Mathematical folklore | Wikipedia audio article

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"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
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As the term is understood by mathematicians, folk mathematics or mathematical folklore is the body of theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word of mouth but have not appeared in print, either in books or in scholarly journals. Knowledge of folklore is the coin of the realm of academic mathematics.Quite important at times for researchers are folk theorems, which are results known, at least to experts in a field, and considered to have established status, but not published in complete form. Sometimes these are only alluded to in the public literature.
An example is a book of exercises, described on the back cover:

This book contains almost 350 exercises in the basics of ring theory. The problems form the "folklore" of ring theory, and the solutions are given in as much detail as possible.
Another distinct category is well-knowable mathematics, a term introduced by John Conway. These mathematical matters are known and factual, but not in active circulation in relation with current research. Both of these concepts are attempts to describe the actual context in which research work is done.
Some people, principally non-mathematicians, use the term folk mathematics to refer to the informal mathematics studied in many ethno-cultural studies of mathematics.