I am writing this as a person who has contributed significantly to almost all areas of Statistics, a number of topics in Mathematics, Information Theory, Geometrical Probabilities, Astrophysics etc and as a person who had devoted half of his research career (six months every year) for the training of research students and undergraduates in Kerala in particular and in India in general. In applied areas, I have contributions in social statistics, demography, data analysis, model building, environmental statistics, in geography (city designs of circular versus rectangular-grid cities), pollution problems, dam capacity, input-output models and the like. In theoretical areas, I have contributions to most mathematical of mathematical statistics.
My message to researchers in Kerala is that if you put your mind into any topic, you can produce significant results. You have the potential. What you need is self-discipline and ability to spend some quality time in research.
During my undergraduate and graduate trainings, I never had a proper course in multivariate statistical analysis. I studied the area myself and major part of my contributions in mathematical statistics is in the area of multivariate analysis. A voluminous book of mine around one thousand pages will appear from Springer, New York, in April-June 2022, containing simple and almost all new derivations and with plenty of new results. It will feature multivariate analysis in the complex domain also, very useful to engineers, physicists and others. Until and after I had taken my Ph.D degree, I never heard of Special Functions. I started the study of the area in 1965 in collaboration with Dr R.K. Saxena of Jodhpur, India. Now, I have several research level books and over hundred papers to my credit in the area, establishing a bridge between the mathematical topic of Special Functions and mathematical statistics. When DST (Department of Science and Technology, Government of India) started supporting CMS (Centre for Mathematical Sciences), Dr B.D. Acharya of DST wanted me to look into the area of Fractional Calculus and make CMS a world centre in Fractional Calculus. I started looking into the area in 2009 and by 2013 I had introduced a new definition for fractional integrals and fractional derivatives encompassing all the existing definitions and I could extend Fractional Calculus to the complex domain and to functions of matrix argument, most of the relevant papers of mine appeared in the leading journal: Linear Algebra and Its Applications. For the extension of the theory as well as for giving proper definitions, I have used statistical distribution theory is used, mainly the distributions of products and ratios of real scalar positive variables and real and complex positive definite or Hermitian positive definite matrices. I could make CMS as a world centre for Fractional Calculus as Dr Acharya desired for. In fact, all the leading researchers from around the world in the area of Fractional Calculus had visited CMS also and some had even helped CMS scholars to write joint papers with these leading researchers.
My research collaboration in astrophysics started in 1982 when a German physicist, as a representative of other researchers there, brought to me to McGill University some 12 open problems. I could not find any mathematical technique to solve them at that time. I used the statistical theory of the distributions of products of real scalar variables to solve the basic integral in all their open problems and thus I could solve all their problems. Then, we started writing joint papers, the German team supplying the physics and I supplying the corresponding mathematics. Those papers started appearing in all leading journals in physics such as Journal of Mathematical Physics, Physica A, Astrophysics and Space Science and so on, resulting inmore than fifty papers and two books so far. The book: Special Functions for Applied Scientists (Mathai and Haubold) is very popular, citation-wise. This collaboration resulted in the introduction of Special Functions, especially G and H-functions, in astrophysical research. Now, H-function has become very popular in many theoretical physics areas especially in solving fractional partial differential equations there.
In CMS, I had recruited ordinary M.Sc graduates from colleges in Kerala and gave training at CMS. With self-discipline and some general guidance I could make them produce wonders. The 13 students who received Ph.D through CMS, each had at least half a dozen papers published in international refereed journals, mostly in SCI journals, before they submitted their Ph.D theses. This shows that there is potential in our youngsters.
My message to youngsters is to develop self-discipline, go to bed early and get up early in the morning. During my research career of sixty years, I came across almost all top researchers in Statistics and good number of them in Mathematics. All have the habit of going to bed early and getting up early by 4 to 5 am. For any significant research output, you need to spend a good amount of quality time. Without hard work, nothing substantial can be achieved. You should cultivate the habit of spending long hours of concentrated work. You should develop the habit of reading books published by international publishers and research journals. It is unfortunate to see the situation of some students getting their Ph.D’s in Kerala without ever seeing a research level book or a research journal. Downloading a few papers and writing something parallel or making minor extensions or computations is not proper type of research and proper publications.
