SPEECH AT SALAM PRIZE AWARDING CEREMONY
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.
The Abdus Salam Award, is a most prestigious award that is awarded annually to Pakistani nationals to the field of chemistry, mathematics, physics, biology. The award is awarded to the scientists who are resident in Pakistan, below 35 years of age on 31 December of the year for which the Prize was to be awarded.
ReplyDeleteIT was founded in 1981. The first Abdus Salam Award in Mathematics was given to Prof P.Hoodbhoy in 1984 and the second one was given in 1987 to Prof Q.Mushtaq.