At a time when mathematical fashion despises generality (seen as gratuitous “generalities”, i.e. vacuities) I affirm the principle force in all my work has been the quest for the “general.” In truth I prefer to accent “unity” rather than “generality.” But for me these are two aspects of one quest. Unity represents the profound aspect, and generality the superficial aspect. (Grothendieck, 87, p....

This short note mentions several areas of number theory and related parts of mathematics where model theory can potentially offer important new insights. Many of the listed above situations are very well known to number theorists. In some of them one can feel important similarities between two mathematical theories, which are still not formalized and well understood. A model theoretical analysi...

We review some of the connections between Random Matrix Theory and Number Theory. These include modelling the value distributions of the Riemann zeta-function and other L-functions, and the statistical distribution of their zeros. 1.

At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles. Thus, the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings. In this paper the numbers are considered as the fundamental entities.We discuss the construction of the corresponding physical theory. A hypothesis on the quant...