Transmutation of base metals into gold was the central practical aim of a great deal of alchemy, and it had a name, chrysopoeia, gold-making. It is worth being clear about why intelligent people pursued it for fifteen hundred years, because the usual dismissal misses the point.
Within the sulfur-mercury theory, metals were compounds of two principles in varying proportion and purity. Gold was the perfectly balanced case, lead the corrupted one. On that theory transmutation is not magic; it is refinement, and it is exactly as reasonable an undertaking as purifying an ore. The theory was wrong, but it was a coherent chemical theory, and the project followed from it by ordinary logic.
Laboratory results reinforced it. Adding arsenic or zinc to copper produces alloys that look like silver and like gold. Gilding and amalgamation produce gold-coloured surfaces. Dissolving gold in aqua regia makes it vanish; precipitating it brings it back. To an observer without an atomic theory these are transmutations, and the difference between changing the appearance of a metal and changing the metal itself is not obvious.
The work was not wasted. Distillation apparatus, the mineral acids, laboratory glassware, the systematic recording of procedure, and the isolation of phosphorus and of a range of antimony and arsenic compounds all came out of it. Robert Boyle and Isaac Newton both worked seriously on transmutation, and Newton's alchemical manuscripts are extensive.
Transmutation is in fact possible, and it has been done. In 1980 Glenn Seaborg's group at Berkeley converted a minute quantity of bismuth into gold by stripping protons from the nuclei in a particle accelerator. The result cost immeasurably more than the gold was worth, which is the honest ending to the story: the goal was real, the method was wrong, and the method that works is uneconomic.