Alchemy (the search for the Philosopher’s Stone, which would turn base metal to gold and give the possessor eternal youth) was once believed to be possible and real. However, the central quest of alchemy may be more complex, and less materialistic, than it first appears.
One interpretation of the ‘instructions’ left by the alchemists is that they are symbolic of a spiritual journey, leading the alchemist from ignorance (base metal) to enlightenment (gold). There seems to have been a mystical element to the work the alchemist was engaged upon, which set it apart from chemistry (of which it was undoubtedly both an offshoot and forerunner).
The colours red and white are mentioned many times in old texts on alchemy. One interpretation is that they, like base metal and gold, represent two different sides of human nature, which must be reconciled. This was the inspiration for the Christian names of Rubeus (red) Hagrid and Albus (white) Dumbledore. These two men, both hugely important to Harry, seem to me to represent two sides of the ideal father figure he seeks; the former is warm, practical and wild, the latter impressive, intellectual, and somewhat detached.
Although there are books on alchemy in the library at Hogwarts, and I always imagined that it would be studied by very clever students in their sixth and seven years, Hermione most uncharacteristically ignores the opportunity. Perhaps she feels (as Harry and Ron certainly do) that, far from wishing to make another Philosopher’s Stone, they would be happy never to see another one in their lives.