In 1980, A. P. Calderon published a short seminal paper entitled "On an inverse boundary value problem", which has become the starting point in the mathematical analysis of the following inverse problem: Can one determine the electrical conductivity of a medium by making current and voltage measurements at the boundary of the medium? To this day, this problem serves as a fundamental source of motivation and inspiration for many developments in the field of inverse boundary problems. In this talk we shall give an introduction to the field of inverse boundary problems, survey some of the most important developments, and state some open problems. 

Two very different mathematical topics, where one comes from the social sciences and the other from the physical sciences.  It is easy to expect that they have nothing to do with one another.  Instead, and as it will be developed in this talk,  thanks to connecting power of  mathematics, they share several relationships.