We should agree that mathematics is no longer the Queen of the Sciences; while it is still believed to be the basis of modern education, its role needs to be re-defined. It is necessary to address this challenge. The first step in this direction consists of the adoption of a new perspective. The Latin word transgression means an act that goes beyond generally accepted boundaries. This monograph draws together papers written by mathematicians, educators, pedagogues, psychologists, and philosophers. Their aim is to identify a new role of mathematics and mathematics education in the modern world.