If you are curious, yes you need Alchemy. I found that even with buying and breaking every item i do not use, and digging 2 or 3 times per battle you do not get enough crystals to learn and upgrade all the spells. To do that you need Alchemy 3 before you upgrade any spell. By having alchemy 3 I was able to write all the spells in the game into the spellbook and upgrade them to level 3.
I played Paladin on Hard and wanted to complete the spell book just to learn every spell. I got the Forest Defender Set that gives +9 Intellect so I played using Phantom a lot. The game was not that hard so I could affort to learn all the three schools even if I hardly used damaging spells at all.
On the other hand, in the game I have just finished; a mage on impossible, I did not touch the alchemy skill at all. Well, at least not until level 50. Then I tried to learn all the mage skills just for the fun of it. In this game I maxed Chaos and the damaging skill + all the skills that gives you Intellect and mana as quickly as possible. And I was really selective about which spells to upgrade. Right before the battle with Baal (the very last battle), I broke all the items I did not use, but in this game it did not give enough crystals to upgrade all the spells. During the game I had upgraded some of the big damaging spells to level 3 without Alchemy, and probably used 100-200 more crystals than necessary if I had upgraded them after I got Alchemy 3.
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