The Zilber–Pink conjecture pertains to the “finiteness of unlikely intersections” and
falls within the realms of logic, algebraic, and arithmetic geometry. Smooth
parametrization involves dividing mathematical objects into simple pieces and
then representing each piece parametrically while maintaining control over
high-order derivatives. Originally, such parametrizations emerged and were
predominantly utilized in applications of real algebraic geometry in smooth
dynamics.
The paper comprises two parts. The first part provides informal insights into
certain basic results and observations in the field, aimed at elucidating the recent
convergence of the seemingly disparate topics mentioned above. The second part
offers a retrospective account spanning from 1964 to 1974. During that period, Boris
and I studied at the same places, initially in Tashkent and later in Novosibirsk
Akademgorodok.
