Mathematics has traditionally been blamed for being one of the preponderant factors that explains students’ dropout in universities. This assessment may seem rather violent; however, it is not so far from reality. We miss aspects related to empathy with new generations of students and a closer use of mathematics in the incorporation of new discourses. Therefore, in this communication, we discuss some aspects related to our understanding of mathematics for "non-mathematicians" in the university. Specifically, we reinterpret the idea of mathematically training critical citizens and propose the innovative design of a university mathematics subject taught at the School of Human Sciences at a Colombian university.