Well, not quite, but almost. To understand why, a distinction between “memorizing” and “remembering” is in order.
When you use something in math, like a formula, enough times, you will remember it. Remembering comes from familiarity.
Remembering is part of learning. You can’t claim to have learned something unless you can remember it. However, learning also implies understanding the meaning of something, as well as how it is related to other things. As you use something repeatedly, you will come to understand what it means and how it is related to other things.
“Memorizing” means repetitively exposing yourself to something *for the express purpose of committing it to memory*. Memorization involves time spent dedicated to remembering something, and does not imply understanding meaning or relatedness.
Now, in math certain facts and formulas are used more frequently than others. Generally speaking, the more often you use something, the more important it is. Therefore, the more important something is, the more likely it is that you will remember it, as well as come to understand its meaning and relatedness, because you will be using it more frequently.
Because all of the knowledge available to humankind is instantly accessible to all of us via the Internet, anything worth memorizing is worth looking up whenever you need to. If you look something up enough times, you will *automatically* remember it.
Take, as an example, the formula for the area of a circle:
and the formula for the volume of a sphere:
The formula for the area of a circle is fairly important, and will come up repeatedly in many different applications. Therefore, if you study much math, you will be using it over and over again, and don’t have to bother memorizing it. You can just look it up whenever you need to, and eventually, if you look it up enough times, you will remember it and not need to look it up any more.
The formula for the volume of a sphere, on the other hand, is not as important (depending on how far you progress with your math studies, at least). You probably won’t use it as often, and therefore any time you spend memorizing it will be wasted. You can just look it up whenever you need it, and if you don’t end up looking it up enough times to remember it, then you didn’t need to anyway.
What it comes down to is this: given any fact or formula you encounter, you will either need to use it again in the future, or you won’t. If you need to use it again, you can look it up again, until you don’t need to any more. If you don’t ever use it again, then it wasn’t worth memorizing.
The one exception I can think of is the multiplication table. Taking the time to memorize the multiplication table up to 9 x 9 = 81 will definitely pay off for anybody in terms of the ability to quickly and easily do mental arithmetic.