Introduction.

"Math Everywhere": this title of the conference dedicated to the sixtieth birthday of Vincenzo Capasso just summarizes an evaluation of the role of mathematics in science and society. Mathematics has always been an important part of culture and is respected as a basic discipline for natural sciences, medicine, engineering, economics and social sciences. The rapid progress of computer systems as well as new concepts and methods in mathematical modelling and simulation have strengthened the position of Mathematics. They offer a large potential and new perspectives for solving complex problems and for tackling important technological, medical, environmental, social, economical, and political challenges. [ABSTRACT FROM AUTHOR]