  This is expanded text of a lecture delivered by the author at the conference
"Mat\'eriaux pour l'Histoire des Math\'ematiques au XX\`eme si\`ecle", which
took place in Nice in January 1996. The task was to describe one area in the
development of arithmetical algebraic geometry in Moscow during the 1950s and
1960s. We shall begin by explaining the meaning of the analogy between numbers
and functions, starting with the simplest concepts. In the second part we study
a nontrivial example: the explicit formula for the law of reciprocity. In the
third part we shall become acquainted with certain aspects of the "social" life
of the Moscow school, in particular, with certain seminars, lectures, and
books. In the final part we shall examine another example of this analogy:
arithmetical surfaces and Arakelov theory.
