Other responses are pointing toward this position, but I want to make it explicit: Memorizing an elegant algorithm is a lot more fun and more broadly useful tha

Other responses are pointing toward this position, but I want to make it explicit: Memorizing an elegant algorithm is a lot more fun and more broadly useful than memorizing the look-up table for a limited section of the results; but sometimes caching parts of the look-up table in your memory is necessary for expertise. For example: Many bright kids get frustrated when they have to repeat a section because of calculation errors, when they already get the concept. Even if you know a few good algorithms for multiplication, memorizing "the times tables" for double-digit numbers can be useful. On the other hand, you don't have to memorize everything. If you can reliably re-derive some result from theorems you know well, and you never need that result in a hurry, it's fine to leave it un-memorized.