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 have not appeared in print, either in books or in scholarly journals.
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. Another distinct category is wellknowable mathematics, a term introduced by John Conway. This consists of matters that 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 ethno-cultural studies of mathematics.
In the philosophy of mathematics, mathematical practice is used to distinguish the working practices of professional mathematicians (e.g.
This distinction is considered especially important by adherents of quasi-empiricism in mathematics, which denies the possibility of foundations of mathematics and attempts to refocus attention on the ways in which mathematicians arrive at mathematical statements.
One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the foundations of mathematics remain unclear and ambiguous.
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