Folk mathematics
Encyclopedia
As the term is understood by mathematician
s, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that are found by investigation and may 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, showing relative insight of investigators.
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. For example, in tidying up loose ends of the classification of finite simple groups
around 2004 (a result which had been claimed, somewhat prematurely, to be proved around 1980), Michael Aschbacher
devoted an entire volume to proving various infrastructural results, some of which had not previously been proved in print.
A second example is a book of exercises, described on the back cover:
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.
's A Mathematician's Apology
and ; examples include:
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that are found by investigation and may 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, showing relative insight of investigators.
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. For example, in tidying up loose ends of the classification of finite simple groups
Classification of finite simple groups
In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic...
around 2004 (a result which had been claimed, somewhat prematurely, to be proved around 1980), Michael Aschbacher
Michael Aschbacher
Michael George Aschbacher is an American mathematician best known for his work on finite groups. He was a leading figure in the completion of the classification of finite simple groups in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin...
devoted an entire volume to proving various infrastructural results, some of which had not previously been proved in print.
A second example is a book of exercises, described on the back cover:
- This book contains almost 350 exercises in the basics of ring theoryRing theoryIn abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
. 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
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
. 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 apochryphal) stories or jokes involving mathematicians or mathematics that are told verbally in mathematics departments. Compilations include tales collected in G. H. HardyG. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....
's A Mathematician's Apology
A Mathematician's Apology
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician.-Summary:...
and ; examples include:
- Galileo dropping weights from the Leaning Tower of PisaLeaning Tower of PisaThe Leaning Tower of Pisa or simply the Tower of Pisa is the campanile, or freestanding bell tower, of the cathedral of the Italian city of Pisa...
. - An apple falling on Isaac NewtonIsaac NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
's head to inspire his theory of gravitation. - The drinking, duel and early death of Galois.
- Richard FeynmanRichard FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
cracking safes in the Manhattan Project. - Alfréd RényiAlfréd RényiAlfréd Rényi was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.-Life:...
's definition of a mathematician - "a mathematician is a device for turning coffee into theorems". - The "turtles all the way downTurtles all the way down"Turtles all the way down" is a jocular expression of the infinite regress problem in cosmology posed by the "unmoved mover" paradox. The phrase was popularized by Stephen Hawking in 1988. The "turtle" metaphor in the anecdote represents a popular notion of a "primitive cosmological myth", viz...
" story told by Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
. - Fermat's lost simple proof.
- The unwieldy proof and associated controversies of the Four Color TheoremFour color theoremIn mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color...
.