In mathematics, the terms “necessary” and “sufficient” have technical meanings. These terms come about when looking at two statements P and Q. If we say that P is sufficient for Q, then that means if P is true, Q automatically has to be true (P implies Q). On the other hand, if P is only necessary for Q, having P be true doesn’t mean Q has to be true (but the other way works, so Q implies P). If we have the P is both necessary and sufficient for Q, that means having one gives us the other for free. They are tied together and are inseparable.

Educators have unrealistic views about memorization.

This sounds like an easy question, but I think I have a bit of a different perspective on it.

As a student, there’s no shortage of things I could be doing to help my academic career. I could do some side research, I could read more about my field, I could network with other researchers, I could study more for my upcoming exams, I could work through another textbook, I could volunteer for any number of academic events, and the list goes on. There are so many things I could be doing to advance my career and invest in my future that I could be busy every day for the rest of my life. If I wanted to, I could fill my schedule up with these activities and never be done.