What is Mathematical Folklore?
Mathematical folklore refers to 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. This concept is often used to describe the informal, unpublished knowledge shared among experts in a particular field, particularly in mathematics.
Importance and Significance
Mathematical folklore is significant because it highlights the importance of informal communication and shared knowledge within the mathematical community. Researchers often rely on these "folk theorems" or "folk mathematics" to build upon existing knowledge, making it a crucial aspect of mathematical research.
Types of Mathematical Folklore
There are two distinct categories of mathematical folklore mentioned in the source: "folk theorems" and "well-knowable mathematics." Folk theorems refer to results known to experts in a field, but not published in complete form. Well-knowable mathematics, on the other hand, refers to mathematical matters that are known and factual, but not in active circulation in relation to current research.
Examples and Illustrations
The source provides an example of a book of exercises in ring theory, where the problems are referred to as "folklore" of the field. This illustrates how mathematical folklore can be seen as a collection of common knowledge, shared among experts, but not necessarily documented in formal publications.
History and Development
The term "mathematical folklore" is a relatively recent concept, and its development is closely tied to the ways in which mathematicians communicate and share knowledge. The source does not provide specific dates or events, but it suggests that the concept has evolved over time to describe the informal, unpublished aspects of mathematical research.
Relationship to Research
Mathematical folklore is often used by researchers as a starting point for new investigations. By building upon existing, shared knowledge, researchers can make progress on complex problems and develop new ideas. This highlights the importance of mathematical folklore in the research process.
FAQ
What is mathematical folklore? Mathematical folklore refers to the body of theorems, definitions, proofs, facts, or techniques that circulate among mathematicians by word of mouth, but have not yet appeared in print.
How is mathematical folklore different from published research? Mathematical folklore consists of informal, unpublished knowledge shared among experts, whereas published research is formally documented and disseminated through journals and books.
Can anyone learn from mathematical folklore? Mathematical folklore is primarily used by experts in a particular field, but it can also serve as a starting point for researchers who are new to the field.
How does mathematical folklore relate to the concept of "well-knowable mathematics"? Well-knowable mathematics refers to mathematical matters that are known and factual, but not in active circulation in relation to current research, whereas mathematical folklore consists of informal, unpublished knowledge shared among experts.