# Only Numbers and Algebra

Learning mathematics in school and doing mathematics in general are *not* the same thing.

Learning mathematics in school and doing mathematics in general are *not* the same thing.

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.