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According and Gödel
According to his classmate Klepetař, like most residents of the predominantly German Sudetenlaender, " Gödel considered himself always Austrian and an exile in Czechoslovakia " (" ein Österreicher im Exil in der Tschechoslowakei ").
According to the fundamental theorem of arithmetic, any number obtained in this way can be uniquely factored into prime factors, so it is possible to recover the original sequence from its Gödel number ( for any given number n of symbols to be encoded ).
According to Dawson's biography of Gödel ( Dawson 1997: 216 ),

According and mathematical
According to intuitionists ( anti-realists with respect to mathematical objects ), the truth of a mathematical statement consists in our ability to prove it.
According to Husserl, this view of logic and mathematics accounted for the objectivity of a series of mathematical developments of his time, such as n-dimensional manifolds ( both Euclidean and non-Euclidean ), Hermann Grassmann's theory of extensions, William Rowan Hamilton's Hamiltonians, Sophus Lie's theory of transformation groups, and Cantor's set theory.
According to Jewish tradition, the Jewish calendar is calculated based on mathematical rules handed down from God to Moses at the moment the command was given to make sure that Passover always falls in the springtime.
According to the New Schaff-Herzog Encyclopedia of Religious Knowledge, the Kestoi " appears to have been intended as a sort of encyclopedia of the material sciences with the cognate mathematical and technical branches, but to have contained a large proportion of merely curious, trifling, or miraculous matters, on which account the authorship of Julius has been questioned.
According to the principle of ontological parsimony, he holds that we do not need to allow entities in all ten of Aristotle's categories ; we thus do not need the category of quantity, as the mathematical entities are not " real ".
According to mathematical physicist Arthur Wightman:
According to Formalism, mathematical truths are not about numbers and sets and triangles and the like — in fact, they aren't " about " anything at all.
According to this view mathematical systems exist, and have structural features
According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein.
According to Sloan Career Cornerstone Center, individuals working in this area, " computational methods are applied to formulate and solve complex mathematical problems in engineering and the physical and the social sciences.
According to the Mathematics Genealogy Project, Chebyshev has 7, 483 mathematical " descendants " as of 2010.
According to the renowned neuropsychologist and neurobiologist Roger Wolcott Sperry though, intuition is a right-brain activity while factual and mathematical analysis is a left-brain activity.
According to Yamaguchi, Sacks ' mathematical explanations are also irrelevant.
According to Gauss, who first described it, it is the " mathematical figure of the Earth ", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations.
According to astrophysicist and math popularizer Mario Livio, since the publication of Luca Pacioli's Divina Proportione in 1509, when " with Pacioli's book, the Golden Ratio started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use ," many artists and architects have been fascinated by the presumption that the golden rectangle is considered aesthetically pleasing.
According to Vandervert, in the emotion-driven prodigy ( commonly observed as a " rage to master ") the cerebellum accelerates the streamlining of the efficiencies of working memory in its manipulation and decomposition / re-composition of visual-spatial content into language acquisition and into linguistic, mathematical, and artistic precocity.
According to this restriction, variables are used in a mathematical sense, with identifiers referring to immutable, persistent values.
According to Asimov's novels, Hari Seldon devised the Seldon Plan using a mathematical analysis he originally developed and called psychohistory.
According to Rosenblum ( 1994 ) " volume visualization examines a set of techniques that allows viewing an object without mathematical representing the other surface.
According to Noh-Varr the Kree have a mathematical equation that disproves the existence of any deity, which is taught to all Kree around " the same time we learn not to soil ourselves with excrement ".
According to the standard mathematical formulation of quantum mechanics, quantum observables such as x and p should be represented as self-adjoint operators on some Hilbert space.
According to Searle, no mathematical function can be used to connect a known VIN with its LPN, but the process of assignment is quite simple — namely, " first come, first served "— and can be performed entirely by a computer.
According to the NEOS statistics AMPL is the most popular format for representing mathematical programming problems.

According and logic
According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic.
According to psychologism, logic would not be an autonomous discipline, but a branch of psychology, either proposing a prescriptive and practical " art " of correct judgement ( as Brentano and some of his more orthodox students did ) or a description of the factual processes of human thought.
According to Gould, punctuated equilibrium revised a key pillar " in the central logic of Darwinian theory ".
According to these theologians, this law is not a law above God that he assents to but, rather, logic is an eternal part of God's nature, like his omniscience or omnibenevolence.
According to Jains, the ultimate principle should always be logical and no principle can be devoid of logic or reason.
According to the logic of the eternal return, the site of each such symbolic Center will actually be the Center of the World:
According to its website, " The GLP Leaf Party is a libertarian party and it encourages individuals and societies to upgrade their way of solving disputes to a cooperative-game logic.
According to S. Jay Olshansky and Bruce Carnes, " there is neither convincing evidence nor scientific logic to support the claim that adherence to a Paleolithic diet provides a longevity benefit.
According to Merton, " paradigm ", refers to " exemplars of codified basic and often tacit assumptions, problem sets, key concepts, logic of procedure, and selectively accumulated knowledge that guide and empirical inquiry in all scientific fields ".
According to Watts, and in keeping with the common practice of logicians of his day, Watts defined logic as an art ( see liberal arts ), as opposed to a science.
According to Watts, as a practical art, logic can be really useful in any of our inquiries, whether they are inquiries in the arts, or inquiries in the sciences, or inquiries of an ethical kind.
According to Ibn al-Nadim, al-Kindi wrote at least two hundred and sixty books, contributing heavily to geometry ( thirty-two books ), medicine and philosophy ( twenty-two books each ), logic ( nine books ), and physics ( twelve books ).
According to Burgess, philosophical logic in this sense, has its center of gravity in theoretical computer science, because many non-classical logics find applications there.
According to his wife, he first considered formalizing temporal logic in 1953.
According to this logic, if manufacturers ' profits are rising, it follows that they are producing more.
According to Geoffrey Hunter, while logic concerns itself with the " truths of logic ," metalogic concerns itself with the theory of " sentences used to express truths of logic.
According to Hong Kong film critic Perry Lam, writing in Muse magazine, ' unpredictable digressions and swift changes of scene can evoke a dreamer's logic, but his sound and images are always sharp and particular.
According to another tradition, i. e. the one associated with predicate logic and dependency grammars, the subject is the most prominent overt argument of the predicate.
According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic.
According to Hegel, logic is the form taken by the science of thinking in general.
According to Foucault, there are several instances where the Western, " liberal art of government " enters into a period of crisis, where the logic of ensuring freedom ( which was defined against the background of risk or danger ) necessitates actions " which potentially risk producing exactly the opposite.

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