There are two kinds of theorems

This blog post by Mark Dominus discusses the two kinds of theorems in mathematical study: those that validate models and those that derive new insights about phenomena. Dominus emphasizes the importance of understanding this distinction in math education, arguing that many students are confused by the lack of explicit instruction on why certain theorems are proven. The post illustrates this with examples from Euclidean geometry and foundational concepts of real numbers, highlighting that the aim of theorems is not only to prove known truths but to ensure the robustness of the mathematical models used.