In mathematics it is usual to say not all as it is a combination of two mathematical logic operators: not and all. One could introduce a new operator called some and define it as this.
But what does this operator allow? It certainly doesn't allow everything, as one specifically says not all. So some is always a part. Can it allow nothing at all? Yes, because nothing is definitely not all.
Now in ordinary language usage it is much more usual to say some rather than say not all. Is there any differences here from the above? Yes, if someone offered you some potatoes in a bag and when you looked in the bag you discovered that there were no potatoes in the bag, you would be right to feel cheated. Here some definitely means not nothing; now if a friend offered you some cake and gave you the whole cake you would rightly feel surprised, so it means not all; but you will also probably feel surprised if you were offered three-quarters or even half the cake, so it also means a few or not much.
Going back to mathematics it is actually usual to say there exists some - which means that there is at least one, it may be a few or even all but it cannot be nothing.