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 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
the informal mathematics studied in many ethno-cultural
studies of mathematics.
== Stories, sayings and jokes ==
Mathematical folklore may also refer to unusual
(and possibly apocryphal) stories or jokes
involving mathematicians or mathematics that
are told verbally in mathematics departments.
Compilations include tales collected in G.
H. Hardy's A Mathematician's Apology and (Krantz
2002); examples include:
Galileo dropping weights from the Leaning
Tower of Pisa.
An apple falling on Isaac Newton's head to
inspire his theory of gravitation.
The drinking, duel and early death of Galois.
Richard Feynman cracking safes in the Manhattan
Project.
Alfréd Rényi's definition of a mathematician:
"a device for turning coffee into theorems".
The "turtles all the way down" story told
by Stephen Hawking.
Fermat's lost simple proof.
The unwieldy proof and associated controversies
of the Four Color Theorem.
== See also ==
== Notes
