I did this when I watched the first series, and I find myself doing it again with brotherhood. I can't help but compare the representation of alchemy in this anime, with the real life occult. Despite what most people usually thought, Alchemy was never rooted in magic, mysticism, or spirituality, nor did the real life practitioners of the art claim it to be. It was in fact an actual science, and still exists today. We know it today as "Chemistry" which the anime hits right on the nail from the very start.
Alchemy was a movement that originated in ancient Egypt, who passed their teachings on to anyone in Europe, Asia, and the Middle East who were interested, during the medieval period. Medieval scientists from Germany(Which the setting of Fullmetal alchemist is based on), Ireland, England, Russia, Italy, Turkey, Iran, China, and India, were the usual ones who gained interest in it.
The Egyptian priests were the ones who discovered and gained an interest in the chemical make up of different things, when obeserving Metallurgy. They noticed how blacksmiths would first break down a metallic stone found within the earth, only to convert it into a strong metal and forge other objects from them like weapons, tools, and jewelry. These priests hypothesized that if this could be done with metal, than any material could be converted into another.
Centuries later as the teachings of alchemy spread, scientists began to discover other elements and combining chemicals. Most of the elements we have today on our periodic table, were discovered by alchemists. However some of the things they wished to do like transmuting one element into a completely different one was something, although possible, they did not have the technological advancements to do in that time period. Unlike today's scientists who have actually achieved that. Real life alchemists never used anything like transmutation circles, they worked with chemicals and materials in a similar way as modern scientists.
The concept of gaining eternal life and transmuting humans, as seen in the anime, actually came from the alchemy branch in India, which no one took seriously and rightfully so. Those scientists in particular were total nutcases. The concept of Alkahestry also existed, and was the Chinese and branch's main focus(which is why some of the alkahests in Fullmetal Alchemist Brotherhood are Chinese)
The real life Alkahestry was actually the art of deconstruction. The real life Alchemists wanted to invent a material called the philosopher stone, which was not a stone that could do anything like in the anime, but it was a stone that could be converted into any form of matter. The Alkahests wanted to invent the opposite of the philospher stone. Alkahests wanted to invent a fluid called Alkahest Which could break down and destroy almost any material including gold and diamond. Unlike the Alchemists, the Alkahests actually succeeded at creating the fluid. However it wasn't China's branch of Alkahests who did it, but 3 Muslim Alchemists who studied Alkahestry.
The Muslim Alchemists who invented Alkahest were Jabir Ibn Hayyan, Al-Kindi, and Muhammad Ibn Zakariya Razi. They each invented 3 forms of the fluid, which we know today as hydrochloric acid, Sulfuric acid, and Nitric acid. 3 deadly acids that can burn through almost anything. As for the Philosopher Stone, today's chemists and Geophysicists doubt it is something that can be invented, but theorize that phosphorus is the key to changing one material into another, seeing as phosphorus is the one chemical that has been found in nearly all material, including living organisms.