Saturday, 17 August 2019


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.


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.


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’.


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. 


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?


Pursuant to the 18th Amendment of the Constitution of Pakistan, the subject of higher education was devolved to the provinces and the Punjab Higher Education Commission (“PHEC”) was established. PHEC shall redefine its mandate beyond “monitoring, evaluating and accrediting” institutions without, of course, going beyond the authority provided by law under the Punjab Higher Education Commission Act 2014 (the “Act”) or interfering with the freedom of universities provided to them by their respective Acts. Indeed, PHEC shall aspire to lead in education and research, and to benefit society through its commitment to excellence. Its mission shall be to improve the quality and usefulness of higher education by providing guidance so that universities can improve their systems in providing knowledge and skills to produce a modern, competent and useful workforce.  

The administration, academia and stakeholders of universities shall not only be aware of the goals of their universities but shall also be cognizant of recent national as well as global challenges. With the belief that education is the only means through which Pakistan can prosper and become a modern country in the world, PHEC shall endeavour to inculcate social values in its universities by ensuring that its administrators, teachers and students are accordingly trained.

Apart from the weak PHEC, there are four other entities strongly linked to universities, i.e. the Chancellor’s inadequate Secretariat, the over-burdened Higher Education Department, the Provincial Assembly, and the Chief Minister’s Secretariat. In my opinion, while maintaining inclusivity of the aforementioned four entities, PHEC must gather the strength and there should be appropriate regulations which establishes PHEC’s independence and increases its role in accordance with its powers and functions provided under Section 10 of the Act, enabling it to play a more valuable part with respect to the vast number of universities. The insight of all constituents in appropriate extents will shape the broader spectrum and future sketch of universities. PHEC shall commit itself to function in order to ensure that the universities are working in true spirit of the rules and regulations, and in line with the principles of transparency, quality and merit without compromising on the independence of the universities.

Having a large number of universities in the province, PHEC can play a significant role by validating its significant contribution as an academic representative of HEC. Exploiting the fascinating history and geography of the region, PHEC must aim to become the provincial hub of intellectual activities. Competent philosophers, scientists and economists will encounter challenges with their knowledge, expertise and skills. PHEC shall contribute to innovative research, growth and productivity, which shall in turn lend political and economic strength to society. Communal norms, spiritual persuasion, respecting difference of opinions and tolerance shall be embraced by PHEC. Academic innovations are one of the prime objectives of the PHEC and initiating academic programmes that realize the importance of relevance will help meet national challenges and indigenous problems.

PHEC shall ensure systematic and regular review of universities’ research and development to ensure its practical utility as usually claimed. Links between universities, industries and society ought to be established to contribute to the solution of the human resource issue in our country. In this regard, PHEC should ensure that universities conduct regular workshops on various topics to provide modern techniques and guidance to low-income semi-skilled professionals. PHEC shall help in developing courses and systems in universities to conduct such workshops in distant localities.

Unfortunately, outdated content in academic curriculum poses a great challenge to student in the market, industry and society. PHEC shall ensure that rapid changes in environment, science and technology, social progression, economic challenges and political philosophies will not only be understood but also be incorporated in the curriculum. The need for revision or upgradation shall be identified and conveyed to the relevant bodies. 

PHEC shall work for the betterment of education beyond the boundaries of a university. In the recent past, there has been profuse proliferation of affiliated colleges administered by various universities which has adverse effects on the standard of education being imparted to students. PHEC shall collect data about all such colleges, their teachers and students in order to regulate the affiliation system with the ultimate aim of gradually, but considerably, reducing the number of affiliated colleges. There is no logical social utility in having multiple public colleges in the same city (or vicinity) where a main university is located. Instead of shutting them down entirely, such colleges shall eventually be converted into certificate/diploma awarding skills colleges affiliated with technical universities which would supplement PHEC’s goal to cure the disease of human resource shortage in the country.

Though a university is never recognized exclusively for its buildings and structural set-up, there is no denying that these are fundamental parameters. The development process to a great extent depends on the general economic situation of a country. The requirements of modern universities are changing at a phenomenal pace. Our public universities lack modern infrastructure, depriving our youth of the facilities of the current day and age. State-of-the-art laboratories, libraries, conference/meeting rooms, sophisticated class rooms, work stations for faculty and administration, sports complex, hostels and transport for students are some of the major resources promptly needed once a university is established. PHEC shall guide universities in enhancing their infrastructure in accordance with its future plans.

