In order to investigate how high school students and researchers perceive science-related (STEM) subjects, we introduce forma mentis networks. This framework models how people conceptually structure their stance, mindset or forma mentis toward a given topic. In this study, we build forma mentis networks revolving around STEM and based on psycholinguistic data, namely free associations of STEM concepts (i.e., which words are elicited first and associated by students/researchers reading "science"?) and their valence ratings concepts (i.e., is "science" perceived as positive, negative or neutral by students/researchers?). We construct separate networks for (Ns = 159) Italian high school students and (Nr = 59) interdisciplinary professionals and researchers in order to investigate how these groups differ in their conceptual knowledge and emotional perception of STEM. Our analysis of forma mentis networks at various scales indicate that, like researchers, students perceived "science" as a strongly positive entity. However, differently from researchers, students identified STEM subjects like "physics" and "mathematics" as negative and associated them with other negative STEM-related concepts. We call this surrounding of negative associations a negative emotional aura. Cross-validation with external datasets indicated that the negative emotional auras of physics, maths and statistics in the students' forma mentis network related to science anxiety. Furthermore, considering the semantic associates of "mathematics" and "physics" revealed that negative auras may originate from a bleak, dry perception of the technical methodology and mnemonic tools taught in these subjects (e.g., calculus rules). Overall, our results underline the crucial importance of emphasizing nontechnical and applied aspects of STEM disciplines, beyond purely methodological teaching. The quantitative insights achieved through forma mentis networks highlight the necessity of establishing novel pedagogic and interdisciplinary links between science, its real-world complexity, and creativity in science learning in order to enhance the impact of STEM education, learning and outreach activities.