I've been recently thinking about what I've learned in mathematics, and I realised that in contrast to physics (or the other sciences), I tend to take the concepts and definitions for granted in that I assume they are "obvious" and have always been known. Of course this cannot be the case, and just as in physics, behind each concept or definition is probably a long history of concepts and definitions abandoned because they were not useful or simply incorrect. However, this history is rarely mentioned in classes, which motivates my question:
Are there examples of concepts, definitions, or entire (sub)fields of mathematics that were once influential and actively studied, but which were later abandoned because they were not useful, or because they were replaced by something more useful?