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Dmitry Faddeev Dmitry Konstantinovich Faddeev (Russian: Дми́трий Константи́нович Фадде́ев, IPA: [ˈdmʲitrʲɪj kənstɐnʲˈtʲinəvʲɪtɕ fɐˈdʲe(j)ɪf]; 30 June 1907 – 20 October 1989) was a Soviet mathematician. Biography Dmitry was born June 30, 1907, about 200 kilometers southwest of Moscow on his father's estate. His fathe...
Isaak Yaglom Isaak Moiseevich Yaglom[1] (Russian: Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988)[2][3] was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom. Isaak Yaglom Born(1921-03-06)6 March 1921 Kharkov Died17 April 1988(1988-04-17) (aged 67) Moscow, Soviet ...
Mikhail Lavrentyev Mikhail Alekseyevich Lavrentyev (or Lavrentiev, Russian: Михаи́л Алексе́евич Лавре́нтьев) (November 19, 1900 – October 15, 1980) was a Soviet mathematician and hydrodynamicist. Mikhail Lavrentyev Born Mikhail Alekseyevich Lavrentyev (1900-11-19)November 19, 1900 Kazan, Russian Empire DiedOctober 1...
Mikhail Menshikov Mikhail Vasilyevich Menshikov (Russian: Михаи́л Васи́льевич Ме́ньшиков; born January 17, 1948) is a Russian-British mathematician with publications in areas ranging from probability to combinatorics. He currently holds the post of Professor in the University of Durham. Mikhail Menshikov Born (1948-0...
Sergei Sobolev Prof Sergei Lvovich Sobolev (Russian: Серге́й Льво́вич Со́болев) FRSE (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. Sergei Lvovich Sobolev Sobolev in Nice in 1970 Born(1908-10-06)6 October 1908 Saint Petersburg, Russian...
Kelvin transform The Kelvin transform is a device used in classical potential theory to extend the concept of a harmonic function, by allowing the definition of a function which is 'harmonic at infinity'. This technique is also used in the study of subharmonic and superharmonic functions. In order to define the Kelvi...
Elon Lindenstrauss Elon Lindenstrauss (Hebrew: אילון לינדנשטראוס, born August 1, 1970) is an Israeli mathematician, and a winner of the 2010 Fields Medal.[1][2] Elon Lindenstrauss Born (1970-08-01) August 1, 1970 Jerusalem, Israel NationalityIsraeli Alma materHebrew University of Jerusalem AwardsBlumenthal Award (200...
Oded Schramm Oded Schramm (Hebrew: עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.[1][2] Oded Schramm Schramm in 2008 Born(1961-12...
Saharon Shelah Saharon Shelah (Hebrew: שהרן שלח; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Saharon Shelah Shelah in 2005 Born (1945-07-03) July 3, 1945 Jerusalem, British Mandate for Palestine (now Israe...
Modern Arabic mathematical notation Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most ...
2 2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. ← 1 2 3 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers • Integers ← 0 ...
4 4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. ← 3 4 5 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers • Integers ← 0 10 20 30 40 50 60 70 80 90...
5 5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits. ← 4 5 6 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers ...
−1 In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0. ← −2 −1 0 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers • Integers ← 0 10 20 30...
Fifth power (algebra) In arithmetic and algebra, the fifth power or sursolid[1] of a number n is the result of multiplying five instances of n together: n5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powe...
Sixth power In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squari...
Seventh power In arithmetic and algebra the seventh power of a number n is the result of multiplying seven instances of n together. So: n7 = n × n × n × n × n × n × n. Seventh powers are also formed by multiplying a number by its sixth power, the square of a number by its fifth power, or the cube of a number by its ...
7 7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube. ← 6 7 8 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers • Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinalseven Ordinal7th (seventh) Numeral systemseptenary Factorizationprime Prime4th Divisors1, 7 Greek nu...
9 9 (nine) is the natural number following 8 and preceding 10. ← 8 9 10 → −1 0 1 2 3 4 5 6 7 8 9 → • List of numbers • Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinalnine Ordinal9th (ninth) Numeral systemnonary Factorization32 Divisors1,3,9 Greek numeralΘ´ Roman numeralIX, ix Greek prefixennea- Latin prefixnon...
