Ph.D. scholars also reduced the number of applicants for the degree. Lack of literature, especially mathematical journals, and library facilities for accession of mathematical literature, lack of financial and professional incentives for Ph.D. producers, appointments of too many locally educated faculty members in the same branch of mathematics have all reduced the variety of options for promising scholars to do Ph.D. The encouragement of joint supervision of M.Phil. and Ph.D. dissertations and theses have also been counter productive for young potential Ph.D. producers.
In the light of these above observations, a number of steps are needed to increase the production of PhDs, the quality of their theses, and the variety of theses topics.
M.Phil. and Ph.D. Programmes should be advertise effectively with marketing skills through brochures and prospectuses distributed across the country. It will give potential candidates information about the requirements for admission, admission procedure, scholarships available, the available areas of research and an introduction to the would-be research guides.
The universities buildings have been neglected for years. They lack basic necessities and comfort according to the two extreme weathers in the country, and they are highly unattractive. It is imperative that the buildings be improved and they be quipped with modern amenities.
Ph.D. supervisors should be given marks per Ph.D. scholar for promotions/selections to higher grades. This will give them incentive to work hard and look forward to supervise Ph.D. scholars. M.Phil. and Ph.D. scholars need financial support for themselves and their families. They should not be worried about financial matters while they are students. Most of them are either on no-pay leave or they have to work extra to earn their livelihood. In order to let them be free from financial worries and have abundant free time to devote solely to their research pursuits, they should be provided a handsome honorarium.
Due to the emergence of private universities and institutes, teaching has become more attractive than research. Teaching is less difficult than doing research and yet is more rewarding in financial terms. In order to encourage experts to devote time to supervising Ph.D. and M.Phil. scholars, it is imperative that they be provided financial incentives. Therefore, supervisors should be provided handsome honorarium for supervising a Ph.D. scholar. Mathematicians with at least five years experience and PhD should be advised to take on the average one Ph.D. scholar a year. This will streamline the production of our M.Phils and PhDs without overburdening the supervisors and without compromising on the quality of dissertations and theses.
The two-year M.Phil. programme in Mathematics, which began in 1978, set a new trend of mathematical research in Pakistan. Although the production of research papers from M.Phil. dissertations is not an official requirement for qualifying for the degree as such, by and large, the dissertations contain publishable research work. For example, the department of mathematics at Quaid-i-Azam university alone has achieved an international reputation in a rather short span of 22 years. By now about 350 number of M.Phil. dissertations have been produced. These scholars usually seek places at international universities for doctoral studies. They should be provided funds to study abroad in subjects specified by their local supervisors. They should also be given sufficient incentive in order to ensure that they come back to Pakistan after completion of their studies abroad.
Link between research productivity and annual monetary incentive on the basis of the criterion of impact factor and citation count is counter productive for researchers in mathematics. Examples of the quality and quantity of research - before the introduction of this criteria - at Quaid-i-Azam University and HEJ International Institute of Chemistry as compared to other institutions in Pakistan testifies that the criterion is not necessary in fact. Only seven mathematicians have been able to get the ‘research productivity allowance’ last year. It is not that the rest of them were not good enough as researchers. There are numerous examples of Pakistani mathematicians with impact factors and citations count who are considered ‘not worthy’ of ‘research productivity allowance’ who are working abroad and are earning much more money per month than those who have received ‘research productivity allowance’ in Pakistan. Many young mathematicians will think twice about coming back to Pakistan for the sake of extra money in the shape of ‘research productivity allowance’ which they are unlikely to get anyway. This criterion therefore should be abandoned or changed.
7. INTERNATIONAL CONNECTION
Conferences provide a novel opportunity for researchers to meet and share their work. Many Ph.D. and M.Phil. students also attend conferences in order to update themselves to a level that is required to do original and better research. The lecturers/teachers and Ph.D. scholars should be encouraged to go abroad at least once a year to attend an international conference/workshop. It will give the mathematical community a chance to compare themselves with their counterparts working in other countries and also provide them the opportunity to enhance their knowledge and skills. It will certainly bring a qualitative change in them.
8. STATE PATRONAGE
State of tertiary or higher education in the country has unfortunately not been a focal subject as much as literacy or primary education has been, despite the fact that it is an important area that badly needs attention and all the more so given the current government's drive to promote scientific and technological research and development.
There is no argument about the importance of scientific and technological research in the country. But there should be some sanity in the distribution and allocation of funds. Especially important is the question of how all this scientific and technological research is going to be carried out when the infrastructure and base for it is barely available in the 170 odd research and development (R&D) organizations and public universities throughout the country. Apart from very few R&D organizations, the research facilities in the rest and especially in all the public universities are very primitive. The university's laboratories are not in a shape fit for any worthwhile research and development. The university's buildings, the lecture halls, and the rooms of the faculty members are in a dilapidated condition. The problems are very obvious. What kind of five-year plans can these universities draw up when they lack even the very basic things required to run an ordinary modern office?
Instead of simply putting in more funds to shape up the universities and put them in proper running order at least, a lot of money and time is being spent on setting up new universities. Governments abroad plan very carefully before establishing any institution as important as a university or a scientific research organization. In this country, however, these kinds of organizations are set up at a whim, thus spreading resources even thinner and compromising on the quality of higher education and research work. The problems that our universities face are more than mere lack of funding. It is also one of lack of dynamism at the management and administrative levels.
It makes more sense to have a few good institutions providing quality tertiary education and producing quality research work than having tens of them that are good for nothing. Until and unless we build a strong base in higher education by changing drastically the state of affairs in our universities, how can we think of ever taking off in scientific and technological research and development?