In Chapter 2 of Frankenstein by Mary Shelley, Victor Frankenstein relates his history to the sea captain, Robert Walton. In so doing, he describes his hunger to know the secrets of science, a hunger that has not been fostered by his family who are "not scientific." Victor says that he works under the guidance of his preceptors and diligently searches for the "philosopher's stone"--a base metal that could be turned to gold--and the elixir of life.
At this point, Victor's fascination with the "philosopher's stone," used metaphorically to mean the secrets of science is an admirable one since he expresses this reason:
"Wealth was an inferior object; but what glory would attend the discovery, if I could banish disease from the human frame, and render man invulnerable to any but a violent death!"
In addition, Victor is also intrigued by the power of electricity. At first, he states that he has "the spirit of good." However, "Destiny was too potent." His interest in alchemy as a means of obtaining knowledge of science which could be utilized in curing diseases is admirable. However, in seeking knowledge about nature and existence, Victor ventures beyond the ethical limits of man.
In Frankenstein by Mary Shelley, Victor's mention of his desire to discover the philosopher's stone is one of our major signals that he is a character who will go beyond the bounds of ethics and common bounds of knowledge. Victor is a figure meant not as a positive role model but a cautionary example of what happens when people delve into matters beyond what they should and are so dedicated to their own curiosity that they trample over the rights and feelings of others.
The philosopher's stone was considered by alchemists a catalyst used in the process of transmutation of base metals to gold. In the period in which Shelley was writing, alchemy had already been discredited as unscientific. Also, alchemy was regarded as superstitious and somewhat ethically dubious, associated with such things as magic and witchcraft.
Saying that Victor was interested in the philosopher's stone is a way of signalling that he is a slightly shady character who is engaged in activities that most of his contemporaries would consider at best eccentric and at worst unethical.