Exceptional financial management is mandatory for sustainability and progression. PHEC must pursue alternate sources of income for the universities in Punjab in order to ensure financial independence. PHEC shall develop its own strategy for raising funds within a fixed timescale. It shall make most of the commercial value from the universities’ intellectual property and research, and develop commercial income opportunities from the universities’ estates and other facilities. PHEC should have the capability to help universities in Punjab develop sustainable independent revenue earning systems.

There is a dire need for a strong and effective administration in universities. PHEC must establish a system that educates university administrators up to the level of BS-19 who can reinforce their own systems. Competent administrative set-ups in universities will not only have the capabilities to resolve a majority of complications, but also foresee the future and provide guidance to touch new horizons. This will ensure administrative and academic excellence and performance, which will sketch universities’ needs over a much longer timescale.

PHEC needs to recognize the importance of alumni in nation-building. Alumni generate invaluable word-of-mouth marketing among their social and professional networks. They are the most likely group to give back to their institution and society (if the institution has done its job right) owing to their sense of pride and gratitude towards their institution. A strong link between alumni relations and fundraising will not only enable universities to generate finances by way of alumni contributions of varying amounts by making them self-sufficient to a great extent, but provide an avenue for institutions to be engaged in the professional lives of alumni.

Rapid demographic transition and the resultant increase in young adults entering the labour market holds vast potential in catalyzing growth and raising living standards in Pakistan. 64% of the country’s population is under the age of 29 and the youth between the ages of 15 and 29 make up 30% of the country’s total labour force. With their demographic size and more importantly their fresh ideas and energy, if provided with a conducive environment, they can lead the way to sustainable human, social and economic development in the country. The foregoing are the broad ideas that one should like to implement to ensure that educational institutions in Pakistan have competent administrative, financial and examining systems, freeing them from all kinds of social, political and internal pressures and rendering them wholly and solely committed to excellence, community development to foster innovation and creativity, develop leadership, argument and debate, inculcate tolerance and openness and promote peace, and build the character and personality of learners. It is believed that the future of higher education is bright in Pakistan and academic excellence can be achieved by following PHEC’s road map with enthusiasm, with commitment, and without fears.  

Friday, 16 August 2019


Pak. Math. Soc. Newsl., Issue 2, Volume 5, 2006

The history of mathematics is an enticing but neglected field in Pakistan. One reason for this lies in the nature of intellectual history in Pakistan. Telling the story of mathematics is not a conceptually distinct undertaking from describing the theory of mathematics, though the two presentations appear in different guises.

The Mathematics Department of Quaid-i-Azam University, born in 1967, being the only federal and post-graduate department, has played a leading role in establishing traditions in mathematical research in Pakistan. Its contribution in producing a locally educated mathematical workforce in Pakistan has yielded a mathematical culture, which has its own peculiar dimensions and effects. It is worthwhile to look at the history of the Mathematics Department of Quaid-i-Azam University analytically and see its influence on research in mathematics. 

The Commission on National Education came to the conclusion in 1958-59 that the post graduate studies in scientific and technological disciplines required a great deal of reorganization and development. In 1962 the case of post-graduate studies in the basic sciences was taken up again and it was proposed that one center of Advanced Studies and Research should be developed in each university of Pakistan. The international component of the financial support was supposed to have been received from UNESCO, USAID, and Ford Foundation. But at the time UNESCO ran into political and financial crises and therefore the plan received a setback. Later in the same year, the Commission on National Education decided on an alternative plan. It decided to establish a post-graduate university at the national capital.

Dr.M.Raziuddin Siddiqi, who was then the chief of Higher Education in the Reforms Implementation Unit and Vice Chancellor of the University, managed to win support from Dr Herman B.Wells, President of Indiana University, Dr.McGeorge Bundy, President of the Ford Foundation, Dr.David Bell, Vice-President Ford Foundation and Dr.George Gant, Representative of the Ford Foundation. On 5th December 1964, Dr.M.Raziuddin Siddiqi assumed charge of the Vice-Chancellor’s office of the University of Islamabad in the office of the Science and Technology Research Division, of which he was the in-charge, in a building near the Ministry of Education at Chaklala. When Dr Siddiqi relinquished charge of the Division, a spacious building in Satellite Town near the Holy Family Hospital in Rawalpindi was rented for the university office early in 1966, and very soon after that when teaching and research work started on a regular basis, a number of other buildings were hired in the neighbourhood. The foundation-laying ceremony of the permanent campus took place in June 1967 and the University of Islamabad Act was approved by the National Assembly on 2nd July 1967.  