Celsius The degree Celsius is the unit of temperature on the Celsius scale[1] (originally known as the centigrade scale outside Sweden),[2] one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The degree Celsius (symbol: °C) can refer to a specific temperature...
ℓ-adic sheaf In algebraic geometry, an ℓ-adic sheaf on a Noetherian scheme X is an inverse system consisting of $\mathbb {Z} /\ell ^{n}$-modules $F_{n}$ in the étale topology and $F_{n+1}\to F_{n}$ inducing $F_{n+1}\otimes _{\mathbb {Z} /\ell ^{n+1}}\mathbb {Z} /\ell ^{n}{\overset {\simeq }{\to }}F_{n}$.[1][2] Bhatt–...
Module (mathematics) In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Algebraic structure → Rin...
Maplet A maplet or maplet arrow (symbol: ↦, commonly pronounced "maps to") is a symbol consisting of a vertical line with a rightward-facing arrow. It is used in mathematics and in computer science to denote functions (the expression x ↦ y is also called a maplet). One example of use of the maplet is in Z notation, a ...
If and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence),[1] and can be li...
Partial function In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition or natural domain of f. If S equals X, that is, if f is defined on every e...
Uniqueness quantification In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition.[1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!"[2] or "...
Function composition In mathematics, function composition is an operation  ∘  that takes two functions f and g, and produces a function h = g  ∘  f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are co...
Radical symbol In mathematics, the radical symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as ${\sqrt {11}},$ while the nth root of x is written as ${\sqrt[{n}]{x}}.$ It is also used for other meanings in m...
Right angle In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or $\pi $/2 radians[1] corresponding to a quarter turn.[2] If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.[3] The term is a calque of Latin angulus rectus; here ...
Internal and external angles In geometry, an angle of a polygon is formed by two adjacent sides. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a point within the angle is in the interior of the polygon. A po...
Monus In mathematics, monus is an operator on certain commutative monoids that are not groups. A commutative monoid on which a monus operator is defined is called a commutative monoid with monus, or CMM. The monus operator may be denoted with the − symbol because the natural numbers are a CMM under subtraction; it is ...
Wreath product In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used in the classification of permutation groups and also provide...
≬ Wikipedia does not currently have an article on "≬", but its sister project Wiktionary does: Read the Wiktionary entry on "≬" You can also: • Search for ≬ in Wikipedia to check for alternative titles or spellings. • Start the ≬ article, using the Article Wizard if you wish, or add a request for it; but please...
Double turnstile In logic, the symbol ⊨, ⊧ or $\models $ is called the double turnstile. It is often read as "entails", "models", "is a semantic consequence of" or "is stronger than".[1] It is closely related to the turnstile symbol $\vdash $, which has a single bar across the middle, and which denotes syntactic conse...
Ordered set operators In mathematical notation, ordered set operators indicate whether an object precedes or succeeds another. These relationship operators are denoted by the unicode symbols U+227A-F, along with symbols located unicode blocks U+228x through U+22Ex. Mathematical Operators[1] Official Unicode Consortiu...
Normal subgroup In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup)[1] is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup $N$ of the group $G$ is normal in $G$ if and only if $gng^{-1}\in N$ for...
Hermitian matrix In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: $A{\text{...
Exclusive or Exclusive or or exclusive disjunction or exclusive alternation, also known as non-equivalence which is the negation of equivalence, is a logical operation that is true if and only if its arguments differ (one is true, the other is false).[1] Exclusive or XOR Truth table$(0110)$ Logic gate Normal forms Di...
Logical NOR In Boolean logic, logical NOR or non-disjunction or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both of p and q are false. It is logically equivalen...
Diamond operator In number theory, the diamond operators 〈d〉 are operators acting on the space of modular forms for the group Γ1(N), given by the action of a matrix (a b c δ ) in Γ0(N) where δ ≈ d mod N. The diamond operators form an abelian group and commute with the Hecke operators. Unicode In Unicode, the diamond...
