The R-function theory of Thomas is used to model neutron inelastic scattering
and the fine, intermediate, and gross structure observed in the Dow Jones
Industrial Average on a typical trading day.
In this article, we discuss the remarkable connection between two very
different fields, number theory and nuclear physics. We describe the essential
aspects of these fields, the quantities studied, and how insights in one have
been fruitfully applied in the other. The exciting branch of modern
mathematics, random matrix theory, provides the connection between the two
fields.
A non-traditional proof of the Gregory-Leibniz series, based on the
relationships among the zeta function, Bernoulli coefficients, and the Laurent
expansion of the cotangent is given. New series for calculating pi are
obtained.