And it doesn't necessarily have to be math. You can also train yourself by memorizing poetry, Chinese characters, foreign language words, and so on. And somehow all of these activities are getting sidelined in the modern education. After all, what use is memorization when you can always look up the answer on a phone?
Memorizing all of the theorems you need, proofs, and a diverse set of examples is going to make it substantially easier to approach new problems.
I've heard it from people conducting interviews, when we're discussing what we want from candidates: "I'm not looking for memorization, I'm looking for problem solving!" - if you've memorized 1000 problems, you'll be better at problem solving than if you didn't!
There are lots of folk who can remember all sorts of details but never seem to be able to figure out how to put the pieces together.
(For jor can inte far opp min kokosnutt btw)
I think the commenters need to agree on a more-nuanced set of terms to reach agreement on this.
But "understanding" on its own doesn't allow you to reproduce a textbook full of theorems, you have to actually study and memorize at least a bit.
Once, in medieval times, rote memorization was a large part of the education process. This system was renowned for not producing flexible or imaginative thinkers. Medieval times produced very significant mathematicians, notably and mathematical advances actually detoured around medieval Europe, going from ancient Rome and Greece to India and the Muslim world and returning to Italy with the Renaissance.
I think people are trying to say memorising is critical, understanding follows, not leads. Sure, I think those posters framing things this way are incorrect. Problem solving may be something one learns and remembers but rote memorization, as in the medieval trivium, isn't significant part of such learning.