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Ender comments on Truly Part Of You - Less Wrong
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I make it a habit to learn as little as possible by rote, and just derive what I need when I need it.
Do realize that you're trading efficiency (as in speed of access in normal use) for that space saving in your brain. Memorizing stuff allows you to move on and save your mental deducing cycles for really new stuff.
Back when I was memorizing the multiplication tables, I noticed that
9 x N = 10 x (N-1) + (9 - (N-1))
That is, 9 x 8 = 70 + 2
So, I never memorized the 9's the same way I did all the other single digit multiplications. To this day I'm slightly slower doing math with the digit 9. The space/effort saving was worth it when I was 8 years old, but definitely not today.
There were actually a few times (in my elementary school education) when I didn't understand why certain techniques that the teacher taught were supposed to be helpful (for reasons which I only recently figured out). The problem of subtracting 8 from 35 would be simplified as such;
35 - 8 = 20 + (15 - 8)
I never quite got why this made the problem "easier" to solve, until, looking back recently, I realized that I was supposed to have MEMORIZED "15 - 8 = 7!"
At the time, I simplified it to this, instead. 35 - 8 = 30 + (5 - 8) = 20 + 10 + (-3) = 27, or, after some improvement, 35 - 8 = 30 - (8 - 5) = 30 - 3 = 20 + 10 - 3 = 27.
Evidently, I was happier using negative numbers than I was memorizing the part of the subtraction table where I need to subtract one digit numbers from two digit numbers.
I hated memorization.