In common mathematical parlance, a mathematical result is called folklore if it is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists. More specifically, folk mathematics, or mathematical folklore, is the body of theorems, definitions, proofs, facts or techniques that circulate among mathematicians by word of mouth, but have not yet 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 are considered to have established status, though 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:
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 (i.e., untrendy). Both of these concepts are attempts to describe the actual context in which research work is done.
Some people, in particular non-mathematicians, use the term ''folk mathematics'' to refer to the
informal mathematics
Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos ...
studied in many ethno-cultural studies of mathematics. Although the term "mathematical folklore" can also be used within the mathematics circle to describe the various aspects of their esoteric culture and practices (e.g., slang, proverb, limerick, joke).
Stories, sayings and jokes
Mathematical folklore can also refer to the 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 ; examples include:
*
Srinivasa Ramanujan
Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, ...
's
taxicab numbers
*
Galileo
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
dropping weights from the
Leaning Tower of Pisa
The Leaning Tower of Pisa ( it, torre pendente di Pisa), or simply, the Tower of Pisa (''torre di Pisa'' ), is the ''campanile'', or freestanding bell tower, of Pisa Cathedral. It is known for its nearly four-degree lean, the result of an unst ...
.
*An apple falling on
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
's head to inspire his theory of gravitation.
*The drinking, duel and early death of
Galois.
*
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ...
cracking safes in the Manhattan Project.
*
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory.
Life
Rényi was born in Budapest to A ...
's definition of a mathematician: "a device for turning coffee into theorems".
*
Pál Turán's suggestion that weak coffee was only suitable for
lemma
Lemma may refer to:
Language and linguistics
* Lemma (morphology), the canonical, dictionary or citation form of a word
* Lemma (psycholinguistics), a mental abstraction of a word about to be uttered
Science and mathematics
* Lemma (botany), ...
.
*The "
turtles all the way down" story told by
Stephen Hawking.
*
Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is ...
's
lost simple proof.
*The unwieldy proof and associated controversies of the
Four Color Theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...
.
See also
*
List of mathematical jargon
The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in ...
References
Bibliography
*
* David Harel, "On Folk Theorems", ''
Communications of the ACM
''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members.
Articles are intended for readers wi ...
'' 23:7:379-389 (July 1980)
{{Refend
External links
Mathematical humor: Collection of mathematical folklore
Philosophy of mathematics
Mathematics and culture
Scientific folklore
Sociology of scientific knowledge