Foundations problem in mathematics
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The foundations problem in mathematics was the late 19th century and early 20th century term for the search for the simplest metamathematics.
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.
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".