In the first Five-Year Plan (1965-70), it was decided that the university would be purely unitary type, without any affiliated colleges – it would consist only of its own teaching institutes. Each institute would be of inter-disciplinary character containing all the major branches of the subject. As a result, there would be no separate departments of Pure Mathematics, Applied Mathematics, and Statistics as in the other universities of the South Asian subcontinent, but only one Institute for Mathematical Sciences encompassing all the branches of mathematics shall be developed. The M.Phil. and M.Sc. classes in Mathematics and Theoretical Physics started in September 1966. Eminent visiting professors from abroad were appointed to give regular course of lectures in these subjects.

The Ford Foundation first started to help the Government of Pakistan in founding Quaid-i-Azam University by funding foreign faculty members, followed later by UNESCO. The list of foreign faculty members funded by the Ford Foundation include Marvin Marcus (linear algebra, spring 1970); W. D. Rannie (fluid mechanics); F. A. Graybill (statistics, spring 1971); S. Eilneberg (mathematics, spring 1971). The latter wrote his book on "Automata, machines and languages" while he was at Quaid-i-Azam University. The foreign faculty funded by UNESCO includes R. Wiegandt (algebra, August 1970 - July 1972); H. Klitzing (computer science, arrived in spring 1972); A. V. Arhangelskii (topology, arrived late spring 1972 and spent about 3 years).


Pak Math Soc Newsle, Issue 3, Vol  5, 2006

Production per year of research papers in mathematics has increased with the passage of time. In 1977 the first research paper out of an M.Phil. dissertation at Quaid-i-Azam University was published in an Indian journal. Incidentally it was a paper in the area of Group Theory and its Generalizations.  It was a produce of the first two-year M.Phil. in Pakistan. The author was Qaiser Mushtaq. Many years later years, an upsurge in mathematical research even at M.Phil. level was seen. Nowadays, a large number of M.Phil. dissertations contain original research, which students publish in the form of paper(s) with joint authorship of their supervisors. 

The production of Ph.D.s has also increased since the first local Ph.D. was produced, again at Quaid-i-Azam University in 1971. With the increase in production of doctoral theses, the number of research papers has thus increased as well.

Another factor which has increased the production of mathematical research papers, is that universities have started giving money per paper per year. Productivity allowance per year has also contributed to an increase in research papers in science in general and mathematics in particular.

Yet another factor for the increase in mathematical research papers is that many Pakistani mathematicians who had left Pakistan for ‘greener pastures’ have been returning to Pakistan due to retirement from foreign universities on the one hand and due to lucrative salary offers from the Higher Education Commission on the other hand.

Where these factors have increased the production of mathematical research papers, they also have had adverse effects on the mathematical culture in the country. Multiplicity of authorship has increased. For instance, research papers from dissertations and theses contain authors other than the supervisors and supposedly the authors of the dissertations and theses. This has given way to bribery and nepotism in research. For example, if one is short of a few papers to qualify for a selection/promotion, he/she will befriend a researcher to have his/her name included in a research paper. Particular research groups have attained the character of mafias. Rehash of mathematical research has become an acceptable fashion. Certain branches of mathematics in which research is comparatively easier have become popular and those branches of mathematics which are considered mainstreams of research and in which research is difficult are becoming unpopular. There is no realization of this trend. Consequently, there is no effort on the part of universities authorities or most of the researchers or the Higher Education Commission to stop these practices. On the contrary, heads of these organizations are happy as they take pride in showing off the rise in the statistical data of ‘productivity’.

An analysis was conducted on the basis of data collected from the Mathematical Reviews of the American Mathematical Society with the purpose of seeing in which areas Pakistani mathematical researchers are producing papers. It has been observed that the following branches have been the main thrust of mathematical research in Pakistan:

Order, lattices, ordered algebraic structures (O5), Associative rings and algebras (16), Group theory and generalizations (20), Operator theory (47), Numerical analysis (65), Fluid mechanics (76), Statistical physics, structure matter (82), Relativity (83).


