Amethyst is, in real life and this game a purple quartz crystal, and is mostly used in jewelery. In this game you can mine it with any pickaxe. It can be used as a currency or you can just dump it into the ocean with the rest of your old useless stone age tools( when i'm in a server you might want to look around the ocean one mans trash is another mans treasure!).
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Here is me with my thrusty stone pickaxe with some large Coal and 2 large amethyst.

Also is somtimes sold in shops.