Editing Informal mathematics

{{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]]''.

==Terminology==

''Informal mathematics'' means any informal mathematical practices, as used in everyday life, or by aboriginal or ancient peoples, without historical or geographical limitation. Modern mathematics, exceptionally from that point of view, emphasizes formal and strict [[mathematical proof|proofs]] of all statements from given [[axiom]]s. This can usefully be called therefore ''formal mathematics''. Informal practices are usually understood intuitively and justified with examples—there are no axioms. This is of direct interest in [[anthropology]] and [[psychology]]: it casts light on the perceptions and agreements of other cultures.  It is also of interest in [[developmental psychology]] as it reflects a naïve understanding of the relationships between numbers and things. Another term used for informal mathematics is ''folk mathematics'', which is ambiguous; the [[mathematical folklore]] article is dedicated to the usage of that term among professional mathematicians.

The field of [[naïve physics]] is concerned with similar understandings of physics. People use mathematics and physics in everyday life, without really understanding (or caring) how mathematical and physical ideas were historically derived and justified.

==History==
There has long been a standard account of the development of [[Egyptian geometry|geometry in ancient Egypt]], followed by [[Greek mathematics]] and the emergence of deductive logic. The modern sense of the term ''mathematics'', as meaning only those systems justified with reference to axioms, is however an [[anachronism]] if read back into history. Several ancient societies built impressive mathematical systems and carried out complex calculations based on proofless [[heuristic]]s and practical approaches. Mathematical facts were accepted on a [[wikt:pragmatic|pragmatic]] basis. [[Empirical method]]s, as in science, provided the justification for a given technique. Commerce, [[engineering]], [[calendar]] creation and the prediction of [[eclipse]]s and [[stellar progression]] were practiced by ancient cultures on at least three continents.

==See also==
* [[Ethnomathematics]]
* [[Folk psychology]]
* [[Mathematical Platonism]]
* [[Numeracy]]
* [[Pseudomathematics]]

== References ==
{{reflist}}

{{Areas of mathematics}}

[[Category:Philosophy of mathematics]]
[[Category:Critical pedagogy]]
[[Category:Sociology of scientific knowledge]]
[[Category:Mathematics and culture]]
[[Category:Scientific folklore]]