SPEECH AT SALAM PRIZE AWARDING CEREMONY

Delivered in August 1988

Professor Atta-ur-Rehman, Professor Murtaza, Professor Qadir, honuorable guests, ladies and gentlemen. I thank the Salam Prize Committee for recognizing the worth of my research work in algebra. I thank particularly, Professor Abdus Salam, for instituting one of the very few prizes available in Pakistan.
            Whatever we are today, our teachers have had a substantial contribution in it. I share the honour bestowed upon me today with my teachers. Some of the teachers who had a great influence on me include Professor Graham Higman, Professor Kh Masud and Mr Dilshad Hussain. I am greatly indebted to them.
            Since 1951, at least two quite distinctive factors have contributed to the renewed interest in the theory of groups. First, there was systematic study of groups of Lie type, begun by Chevalley and continued by Steinberg, Tits and others. Secondly, there are the efforts that have been made by Brauer, and by those who, directly or indirectly, are of his school, to characterize classes of groups by internal properties. My humble contribution belongs to the second school of thought, that is, to characterize classes of groups. I have used coset diagrams to achieve this.
            The coset diagrams for the modular group were basically propounded by Graham Higman in 1979. Coset Diagrams are a graphical representation of the permutation actions of a finitely generated group. These coset diagrams consist of sets of small triangles and edges. The vertices of the triangles are identified with cosets of the group. I have linked these diagrams with the parameterization of actions of the extended modular group on the projective lines over Galois fields. I have proved that for each conjugacy class of these actions there exists a unique coset diagram. This enables us to classify all the subgroups of the permutation groups yielded by these actions. This has a close relevance with the famous work of professor G.J.Thompson on rigidity classes.
            A partial answer to the famous Construction Problem has also been provided with regards these diagrams. I have found a necessary and sufficient condition for the existence of a fragment of a coset diagram corresponding to a conjugacy class of actions. In this way, I have been able to classify all the Hurwitz groups.
            Our scientists are faced with many problems. All these problems can be divided into two main categories, that is, problems that scholars encounter from the government and the problems that scholars face within their community.
           The first set of problems is due mainly to bureaucratic red tapism and unnecessary governmental control over scholars. For example, the NOC requirement for scholars to go abroad to interact with the international scientific community. If you want to go abroad to attend a one week conference you need to spend about three months of hard efforts and precious time running about from one department to another to get travel grant, leave and NOC. Apart from that, we need a very special heart to keep your blood pressure under control because you are likely to come across all sorts of nonsense that one can think of.
            The manner in which people are selected for scholarships abroad is also harmful to the progress of the scientific and scholastic community in the country. The criteria for selection is arbitrary and very often, worthy and capable candidates are rejected.
            The second set of problems is those, which the scientists face within their own academic environment. The stage has come where apparently we know what the problems are. We know what is happening to science in Pakistan. But, unfortunately, we are not willing to change the situation. This is where professional and intellectual honesty comes in. I do not believe that our country lacks resources as much as it has been projected in the past. I do not believe also that we lack capable workforce. Our land is very fertile in this regard. But frankly speaking, what we lack is honesty at all levels.
            Dishonesty stems basically from jealousy. Professional jealously is prevalent in all societies but it is especially widespread here in Pakistan. Instead of appreciating each other's good points we talk bad about each other. The overall academic atmosphere is in fact very discouraging. Particularly discouraging for many capable scientists is the way that the promotions are being conducted. There is no regular system of promotion/selection for scholars. Sometimes, positions are vacant but the posts are not advertised or are advertised at a particular time in order to favour some people. Moreover, selections are based on arbitrary criteria. The result is that really deserving and capable scholars are not promoted duly. Rather they become victims of politics and rules.
            If we want this country to prosper in scientific and technological know how, we have to work hard to eradicate these vices from the social and scientific fabric of our society. There is a need for the government to recognize these problems and do something to solve them.
            I thank you ladies and gentlemen.