Pak Math Soc Newsl, 1, 6, 2007

In July 1987, Professor Qaiser Mushtaq organized a unique mini conference on algebra, the first such international activity in algebra in the history of Pakistan.

Image result for norman blameyProfessor Graham Higman FRS, former Waynflete Professor of Pure Mathematics at Oxford University and former President of the London Mathematical Society, was invited to deliver lectures at the conference. The conference was attended by mathematicians from all over Pakistan and was sponsored by the National Academy of Higher Education, (University Grants Commission) and the Quaid-i-Azam University, Islamabad, Pakistan. Professor Graham Higman FRS delivered four one-hour lectures. Experts and senior students from all over the country attended the conference.

Professor Higman flew to Pakistan from Singapore where he had attended an international conference on Group Theory in June 1987 where many eminent group theorists also attended, and Professor Higman who was one of the keynote speakers. Professors Mario Suzuki and J.P.Serre and many other such mathematical giants  were amongst his audience. His lecture was as usual rich with outstanding mathematical substance. In his typical scholarly style, he won  hearts of the audience. He received several questions which he candidly answered.

I had the honour to be a doctoral student of Professor Graham Higman with whom I spent three years at Oxford from 1980 to 1983. When Professor Higman retired from Oxford in 1984, an international conference was held in his honour. I had returned to Islamabad by then working as a lecturer in mathematics at Quaid-i-Azam University. Surmounting several obstacles created by the University Grants Commission, Ministry of Education and the Ministry of Finance, I finally obtain the travel grant and the No Objection Certificate to proceed abroad to attend the conference held in Professor Higman’s honour.

That was my first meeting with Professor Graham Higman after having returned from Oxford obtaining D.Phil. from there by writing a thesis on Coset Diagrams for the Modular Group. Coset diagrams are visible in the background of Professor Higman’s portrait, by Norman Blamey, which was displayed in the Higman Seminar Hall in the Mathematical Institute, 24-29 St Giles, at Oxford.

My next meeting with Professor Higman was at a conference three years later in Singapore in 1987 where I went to read a paper. I remained in Singapore after the conference and had the opportunity to have several meetings with him. Professor Higman had returned from Illinois at Urbana Champagne where he spent about two years. He was now on his way home to Headington in England, and I requested him to spend some time in Islamabad before returning to Oxfordshire. Luckily, he agreed.

Professor Higman spent some three weeks in Pakistan. I organized a four-day conference at the Mathematics Department, Quaid-i-Azam University. The mini-conference attracted a handsome number of participants from all over the country. Professor M.Rauf Qureshi, Professor Asif Kazi, Professor Karamat Hassan Dar, and Professor Khuda Dino Soomro were amongst them.

At the end of the conference, Professor Higman and the participants were brought to Murree Hills for recreation.

During his visit to Pakistan, Professor Higman was requested by the Pakistan Television (PTV) for an interview in the then popular programme, Visitor’s Book. I was asked to interview him. The interview lasted for about twenty minutes. For several days afterwards, I kept receiving comments, messages, and questions for Professor Higman.

Professor Higman is famous for his difficult and breakthrough results in mathematics. His work on the famous “Embedding Theorems, Hignam-Neumann-Neumann Extensions, and Finite Simple Groups are a few examples.

After the conference, Professor Higman wanted to take respite from mathematics for a while and spend some time on his own watching birds in some remote area. I therefore arranged a trip for him to Gilgit. He asked my wife and I to accompany him, but I preferred to do otherwise. . He spent about ten days in Gilgit, and returned to Islamabad by road due to uncertainty of the weather. The journey took around 18 hours, and when he eventually arrived at my place, he looked very tired. I took him straight to Hotel Margala for an overnight stay. Next day, in the evening we had the interview at the PTV on 16th August 1987. I enjoy recalling his comments at the end of the interview: 

"We do fundamental research, not only to acquire results solely but because the process is an ennobling one; it is one that makes you more worthwhile than before; it is something that if  you cut yourself off, you are making yourself less human than you ought to be."

Wednesday, 7 August 2019


Pak Math Soc, Newsl, 4(4), 2005.

INCREASE in scientific and mathematical activities led to the formation of groups of persons who met, sometimes regularly, for discussions and exchange of ideas. Some of these groups later emerged as academies, schools, or societies. The first of these well known perhaps were, Plato’s Academy in Athens, or the school of Euclid in Alaxandria, or the House of Wisdom (Bait ul Hikma) in Baghdad, or Society of Brother’s of Banu Musa in Baghdad.

