Pseudomathematics

For broader coverage of this topic, see Pseudo-scholarship.
Squaring the circle: the areas of this square and this circle are both equal to π. Since 1882, it has been known that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge. Nevertheless, "proofs" of such constructions were still published even 50 years later.

Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable areas. A person engaging in pseudomathematics is called a pseudomathematician or a pseudomath.[1] Pseudomathematics has equivalents in other scientific fields, and may overlap with other topics characterized as pseudoscience.

Pseudomathematics often contains mathematical fallacies whose executions are tied to elements of deceit rather than genuine, unsuccessful attempts at tackling a problem. Excessive pursuit of pseudomathematics can result in the practitioner being labelled a crank. Because it is based on non-mathematical principles, pseudomathematics is not related to misguided attempts at genuine proofs. Indeed, such mistakes are common in the careers of amateur mathematicians, some of whom go on to produce celebrated results.[1]

The topic of mathematical crankery has been extensively studied by mathematician Underwood Dudley, who has written several popular works about mathematical cranks and their ideas.

  1. ^ a b Lynch, Peter. "Maths discoveries by amateurs and distractions by cranks". The Irish Times. Retrieved 2019-12-11.