In this article, we analyze the state of research data in mathematics. We find that while the mathematical community embraces the notion of open data, the FAIR principles are not yet sufficiently realized. Indeed, we claim that the case of mathematical data is special, since the objects of interest are abstract (all properties can be known) and complex (they have a rich inner structure that must be represented). We present a novel classification of mathematical data and derive an extended set of FAIR requirements, which accomodate the special needs of math datasets. We summarize these as deep FAIR. Finally, we show a prototypical system infrastructure, which can realize deep FAIRness for one category (tabular data) of mathematical datasets.