It is difficult to say where and when the first mathematical society in the modern sense was founded, but the oldest one that still exists is the Mathematische Gesellschaft in Hamburg. It was founded in 1690 as the Kungstrechnungsliebande Societat. Another early one is the Spatalfields Mathematical Society, which lasted from 1717 to 1846. But these were not societies of national stature. The first society of national stature is the Wiksunding Genootschap, which was founded in Amsterdam in 1778. Later the Moscow Mathematical Society was founded in 1864, the London Mathematical Society in 1865, the Societe Mathematique de France in 1872, the Mathematical Society of Japan in 1877, the Edinburgh Mathematical Society in 1883, the Circolo Matematic di Palmero in 1884, the New York Mathematical Society, which was later renamed as the American Mathematical Society, in 1888 and the Deutsche Mathematiker-Vereinigung in 1890.

The Late Dr Raziuddin Siddiqui founded the first mathematical society in Pakistan in 1952 by the name of All Pakistan Mathematics Association. He remained its President form 1952 to 1972.  After his ‘retirement’ from the Association, tussle between mathematicians from Karachi and Lahore split the Society into two factions. The late Hakim Mohammad Said, as Chairman of the Hamdrad Foundation, financed the Karachi faction. This faction in Karachi convened the first International Conference of Mathematical Sciences in 1975. It was at this conference’s concluding session that due to the personal efforts of the late Dr Raziuddin Siddiqui that the two factions merged together to reform the old All Pakistan Mathematics Association. It was then decided to reformulate its constitution to accommodate various chapters at the provincial capitals, namely, Karachi, Quetta, Lahore and Peshawar. The Society remained inactive for quite some time. Later Professor Dr Q.K.Ghori, tried to bring some life into it in 1983 when he became its President.

Wednesday, 31 July 2019


Dawn, 16th August 2009

           Professor Philip Hall (1904 - 1982), FRS, an eminent mathematician was Sadlerian professor of Pure Mathematics at Cambridge from 1953 to 1967. In daily Telegraph it has been stated that he was the world’s leading group theorist of the 20th century. Recipient of prestigious the Sylvester Medal of the Royal Society, the de Morgan Medal and the Larimor prize of the London Mathematical Society, he was elected Honorary Secretary and the President of the London Mathematical Society. Hall exercised a profound influence on English mathematics, and an influence which was felt throughout the mathematical world. Hall has published 40 papers in his career of 47 years.

Hall’s cumulative Impact Factor, based on HEC’s criterion, is only 19.844. According to the HEC criterion for civil award of Pakistan (Impact Factor for Tamgha-i-Imtiaz 34 – 49, Pride of Performance 50 – 99, Sitara-i-Imtiaz  100 – 198, Hilal-i-Imtiaz  200), Hall will not qualify even for Tamgha-i-Imtiaz. There are many more such outstanding mathematicians who would not qualify the HEC criterion for awards, research projects, distinguish professorship, etc., whereas, ironically, there are some Pakistani mathematicians who are no match to such outstanding mathematicians such as Professor Philip Hall and yet have received awards and research projects worth millions of rupees.  
The impact factor is a measure of the relative number of citations in years 2 and 3. It is calculated by dividing the number of current citations a journal receives to articles published in the two previous years by the number of articles published in those same years. So, for example, the 1999 impact factor is the citations in 1999 to articles published in 1997 and 1998 divided by the number articles published in 1997 and 1998. The number that results can be thought of as the average number of citations the average article receives per annum in the two years after the publication year.

In June 2008, the International Mathematical Union (IMU) issued a report “Citation Statistics”, which addresses the use of quantitative measures in assessment of research. It states that while numbers, that is, impact factors, appear to be “objective: their objectivity can be illusory. The meaning of a citation can be even more subjective than peer review. Because this subjectivity is less obvious for citations, those who use citation data are less likely to understand their limitations. It states that the sole reliance on citation data provides at best an incomplete and often shallow understanding of research. Numbers are not inherently superior to sound judgments. But citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused. Research is too important to measure its value with only a single coarse tool. It is important that those involved in assessment will understand that if we set high standards for the conduct of science, they should set equally high standards for assessing its quality. (For details see the September 2008 issue of the NOTICES of the American Mathematical Society.)

