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Pseudomathematics
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Pseudomathematics
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. 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.
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.
One common type of approach is claiming to have solved a classical problem that has been proven to be mathematically unsolvable. Common examples of this include the following constructions in Euclidean geometry – using only a compass and straightedge:
For more than 2,000 years, many people had tried and failed to find such constructions; in the 19th century they were all proven impossible.
Another notable case were "Fermatists", who bombarded mathematical institutions with requests to check their proofs of Fermat's Last Theorem.
Another common approach is to misapprehend standard mathematical methods, and to insist that the use or knowledge of higher mathematics is somehow cheating or misleading (e.g., the denial of Cantor's diagonal argument or Gödel's incompleteness theorems).
The term pseudomath was coined by the logician Augustus De Morgan, discoverer of De Morgan's laws, in his A Budget of Paradoxes (1872). De Morgan wrote:
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Pseudomathematics
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. 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.
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.
One common type of approach is claiming to have solved a classical problem that has been proven to be mathematically unsolvable. Common examples of this include the following constructions in Euclidean geometry – using only a compass and straightedge:
For more than 2,000 years, many people had tried and failed to find such constructions; in the 19th century they were all proven impossible.
Another notable case were "Fermatists", who bombarded mathematical institutions with requests to check their proofs of Fermat's Last Theorem.
Another common approach is to misapprehend standard mathematical methods, and to insist that the use or knowledge of higher mathematics is somehow cheating or misleading (e.g., the denial of Cantor's diagonal argument or Gödel's incompleteness theorems).
The term pseudomath was coined by the logician Augustus De Morgan, discoverer of De Morgan's laws, in his A Budget of Paradoxes (1872). De Morgan wrote:
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