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The foundational philosophy in mathematics call "intuitionism" is NOT about intuitive understanding of mathematics, so the link was not appropriate. |
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'''''Folk mathematics''''' can also mean informal mathematical practices, as used in everyday life or by aboriginal or ancient people. While modern mathematics emphasizes formal and strict [[mathematical proof|proofs]] of all statements from given [[axiom]]s, practices in folk mathematics are usually understood intuitively and [[mathematical constructivism|justified with examples]] -- there are no axioms.
Some prefer the longer term '''ethno-cultural studies of mathematics''' to try to preserve the modern sense of the term 'mathematics' as meaning only those systems justified with reference to axioms. This sense however is very much a modern one, and most cultures historically have used methods and principles of mathematics with no great concern for axiomatic proof. The use by modern mathematicians of the term 'folk', however, is evidence that word of mouth evidence without rigorous application of current [[mathematical practice]] occurs even among professionals today - influencing the course of their work if not their publications of "[[finished mathematics]]".
Several ancient societies have built rather impressive mathematical systems and carried out complex and fragile calculations based on proofless "[[heuristics|heuristic]]" or "practical" approaches: mathematical facts were accepted simply because they consistently allowed one to perform a desired task, not because they were logically derived from "obvious" truths. [[Empirical methods]], as in science, provided the justification for a given technique.
Sophisticated [[business|commerce]], [[engineering]], [[calendar]] creation and the prediction of [[eclipse]]s and [[stellar progression]] were quite accurately practiced by several ancient cultures, on at least three continents, without the presence of an axiomatic approach to deriving the underlying mathematical relations.
However, it is assessed that the inability to discern between statements given by ''[[inductive reasoning]]'' (as in approximations which are deemed "correct" merely because they are useful) to statements derived by ''[[deductive reasoning]]'' is a major characteristic of folk mathematics. Historically, this was also a significant drawback in the development of [[geometry]] in [[ancient Egypt]], which was much later revised by [[Greek philosophy|Greek philosophers]] with the emergence of the modern mathematical practice of deductive logic.
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