6,052 articles
AKS primality test
The AKS primality test, or Agrawal-Kayal-Saxena primality test, is a deterministic polynomial-time algorithm deciding whether an integer is prime, announced in 2002 by three researchers at IIT Kanpur.
Al-Khwarizmi (محمد بن موسى الخوارزمي)
Al-Khwarizmi (Muhammad ibn Musa al-Khwarizmi, ca. 780–850) was a mathematician and astronomer at the House of Wisdom in Baghdad whose algebra treatise gave us "algebra", and whose Latinized name gave "algorithm".
Albert algebra
The Albert algebra, also called the exceptional Jordan algebra, is the 27-dimensional real Jordan algebra of 3×3 Hermitian matrices over the octonions, the only simple Jordan algebra that is not special.
Albert W. Tucker
Albert W. Tucker, born Albert William Tucker, was a Canadian-American mathematician at Princeton University who named the prisoner's dilemma and co-created the Karush–Kuhn–Tucker conditions in nonlinear programming.
Aleph number
Aleph numbers (ℵ₀, ℵ₁, …) are Cantor's indexed infinite cardinals; ℵ₀ counts the naturals, ℵ₁ the countable ordinals, and under the axiom of choice every infinite cardinal is an aleph.
Alex Chui
Alex Chui (Alex Chui Tsz Fung), born in Hong Kong in 2008, is a British mathematician who won seven medals, including five golds, in seven consecutive International Mathematical Olympiads from 2020 to 2026.
Alex Kontorovich
Alex Kontorovich is an American mathematician at Rutgers University known for work on thin orbits in number theory and for winning the AMS's 2014 Conant Prize.
Alexander horned sphere
The Alexander horned sphere, also called the horned sphere, is a wildly tangled embedding of the sphere in 3-dimensional space constructed by J. W. Alexander in 1924.
Alexander polynomial
The Alexander polynomial is a polynomial invariant of knots and links in three-dimensional space, introduced by James Waddell Alexander II in 1923 and the only known polynomial knot invariant until 1984.
Algebra
Algebra, historically called the cossic art, is a branch of mathematics studying operations and structures, from solving equations with unknowns to abstract algebra's groups, rings, and fields.
Algebra of random variables
The algebra of random variables is the set of arithmetic operations, addition, multiplication, and division, that can be performed on random variables, with rules for finding the resulting distributions.
Algebra over a field
An algebra over a field, or K-algebra, is a vector space over a field k with a bilinear multiplication, making it both a ring and a vector space.
Algebraic closure
An algebraic closure of a field F is an algebraically closed algebraic extension of F; every field has one, unique up to isomorphism fixing F.
Algebraic closure (model theory)
In model theory, the algebraic closure of a set is the collection of elements lying in some finite set definable from it, and in algebraically closed fields it matches the usual field-theoretic algebraic closure.
Algebraic cobordism
Algebraic cobordism, a cohomology theory for algebraic varieties built by Marc Levine and Fabien Morel, is the algebro-geometric analog of complex cobordism and the universal oriented cohomology theory on smooth varieties over fields of characteristic zero.
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics applying algebra, topology, and geometry to combinatorial problems, defined by method rather than subject matter and named in the late 1970s.
Algebraic Combinatorics (journal)
Algebraic Combinatorics (ALCO) is an open-access mathematics journal publishing papers where algebra and combinatorics interact, founded in 2018 by editors who resigned from Springer's Journal of Algebraic Combinatorics.
Algebraic connectivity
The algebraic connectivity, also called the Fiedler value, is the second smallest eigenvalue of a graph's Laplacian matrix; introduced by Miroslav Fiedler in 1973, it measures overall connectivity.
Algebraic curve
An algebraic curve, in the plane case also called a plane algebraic curve, is a one-dimensional variety defined by polynomial equations, central to algebraic geometry and used in cryptography.
Algebraic cycles and Chow groups
In algebraic geometry, an algebraic cycle is a finite integer combination of subvarieties, and the Chow groups are the groups of cycles modulo rational equivalence.
Algebraic data type
An algebraic data type (ADT), also called an algebraic type, is a composite type built by combining simpler types with sum and product operations, a core feature of Haskell.
Algebraic equation
An algebraic equation is a polynomial set equal to zero, such as a0x^n + ... + an = 0; finding its roots is one of mathematics' oldest problems.
Algebraic expression
An algebraic expression, also called an expression in algebra, combines numbers, letters standing for numbers, and operation symbols without an equality sign, as in 2x^2 + 3x + 8.
Algebraic function
An algebraic function is a function defined by a polynomial equation over a field, such as y = √(x²+1); it is generally many-valued, with branches and algebraic branch points.
Algebraic geometry
Algebraic geometry is the branch of mathematics that studies geometric objects defined by polynomial equations, principally algebraic varieties and schemes, and it underlies elliptic-curve cryptography and algebraic-geometry codes.
Algebraic integer
An algebraic integer is a complex number that is a root of a monic polynomial with integer coefficients; examples include √2 and i, but not 1/2.
Algebraic K-theory
Algebraic K-theory is a branch of mathematics that assigns sequences of abelian K-groups to rings and schemes, with applications in number theory, topology, and algebraic geometry.
Algebraic logic
Algebraic logic, also called the algebra of logic, studies logical systems through algebras, so deduction and completeness become algebraic properties, a tradition begun by Boole in 1847.
Algebraic matroid
An algebraic matroid is a matroid whose independent sets are the algebraically independent subsets of elements in a field extension, first studied in the 1930s by van der Waerden and Mac Lane.
Algebraic number
An algebraic number is a complex number that is a root of a polynomial with rational coefficients, such as √2 or the golden ratio; numbers like e and pi are transcendental.