Mizanur Rahman by Michael Hoare
(pp. 26-27 in "Theory and Applications of Special Functions",
Developments in Mathematics, Volume 13, Springer-Verlag, 2005;
reproduced here with kind permission of Springer-Verlag)

This is an outline of how we first met and how Mizan came to branch
out on his extraordinary mathematical career. We first corresponded
and eventually met at Bedford College, London University in
1971/72. He was then working on Neutron Transport Theory (singular
integral equations), his Ph.D. subject, in which I had an interest
from a more general statistical physics viewpoint. With a sabbatical
coming up he had written to the outstanding English expert on neutron
transport, Mike Williams at Queen Mary College Nuclear Engineering
Department, with a view to spending a year there. For some reason Mike
couldn't take him in and suggested that he come to me at Bedford
instead. This worked splendidly, and I dare say the liberal arts
atmosphere of the college, set idyllically in Regent's Park, was a
distinct improvement on that of Nuclear Engineering in the East
End. The only downside was that we were a very small Physics
department and there was little resonance with the heavily
algebraicized Math department under Paul Cohn. This hardly seemed to
matter, since we were both to an extent outsiders from what were the
fashionable subjects at the time.

We started out on his home ground, the singular integral equation
arising from the form of one-dimensional gas model known as
'Rayleigh's piston' and this led to the first calculations of its
eigenvalue spectrum, with characteristic mixed discrete and continuum
sets. In the course of this he admitted me to the faith, convincing me
that Cauchy Principal Values and Hadamard finite parts could be made
tangible and did not need to handled as though matters of higher
metaphysics. About this time I happened to mention a problem in
combinatorics that had been fascinating me for some time, in fact
since my post-doc days at the University of Washington. This arose
from a disarmingly simple model in chemical kinetics which involved
the partitioning of energy quanta between different vibrational
degrees of freedom in colliding polyatomic molecules. Reformulated as
a 'urn model,' its iterations corresponded to a Markov chain for
partitioning balls in boxes, with only a subset ran- domized at each
event. My earlier eigenvalue solution for a continuum version of this
had come out in Laguerre polynomials and led to probability transition
kernels with action very similar to formulae of Erdélyi and
Kogbetlianz in 1930s special function theory, though at the time
without any probabilistic interpretation. (I was happily able to meet
Erdélyi in Edinburgh shortly before his death and he was delighted to
know that the formulae had a 'practical' side.) Mizan seized on the
implications of this problem and its generalizations and before long
was off and running with his first series of papers on special
function theory, while my 'statistical physics' by-products followed
at more leisurely intervals. I tended to keep cautiously within the
bounds of 'physical' models, while Mizan was soon off into the never
never land of q-theory. After he returned to Carleton we managed to
strike lucky with grants from the NRC of Canada and the SRC in London,
which kept us in funds for severalyears of visits to and fro as the
work progressed. (Happy days of the '70s and beneficent Research
Councils). Mizan even managed to come to Stuttgart in '77 when my turn
for a sabbatical came round and it was here that we sorted out what I
have ever since felt was the real 'gem' among our various
generalizations. This was the discovery of a new take on Bernoulli
Trials --- the idea of 'cumulative trials' in which one has the right
to 'throw again' on the subset of trials that fail, in order to
achieve complete success. That such a simple idea could have lain
dormant for over 200 years still amazes me, but no trace of our
results in the earlier literature has ever turned up.