Mathematics as a Tool?

I analyze the new emerging role of mathematics for extracting structure from data. This role is different from the traditional role of mathematics as a tool for other sciences that provided a theoretical framework in which experiments acquired meaning, with which the quality of data could be assessed and which could be explored with the formal methods of mathematics. The challenge for mathematics now is to handle data without such theoretical guidance from other disciplines. This calls for new principles that are structural, abstract and independent of specific content.