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.

**2. RESEARCH**

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.

**4. EXAMINATION**

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.

**5. TEACHING**

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?