The value of the impact factor is affected by sociological and statistical factors. Sociological factors include the subject area of the journal, the type of journal (letters, full papers, reviews), and the average number of authors per paper (which is related to subject area). Statistical factors include the size of the journal and the size of the citation measurement window.

In general, fundamental and pure subject areas have lower impact factors than specialized or applied ones. The variation is so significant that the top journal in one field may have an impact factor lower than the bottom journal in another area. Closely connected to subject area variation is the phenomenon of multiple authorship. The average number of collaborators on a paper varies according to subject area, from pure mathematics (with about two authors per paper) to applied mathematics (where there are four or more). Not unsurprisingly, given the tendency of authors to refer to their own work, there is a strong and significant correlation between the average number of authors per paper and the average impact factor for a subject area. So comparisons of impact factors should only be made for journals in the same subject area.

The value of the impact factor is affected by the subject area, type and size of a journal, and the period of measurement used. Journals of Physics and Engineering for instance, have much greater impact factors than the mathematical journals not because they are qualitatively better but because they have a wider readership and the time spent from acceptance of a paper to its publication is much shorter. The ISI has listed 321 journals under the subject of mathematics, and only 15.58 % mathematics journals have impact factors greater than 1. Only 4 journals have impact factors greater than 2, the highest being 2.75.

Use of impact factors, outside of the context of other journals within the same subject area, is virtually meaningless; journals ranked top in one field may be bottom in another. Extending the use of the journal impact factor from the journal to the authors of papers in the journal is highly suspect; the error margins can become so high as to make any value meaningless. The use of journal impact factors for evaluating individual scientists is even more dubious, given the statistical and sociological variability in journal impact factors. Impact factors, as one citation measure, are useful in establishing the influence journals have within the literature of a discipline. Nevertheless, they are not a direct measure of quality and must not be used.

In Pakistan, the rationale for the use of the Impact Factor is to “help the administrators of science to evaluate the quality and output of scientists who seek key positions”. The National Commission on Science has made it a part of its policy to rate scientists and their work on the basis of impact factors of their research papers in accordance with the list of Impact Factors published by the ISI. However, as Professor Milman in his article has argued, ISI’s impact factor puts mathematicians in a disadvantageous position because the index is not suitable for research in mathematics.

It is bizarre that one's status could be determined by the arbitrary assignments of numbers to the journals in which one happened to publish. Most intelligent scientists and administrators are well aware of two facts: firstly, that we do not yet have reliable bibliographic measures for comparing or making absolute ratings of the value of the work done by research workers; secondly, that in any event, bibliographic measures appropriate in one field are inappropriate in others.  An impact value based on the simple measurement of how many times a journal is cited makes no sense as a measure of the quality of the papers published in it, let alone the quality of the mathematicians publishing there. Such use of management-type figures which claim to enable comparisons to be made, can be utterly misleading and damaging.  Figures are only as good as the premises on which the figures are based and often, the premises of many widely-touted management figures are seriously flawed.  The only real criterion of an individual’s scholarship is quality of work and that does not admit of simple numerical assessment.

The misuse of impact factors and the citation index has already borne adverse effects in Pakistan. Applied mathematicians for instance are at a more advantageous position. They have the choice of publishing papers in journals of physics, computational mathematics and engineering. Their choice of publishing a paper also increases. These journals by and large have much higher impact factors than the journals of mathematics. Consequently the cumulative impact factors of mathematicians who have the choice of publishing papers in such journals increase phenomenally.

Young Pakistani mathematicians are now reluctant to do research in pure mathematics as they feel that publishing papers in top mathematical journals is not only difficult but receives no recognition or appreciation due to low impact factors and citations. Fake multiple authorship has increased. Production of short papers is on the rise. Worthwhile and exhaustive research is compromised. Meaningless mathematical modeling is gaining popularity. Rate race of producing shallow mathematical results with no scientific value has damaged the very purpose of research in basic sciences.

Allocation of funds, grants, awards, appointments, and promotions on the basis of Impact Factor will be disastrous for science in Pakistan. The particular nature and special characteristics of each branch of science have been completely ignored in devising the Rs15.7 billion National Scientific and Technological Research and Development Fund for encouraging scientific research in the country.

It does not require much effort to understand from the information and analysis provided above that the use of Impact Factor needs some modifications to suit the very nature of mathematics. We can adopt a more pragmatic approach to this problem rather than a protectionist approach.