An unscientific field of study which later develops into a science.

Alchemists study and practice Alchemy which is considered a protoscience. While Alchemists are real people with a real purpose, the field they practice has not been proven real, as yet, by scientific protocol.

Using a loose definition, you could call chemists modern alchemists. But there were real alchemists who's main goal was to change one substance into another, usually this a cheap metal, like lead, into gold. Though the methods were primitive, the concepts are considered important work towards modern chemistry.