Representing numbers as sums of squares or more generally as
values of integral quadratic forms is certainly a question that belongs to the very classics
of mathematics and that had a very deep impact on the development of many important
theories of modern algebra and number theory. The goal of my talk will be to substantiate the
above thesis by recalling A. Hurwitz’s theory of integral quaternions, which he used to develop
a new proof of Jacobi’s four squares theorem. In my talk I will give an overview of Hurwitz’s theory
and present a variant of Hurwitz’s proof using the Zeta function of the ring of Hurwitz’s quaternions.