Mathematical beautyMathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. Mathematicians describe an especially pleasing method of proof as elegant.
Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
Central limit theoremIn probability theory, the central limit theorem (CLT) establishes that, in many situations, for independent and identically distributed random variables, the sampling distribution of the standardized sample mean tends towards the standard normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.
Material conditionalThe material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Proof assistantIn computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Densely defined operatorIn mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function. In a topological sense, it is a linear operator that is defined "almost everywhere". Densely defined operators often arise in functional analysis as operations that one would like to apply to a larger class of objects than those for which they a priori "make sense".
Existential quantificationIn predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain.
ProvenceProvence (prəˈvɒ̃s, USalsoprəʊˈ-, UKalsoprɒˈ-, pʁɔvɑ̃s) is a geographical region and historical province of southeastern France, which extends from the left bank of the lower Rhône to the west to the Italian border to the east; it is bordered by the Mediterranean Sea to the south. It largely corresponds with the modern administrative region of Provence-Alpes-Côte d'Azur and includes the departments of Var, Bouches-du-Rhône, Alpes-de-Haute-Provence, as well as parts of Alpes-Maritimes and Vaucluse.
12.7×108mmThe 12.7×108mm cartridge is a 12.7 mm heavy machine gun and anti-materiel rifle cartridge used by the former Soviet Union, the former Warsaw Pact countries, modern Russia, China and other countries. It was invented in 1934 to create a cartridge like the German 13.2mm TuF anti-tank rifle round and the American .50 Browning Machine Gun round (12.7×99mm NATO). It is used in the same roles as the NATO .50 BMG (12.7×99mm NATO) cartridge. The two differ in bullet shape and weight, and the casing of the 12.
ExistenceExistence is the ability of an entity to interact with reality. In philosophy, it refers to the ontological property of being. The term existence comes from Old French existence, from Medieval Latin existentia/exsistentia, from Latin existere, to come forth, be manifest, ex + sistere, to stand. Materialism holds that the only things that exist are matter and energy, that all things are composed of material, that all actions require energy, and that all phenomena (including consciousness) are the result of the interaction of matter.
