Well they mention several times in the show that alchemy is considered a science in their world. The classification of "science" and "magic" is a tricky thing when you start to really think about it. If it's widely accepted and totally explainable, we call it science. If it's either unsubstantiated, or if it works but we're not sure how, we tend to say it's magic.
In real life alchemy has much more to do with the transmutation of the soul, to achieve personal perfection. Kinda like most religions, you attempt to better yourself by meditating on certain principles. Symbolic rituals and glyphs help achieve a certain state of mind, if you know what they mean.
In Hagaren, Alchemy is a physical science involving the comprehension of matter and its components. The alchemist breaks down physical matter into its components and rearranges them to suit her needs. It's a Star Trek food replicator without the technology. The arrays channel energy by acting as symbolic signposts, the components are present, and an outside force is summoned via the array; the energy required to actually perform the transmutation, to move the components around. These techniques are documented and learnable. The reason some can do alchemy and some can't, at least as I took it anyway, is the same reason why I'm shitty at math, but my girlfriend can do computations in her head in a matter of seconds. The same reason some people draw pretty pictures, and others just give up. Sure all these things are learnable, but they just come easier to some than others.
As far as being magic or science? It fits both descriptions. Here's a hypothetical situation for you. If there were a magical practice, a short ritual and a specific engraving let's say, which could...I don't know...decompose food scraps? And if this practice became so well known that scientists studied its effects and documented all the various physical reasons why it worked and could explain what precisely was happening to the food scraps; it would move out of the realm of magic and into rational science. But the ritual and engraving would still be neccessary.
Here's a better example. Demonstrate a working telephone to someone who's never seen one, without explaining the science of how it works. It would be considered magic until you described the electrons vibrating throughout the wire (and even then it would sound a little sketchy).
And I've forgotten my point, which is probably a good thing as this was beginning to stretch on.
Uh...alchemy as illustrated in Hagaren is, to its practitioners, a science which exhibits traits that,
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over here on our side of the gate,
would be described as magic (or at least extremely advanced science). See, that's another thing. People tend to consider telepathy and psychokinesis, science. Theoretical, weird, sketchy, paranormal - but still science. I see no reason to believe that alchemy should not be considered a science in Hagaren. I also, however, see no reason not to call it magic.
But then, I see no reason not to call most modern appliances "magic."
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In the last episode it looks like Hohenheim has fallen in with a crowd of magic-practicing folks. I'm just assuming here, but I'd guess they're a Hermetic order of some sort. Basically; alchemists (but in a more "real-life" sense).