Mathematical abstracts are a kind of formal academic writing in which a short piece of text is attached to the beginning of an academic paper, which serves to inform the reader of the paper's contents. Most abstracts are very short, less than 200 words in length.
Abstracts are a key component of published academic papers, and are very often required by publications, proposals to conferences or publishers, and academic societies. The abstract of a math paper is designed to give an overview of its contents and introduce the reader to the ideas contained within. Abstracts help readers decide if the paper they are attached to is pertinent to their own research or is potentially interesting to read.