Experimental mathematics advocates the use of substantial computation and
extensive searches to create and refine conjectures, discover algebraic
identities, and detect extremal behavior. We describe some recent results
in number theory obtained by using an experimental approach. In particular,
we describe two recent projects involving polynomials in some detail: one
with T. Trudgian concerning an expansion of the known zero-free region of
the Riemann zeta function, and a second with K. Hare regarding some
properties of small Pisot and Salem numbers.