Editing Informal mathematics (section)

{{short description|Any informal mathematical practices used in everyday life}}
'''Informal mathematics''', also called '''naïve mathematics''', has historically been the predominant form of [[mathematics]] at most times and in most cultures, and is the subject of modern [[ethnomathematics|ethno-cultural studies of mathematics]]. The philosopher [[Imre Lakatos]] in his ''[[Proofs and Refutations]]'' aimed to sharpen the formulation of informal mathematics, by reconstructing its role in nineteenth century mathematical debates and concept formation, opposing the predominant assumptions of [[Formalism (philosophy of mathematics)|mathematical formalism]].<ref>Imre Lakatos, ''Proofs and Refutations'' (1976), especially the Introduction.</ref>  Informality may not discern between statements given by ''[[inductive reasoning]]'' (as in [[approximation]]s which are deemed "correct" merely because they are useful), and statements derived by ''[[deductive reasoning]]''.