I think the reason why students might like a lecturer is because they find the lecturer can impart mathematical concepts more clearly than other, and possible &quot;smarter&quot; lecturers.<p>Whilst someone who teaches <i>must</i> clearly understand the material they are teaching, that&#x27;s not enough. They must also be able to explain it clearly, and preferably find a way of engaging with students. Their subject matter expertise probably needs to equal or even be slightly less than their pedagogical skills.<p>I fear you are mistaking the concerns here with the teaching of higher level math courses. Teaching lower level math like Math1A means teaching students who are NOT going on to be professional mathematicians. There are a raft of fields where you need to know foundational mathematics - like civil engineering, electrical engineering, physics and even economics. A good grounding in maths is very important, but students in these courses don&#x27;t have to be doing ground breaking mathematical research.