Editing Mathematical folklore

{{Short description|Communally-attributed mathematical results}}
{{other uses of|folk theorem|Folk theorem (disambiguation)}}

In common mathematical parlance, a mathematical result is called '''folklore''' if it is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists.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.<ref name=":1">{{Cite web|url=https://ncatlab.org/nlab/show/folklore|title=folklore in nLab|website=ncatlab.org|access-date=2019-11-30}}</ref>

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.<ref name=":1" /> Sometimes, these are only alluded to in the public literature. 
An example is a book of exercises, described on the back cover:
{{quote|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.<ref>Grigore Calugareau & Peter Hamburg (1998) ''Exercises in Basic Ring Theory'', Kluwer,[{{isbn|0792349180}}]</ref>}}

Another distinct category is '''well-knowable''' mathematics, a term introduced by [[John Horton Conway|John Conway]].<ref>[[J. W. S. Cassels]] (1976) "An embedding theorem for fields: Addendem", ''Bulletin of the [[Australian Mathematical Society]]'' 14: 479–80 {{doi|10.1017/S0004972700025442}}</ref> 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]] studied in many ethno-cultural studies of mathematics.{{Citation needed|date=September 2019}} 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).<ref>{{Cite web|url=https://www.ams.org/notices/200501/fea-dundes.pdf|title=Foolproof: A Sampling of Mathematical Folk Humor|last1=Renteln|first1=Paul|last2=Dundes|first2=Alan|date=|website=American Mathematical Society|archive-url=|archive-date=|access-date=2019-11-29}}</ref>

==Stories, sayings and jokes==
{{See also|Mathematical joke}}
{{Wikiquote|Mathematicians}}
{{Wikiquote|Mathematics}}
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 {{Harv|Krantz|2002}}; examples include:
* [[Srinivasa Ramanujan]]'s [[taxicab numbers]].
*[[Galileo]] dropping weights from the [[Leaning Tower of Pisa]].
*An apple falling on [[Isaac Newton]]'s head to inspire his theory of gravitation.
*[[John von Neumann]]'s encounter with the famous [[John von Neumann#Mathematical quickness|fly puzzle]].<ref>{{cite web |date=February 15, 2014 |title=Fly Puzzle (Two Trains Puzzle) |url=http://mathworld.wolfram.com/TwoTrainsPuzzle.html |access-date=February 25, 2014 |publisher=Wolfram MathWorld}}</ref>
*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".<ref name=":2">{{Cite web|url=http://mathworld.wolfram.com/Theorem.html|title=Theorem|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-11-30}}</ref>
*[[Pál Turán]]'s suggestion that weak coffee was only suitable for [[Lemma_(mathematics)|lemmata]].<ref name=":2" />
*The "[[turtles all the way down]]" story told by [[Stephen Hawking]].
*[[Fermat]]'s [[Fermat's Last Theorem#Fermat's conjecture|lost simple proof]].
*The unwieldy proof and associated controversies of the [[Four Color Theorem]].
*The murder of [[Hippasus]] by the [[Pythagoreans]] for his discovery of [[irrational numbers]], specifically, [[square root of 2|√2]].<ref>https://www.scientificamerican.com/article/how-a-secret-society-discovered-irrational-numbers/</ref>
*Sir [[William Rowan Hamilton]], in a sudden moment of inspiration, [[History of quaternions|discovered quaternions]] while crossing [[Brougham Bridge]].<ref>https://md.spacegrant.org/quaternions-turn-175/#:~:text=The%20discovery%20was%20made%20%E2%80%94%20in,famous%20equations%20on%20the%20bridge.</ref>

== See also ==

* [[List of mathematical jargon]]
{{Portal|Mathematics}}

==References==
{{Reflist}}
<!--
* MM Hoque and SS Mostafizur Rahman, Wari-Bateshwar, Banglapedia: The National Encyclopedia of Bangladesh, Asiatic Society of Bangladesh, Dhaka, Retrieved: 20 February 2012
* Kamrul Hasan Khan (1 April 2007). "Wari-Bateswar reminds Ptolemy's 'Sounagoura'". The Daily Star.
* Enamul Haque 2001. Excavation at Wari-Bateshwar: A Preliminary Study. Edited by Enamul Haque. Dhaka, The International Centre for Study of Bengal Art, 2001, {{ISBN|984-8140-02-6}}
-->

==Bibliography==
{{Refbegin}}
* {{ Citation | title = Mathematical Apocrypha: Stories & Anecdotes of Mathematicians & the Mathematical | first = Steven G. | last = Krantz | authorlink=Steven G. Krantz | year = 2002 }}
* David Harel, "On Folk Theorems", ''[[Communications of the ACM]]'' '''23''':7:379-389 (July 1980)
{{Refend}}

== External links ==

* [https://www.math.utah.edu/~cherk/mathjokes.html Mathematical humor: Collection of mathematical folklore]

[[Category:Philosophy of mathematics]]
[[Category:Mathematics and culture]]
[[Category:Scientific folklore]]
[[Category:Sociology of scientific knowledge]]