Convention regarding inclusion of both an abstract and introduction in a mathematical paper
The purpose of an abstract and an introduction are very different, so it may be useful to include either or both. An abstract is a summary of the whole paper, focusing on the main result. It might exist separately from the paper itself as, say, an online "teaser" to get people to read the paper. But an introduction is intended to give background on the problem to be addressed in the paper and to situate it within the literature. You would almost always include an introduction. You might also write the abstract, but not actually include it within the paper itself.