Reasoning by similarities, especially the ones associated with formal aspects, is one of the most valuable sources for the development of physical theories. The essential role of formal analogies in science can be highlighted by the fact that several equations for different physical situations have the exact same appearance. Coulomb’s law’s similarity with Newton’s, Maxwell’s application of fluid theory to electromagnetism and Hamilton’s optical mechanical analogy are some among many other examples. These cases illustrate the power of mathematics in providing unifying structures for physics. Despite the relevance of the subject, formal analogies are rarely systematically approached in physics education. In order to discuss this issue with pre-service physics teachers, we planned a lecture and designed a questionnaire with the goal of encouraging them to think about some “coincidences” in well known formulas and to give reasonable justifications. The details of this activity and its main results will be presented. Overall, the outcomes show that although the participants already
knew each one of the given formulas, the majority of students were not able to identify deeper similarities between them. The analysis of the students’ answers to the questionnaires and to the questions posed during semi-structured interviews allows us to propose a set of categories (levels) to classify the quality of analogy perception.