Foundations problem in mathematics
Several schools of the philosophy of mathematics met limitations one after the other in the 20th century. One can refer more ambiguously to the foundations of mathematics to avoid giving the impression that there is a 'problem' that can be solved in the same sense associated with a science or mathematics problem. That is, the term foundations problem makes some implicit assumptions, that can be expressed by saying that there is a single foundation and one could prove that.
The assumption that any foundation could be successfully modelled within mathematics itself was challenged. In the 1970s, those arguing the prevalence of quasi-empiricism in mathematics sometimes denied that assumption. Instead they sought to focus on mathematical practice and later a cognitive science of mathematics (an outright empirical basis for why mathematics works), and "Where Mathematics Comes From".