Floor and ceiling functions In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, den...
Origin (mathematics) In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the s...
Flatness (mathematics) In mathematics, the flatness (symbol: ⏥) of a surface is the degree to which it approximates a mathematical plane. The term is often generalized for higher-dimensional manifolds to describe the degree to which they approximate the Euclidean space of the same dimensionality. (See curvature.)[1] ...
Semicircle In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, π radians, or a half-turn). It has only one line of symmetry (reflection symmetry). Semicircle Areaπr2/2 Perimeter(π+2)r In...
Pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the five points creates a similar symbol referred to as the pent...
Spherical angle A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs of great circles on a sphere. It is measured by the angle between the planes containing the arcs (which naturally also contain the centre of the sphere).[1] Not to be confused with Solid angle. See also ...
Tiny and miny In mathematics, tiny and miny are operators that yield infinitesimal values when applied to numbers in combinatorial game theory. Given a positive number G, tiny G (denoted by ⧾G in many texts) is equal to {0|{0|-G}} for any game G, whereas miny G (analogously denoted ⧿G) is tiny G's negative, or {{G|0}|...
Integral symbol The integral symbol: ∫ (Unicode), $\displaystyle \int $ (LaTeX) ∫ Integral symbol In UnicodeU+222B ∫ INTEGRAL (∫, ∫) Graphical variants $\displaystyle \int $ Different from Different fromU+017F ſ LONG S U+0283 ʃ ESH is used to denote integrals and antiderivatives in mathematics, especial...
Nimber In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim. The nimbers are the ordinal numbers endowed with nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal mu...
Smash product In topology, a branch of mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (X, x0) and (Y, y0) is the quotient of the product space X × Y under the identifications (x, y0) ∼ (x0, y) for all x in X and y in Y. The smash product is itself a pointed...
Hexagon In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon.[1] The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. For the crystal system, see Hexagonal crystal family. Regular hexagon A regular hexagon TypeR...
Soroban The soroban (算盤, そろばん, counting tray) is an abacus developed in Japan. It is derived from the ancient Chinese suanpan, imported to Japan in the 14th century.[1][nb 1] Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators. Constru...
Tangram The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; lit. 'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern (given only an outline) generally found in a puzzle book using all seven pieces witho...
Shinichi Mochizuki Shinichi Mochizuki (望月 新一, Mochizuki Shin'ichi, born March 29, 1969) is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry abo...
Tally marks Tally marks, also called hash marks, are a form of numeral used for counting. They can be thought of as a unary numeral system. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. However, because of...
Chinese numerals Chinese numerals are words and characters used to denote numbers in Chinese. Part of a series on Numeral systems Place-value notation Hindu-Arabic numerals • Western Arabic • Eastern Arabic • Bengali • Devanagari • Gujarati • Gurmukhi • Odia • Sinhala • Tamil • Malayalam • Telu...
Toshikazu Sunada Toshikazu Sunada (砂田 利一, Sunada Toshikazu, born September 7, 1948) is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences. He is professor emeritus of both Meiji University and Tohoku University. He is also distinguished professor of emeritus at Meiji ...
Shisanji Hokari Dr. Shisanji Hokari (穂刈 四三二, Hokari Shisanji, 28 March 1908 – 2 January 2004) was a Japanese mathematician. He was admitted to the American Mathematical Society in 1966.[1] He was a professor emeritus of Tokyo Metropolitan University and the president of Josai University. Year Age Milestone 1926 18 En...
1 1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is...
Percent sign The percent sign % (sometimes per cent sign in British English) is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Related signs include the permille (per thousand) sign ‰ and the permyriad (per ten thousand) sign ‱ (also known as a basis point), which indicate that a num...
Material conditional The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol $\rightarrow $ is interpreted as material implication, a formula $P\rightarrow Q$ is true unless $P$ is true and $Q$ is false. Material implication can also be characte...
Power set In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself.[1] In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set.[2] The powerset of S is va...
Rhombus In plane Euclidean geometry, a rhombus (PL: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playin...