The Enchanting Equation

Many of us associate the concept of folklore with the Brothers Grimm, museums with late romantic paintings, perhaps Roman gods, mythologies or fairy tales and stories. It is, therefore, a rather bold assumption that the world of folklore encompasses the world of numbers or abstract ideation. There already is a mathematical concept called "folklore". Folklore in mathematics comprises small yet important components in theorems, definitions, proofs, and the evasive nature of facts, methods, and techniques. These fleeting ideas move gracefully among mathematicians, skipping journals and textbooks to live solely in the shared halls of knowledge.

From category theory to myths

A famous instance is the cobordism hypothesis, a concept in category theory—which may sound complex and confusing but is, in fact, rather simple. Think of it like creating a map that shows how different mathematical concepts and structures relate to each other. The cobordism hypothesis was introduced in a somewhat informal way using this toolset. The story goes that someone roughly outlined it on the back of an envelope, mimeographed it (whatever that means), and presented it to three individuals in a Chicago seminar in 1973. The twist is that the only evidence we have of these occurrences is a comment reportedly overheard in another seminar at Columbia in 1976. Despite this, if a bold young individual dares to formalize a rigorous proof and try to publish it, they'll likely face harsh criticism because it is not expected to be claimed by someone nor formalized and published.

Some of you might have already heard of the five physicists in a car. It is said that if five physicists are in a car and one is driving, they can be considered "on the way" only if a mathematician is among them. The humour often revolves around the stereotypical traits attributed to physicists and mathematicians. This case suggests that physicists might need a mathematician to navigate or make sense of their journey. It's a lighthearted play on the different perspectives and skills of these two groups of scientists. Mathematicians are believed to grasp the concept of a journey without needing to be on one. This again indicates the level of abstraction and criteria we fulfil to define things! It is beautiful, right? Another well-known saying is that if you place your left foot on a mathematics book during an exam, you will remember the material better. Of course, this is just a myth, but it remains a significant part of the broad culture among those interested in mathematics. These anecdotes arise as a blend of tradition, humour, and the fact that mathematicians often share a love for the subject and its cultural aspects. Moreover, humour is an educational tool that effectively communicates complex or abstract ideas, making the subject more appealing.

In the realm of mathematical folklore, the term "well-knowable mathematics", a term coined by John Conway-a distinguished mathematician born in 1937, is celebrated for his groundbreaking contributions across various mathematical domains, notably the creation of the influential "Game of Life." introduces a unique category that mirrors traditional folklore in some intriguing ways. Just as classic folktales like Little Red Riding Hood are known and factual narratives passed down through generations, well-knowable mathematics consists of mathematical concepts that are recognized and factual but aren't actively circulating in current research, rendering them somewhat passé.

Moreover, the parallel between folklore in general and mathematical folklore extends to the attempt to describe the genuine context within which work occurs. In traditional folklore, stories often serve as cultural expressions and reflections of societal norms. In contrast, in mathematical folklore, anecdotes and traditions reflect the shared culture and practices within the mathematical community.

While non-mathematicians might use the term "folklore math" to denote informal mathematics in ethno-cultural studies, within mathematical circles, "mathematical folklore" encompasses various esoteric elements such as slang, proverbs, limericks, and jokes. This mirrors the multifaceted nature of folklore, which often includes a rich tapestry of language, traditions, and humour. The comparison underscores the human tendency to create, share, and preserve cultural elements, whether in classic tales or the whimsical anecdotes of mathematical exploration.

In conclusion, exploring mathematical folklore takes us beyond the conventional realms of myths, fairy tales, and stories, introducing us to a world where abstraction becomes a tool to express complex concepts. From the cobordism hypothesis in category theory to the whimsical traditions like the five physicists in a car or placing one's foot on a math book during an exam, these anecdotes reflect the intersection of tradition, humour, and the shared love for mathematics. John Conway's concept of "well-knowable mathematics'' further adds a layer of untrendy yet factual elements, providing a unique glimpse into the genuine context of mathematical research. In this intricate tapestry of mathematical culture, folklore is a repository of shared knowledge and a means to make the subject more appealing and accessible.