  The paper provides a review of A.M. Mathai's applications of the theory of
special functions, particularly generalized hypergeometric functions, to
problems in stellar physics and formation of structure in the Universe and to
questions related to reaction, diffusion, and reaction-diffusion models. The
essay also highlights Mathai's recent work on entropic, distributional, and
differential pathways to basic concepts in statistical mechanics, making use of
his earlier research results in information and statistical distribution
theory. The results presented in the essay cover a period of time in Mathai's
research from 1982 to 2008 and are all related to the thematic area of the
gravitationally stabilized solar fusion reactor and fractional
reaction-diffusion, taking into account concepts of non-extensive statistical
mechanics. The time period referred to above coincides also with Mathai's
exceptional contributions to the establishment and operation of the Centre for
Mathematical Sciences, India, as well as the holding of the United Nations
(UN)/European Space Agency (ESA)/National Aeronautics and Space Administration
(NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA)
Workshops on basic space science and the International Heliophysical Year 2007,
around the world. Professor Mathai's contributions to the latter, since 1991,
are a testimony for his social conscience applied to international scientific
activity.
