When students are taught about models, they are not normally encouraged to think about the progress in scientific understanding that led to those models. A good example is the conventional theory of superconductivity, which can be found in standard textbooks, but was for a very long time (50 years) probably the most important unsolved problem in physics. More important than that, it was a problem that every physicist who had any prominence in the field tried to solve, one way or another (Einstein, Landau, Feynman, Frolich, Bloch, Heisenberg, just to name a few). All the “failed” attempts to explain a remarkable body of empirical evidence that culminated with the BCS theory have a lot to teach us about the scientific method and the fundamental creative process of explaining experimental data.

This mini-course of four lectures is intended to stimulate undergraduate students to think critically about the the modeling process in physics. The first two lectures of the course will be devoted to a discourse on the scientific method: each lecture will be devoted to describe an outstanding problem in physics, the cultural challenges, the disputes between different currents of thoughts and at the end, the students will be engaged into the prevailing interpretation and why the mainstream interpretation was empirically considered more successful than the competing approaches. I will address outstanding puzzles, such as the problem of superconductivity, and the interpretation of quantum mechanics between competing schools of thought, that was finally addressed by Bell’s work in the 60s, among others.

In the third lecture, I will explore conservation laws in nature and the concept of order through spontaneously broken symmetries. I will address how conservation laws implied, for instance, in the existence of Dark matter in universe, among other topics. In the final lecture, I will make an overview of important active areas of research, including a modern concept of order that relies on topology, a field of mathematics that deals with properties what remain invariant under continuous deformations of shapes and spaces. This course is intended to engage undergraduate students in contemporary research.