A broad view of mathematics education takes it as the study of how people learn and do mathematics. Starting with this view, the actual and potential relationships of mathematics education as a research discipline to mathematics as a field of knowledge and activity and to the mathematicians carrying out that activity are analyzed. This leads to the picture of a gulf between the two scientific communities which are based in different cultures of thinking and research. A (meta-) study of mathematics and all its facets termed here mathematicology is proposed. It could serve as common ground for cooperative studies by mathematicians and mathematics educators. Thereby the gulf will not necessarily become narrower but a bridge over the differences and mutual misunderstandings could be built.