Abstract:For the purpose of meeting the needs of qualitative and quantitative research, this paper makes an approach to the determi-nant of quality and quantity as well as the characteristics of qualitative and quantitative research, and makes an introduction of the in-frerence from the object of mathematics drawn by Engels, some new formulations on the object of mathematics and some correspondingevaluation to these new formulations from the angle of qualitative and quantitative research. A conclusion is drawn that the object ofmathematics, as Engels pointed out, is still the space form of the real world and the relationship between quantities.