In Fullmetal Alchemist, the most fundamental law of alchemy is Equivalent Exchange; like most real physical laws it’s not always phrased the same, but the basic idea is “To gain something, something of equal value must be given”.
The most-heard phrasing is from the first anime and seems excessively human-centric: “Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy’s first law of Equivalent Exchange.”
In alchemy that does not involve living beings, this is typically seen as a conservation law; elements are only rearranged, not created or destroyed.
Conservation laws are some of the most important and certain ones in science. Qualities like energy or angular momentum are conserved, meaning they can only be redistributed and not created or destroyed.
But at first it seems that in FMA’s alchemy, only matter is conserved, and it seems like energy isn’t. Eventually, the manga and FMA: Brotherhood both make it clear that alchemy taps into geothermal energy, so there’s ultimately no issue. (No conservation of energy issue, anyway; it’s still fantasy.)
But that’s after the point where the first anime diverged from the manga, and the alternate explanation is far darker. In this version, the energy for alchemy comes from the souls of people killed in another world; our world. Now, being fueled by souls sounds more magical than scientific, but then again, “magic” that can be studied scientifically because it follows consistent rules makes more sense than magic that seems to follow consistent rules but allegedly can’t be understood rationally.
But note, in the first anime, the energy source for alchemy is not known to most alchemists, and yet it’s not widely considered a great unsolved mystery either. And that’s what I’m going to say really doesn’t make sense; an industrialized civilization, where steam power is well established, that hasn’t discovered conservation of energy yet. In real life, the understanding of energy (as well as the laws of thermodynamics) and the development of the steam engine were closely linked.