Folk mathematics

As the term is understood by mathematicians, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word-of-mouth but do not appear in print, either in books or in scholarly journals.

---

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 proofs of all statements from given axioms, practices in folk mathematics are usually understood intuitively and justified with examples -- there are no axioms.

The study of folk mathematics is also known as ethno-cultural studies of mathematics.

Several ancient societies have built rather impressive mathematical systems and carried out complex and fragile calculations based on proofless "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 commerce, engineering, calendar creation and the prediction of eclipses and stellar progression[?] were quite accurately practiced by several ancient cultures.

However, it is assessed that the inability of discerning 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 philosophers with the emergence of the modern mathematical practice of deductive logic.

Folk mathematics is of interest in anthropology and psychology as it casts light on the perceptions and agreements of other cultures. It is also of interest in developmental psychology as it reflects a naive understanding of the relationships between numbers and things. The field of naive physics is concerned with similar understandings of physics.

Both fields accept that modern peoples use folk mathematics and naive physics in everyday life, without really understanding how mathematical and physical ideas are derived or studied by science.