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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square (geometry), square with the area of a circle, area of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of Line (geometry), lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the zero of a function, root of any polynomial with Rational number, rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Topics Characterized As Pseudoscience
This is a list of topics that have been characterized as pseudoscience by academics or researchers, either currently or in the past. Detailed discussion of these topics may be found on their main pages. These characterizations were made in the context of educating the public about questionable or potentially fraudulent or dangerous claims and practices, efforts to define the nature of science, or humorous parodies of poor scientific reasoning. Criticism of pseudoscience, generally by the scientific community or skeptical organizations, involves critiques of the logical, methodological, or rhetorical bases of the topic in question. Though some of the listed topics continue to be investigated scientifically, others were only subject to scientific research in the past and today are considered refuted, but resurrected in a pseudoscientific fashion. Other ideas presented here are entirely non-scientific, but have in one way or another impinged on scientific domains or practices. Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He is best known for De Morgan's laws, relating logical conjunction, disjunction, and negation, and for coining the term "mathematical induction", the underlying principles of which he formalized. De Morgan's contributions to logic are heavily used in many branches of mathematics, including set theory and probability theory, as well as other related fields such as computer science. Biography Childhood Augustus De Morgan was born in Madurai, in the Carnatic Sultanate, Carnatic region of India, in 1806. His father was Lieutenant-Colonel John De Morgan (1772–1816), who held various appointments in the service of the East India Company, and his mother, Elizabeth (née Dodson, 1776–1856), was the granddaughter of James Dodson (mathematician), James Dodson, who computed a table of anti-logarithms (inverse logarithms). Augustus De Morgan became blind in one eye within a few months of his bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Underwood Dudley
Underwood Dudley (born January 6, 1937) is an American mathematician and writer. His popular works include several books describing crank mathematics by pseudomathematicians who incorrectly believe they have squared the circle or done other impossible things. He is the discoverer of the Dudley triangle. Education and career Dudley was born in 1937, in New York City. He received bachelor's and master's degrees from the Carnegie Institute of Technology and a PhD from the University of Michigan. His 1965 doctoral dissertation, '' The Distribution Modulo 1 of Oscillating Functions'', was supervised by William J. LeVeque. His academic career consisted of two years at Ohio State University followed by 37 years at DePauw University, from which he retired in 2004. He edited the '' College Mathematics Journal'' and the ''Pi Mu Epsilon Journal'', and was a Pólya Lecturer for the Mathematical Association of America (MAA) for two years. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creationism
Creationism is the faith, religious belief that nature, and aspects such as the universe, Earth, life, and humans, originated with supernatural acts of Creation myth, divine creation, and is often Pseudoscience, pseudoscientific.#Gunn 2004, Gunn 2004, p. 9, "The ''Concise Oxford Dictionary'' says that creationism is 'the belief that the universe and living organisms originated from specific acts of divine creation.'" originally published in Creation/Evolution Journal , Volume 6 , No. 2 , Summer 1986. In its broadest sense, creationism includes various religious views,#Stewart 2010, Haarsma 2010, p. 168, "Some Christians, often called 'Young Earth creationists,' reject evolution in order to maintain a semi-literal interpretation of certain biblical passages. Other Christians, called 'progressive creationists,' accept the scientific evidence for some evolution over a long history of the earth, but also insist that God must have performed some miracles during that history to crea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Scientific Monthly
''The Scientific Monthly'' was a science magazine published from 1915 to 1957. Psychologist James McKeen Cattell, the former publisher and editor of '' The Popular Science Monthly'', was the original founder and editor. In 1958, ''The Scientific Monthly'' was absorbed by ''Science''. References External links Archived The Scientific Monthlyon the Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ... * Hathi Trust records - https://catalog.hathitrust.org/Record/000519252 American Association for the Advancement of Science academic journals Monthly magazines published in the United States Science and technology magazines published in the United States Defunct magazines published in the United States Magazines established in 1915 Magazines disestablished in 195 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tobias Dantzig
Tobias Dantzig (; February 19, 1884 – August 9, 1956) was a Russian-American mathematician, the father of George Dantzig, and the author of '' Number: The Language of Science (A critical survey written for the cultured non-mathematician)'' (1930) and ''Aspects of Science'' (New York, Macmillan, 1937). Biography Born in Shavli (then Imperial Russia, now Lithuania) into the family of Shmuel Dantzig (?-1940) and Guta Dimant (1863–1917), he grew up in Łódź and studied mathematics with Henri Poincaré in Paris.. His brother Jacob (1891-1942) was murdered by the Nazis during the Holocaust; he also had a brother Naftali (who lived in Moscow) and sister Emma. Tobias married a fellow Sorbonne University student, Anja Ourisson, and the couple emigrated to the United States in 1910. He worked for a time as a lumberjack, road worker, and house painter in Oregon, until returning to academia at the encouragement of Reed College mathematician Frank Griffin. Dantzig received his Ph.D. in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Morgan's Laws
In propositional calculus, propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both Validity (logic), valid rule of inference, rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of Logical conjunction, conjunctions and Logical disjunction, disjunctions purely in terms of each other via logical negation, negation. The rules can be expressed in English as: * The negation of "A and B" is the same as "not A or not B". * The negation of "A or B" is the same as "not A and not B". or * The Complement (set theory), complement of the union of two sets is the same as the intersection of their complements * The complement of the intersection of two sets is the same as the union of their complements or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning ''at least' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistency, consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of Mathematical proof, proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cantor's Diagonal Argument
Cantor's diagonal argument (among various similar namesthe diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbersinformally, that there are sets which in some sense contain more elements than there are positive integers. Such sets are now called uncountable sets, and the size of infinite sets is treated by the theory of cardinal numbers, which Cantor began. Georg Cantor published this proof in 1891, English translation: but it was not his first proof of the uncountability of the real numbers, which appeared in 1874. However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the ''Entscheidungsproblem''. Diagonalization arguments ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20 The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of ''Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently, the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, Wiles's proof of Fermat's Last Theorem, the first success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
