1,733 articles
Basel problem
The Basel problem, named for the Bernoulli family of Basel, asks for the exact sum of the reciprocals of the squares of the positive integers.
Basic Linear Algebra Subprograms
Basic Linear Algebra Subprograms (BLAS) is a specification of standard routines for vector and matrix operations in three levels, widely used by software such as LAPACK.
Basis (linear algebra)
A basis of a vector space is a linearly independent set that spans it, letting every vector be written uniquely as a combination of basis vectors.
Baum–Connes conjecture
The Baum–Connes conjecture, from operator algebras and noncommutative geometry, states that the assembly map is an isomorphism; it was posed by Paul Baum and Alain Connes in 1982.
Beal conjecture
The Beal conjecture is an unsolved number theory problem, posed by Andrew Beal in 1993, stating that A^x + B^y = C^z with exponents above 2 forces a common prime factor.
Beilinson–Bernstein localization
Beilinson–Bernstein localization is a theorem in geometric representation theory, announced in 1981, stating that Lie algebra representations are equivalent to D-modules on the flag variety.
Bell number
The Bell number B(n) is the number of ways to partition a set of n labeled elements into non-empty subsets; the sequence begins 1, 1, 2, 5, 15.
Bell numbers
The Bell numbers, named for mathematician Eric Temple Bell, count the partitions of a set of n labeled elements, beginning 1, 1, 2, 5, 15, 52.
Ben Green (mathematician)
Ben Joseph Green, born 1977 in Bristol, is a British mathematician who proved the Green–Tao theorem with Terence Tao in 2004 and is Waynflete Professor at Oxford.
Berkovich space
A Berkovich space is an analytic space over a non-archimedean valued field such as the p-adic numbers, introduced by Vladimir Berkovich in 1990, whose points are multiplicative seminorms.
Bernoulli number
The Bernoulli numbers are a sequence of rational numbers introduced by Jacob Bernoulli to sum powers of integers, appearing in the Euler–Maclaurin formula and the Riemann zeta function.
Bernoulli numbers
The Bernoulli numbers are a sequence of rational numbers named for Jacob Bernoulli, who introduced them in his 1713 Ars Conjectandi to compute sums of powers of integers.
Bertini (software)
Bertini is a software package for numerical algebraic geometry that solves polynomial systems by homotopy continuation, written in C and distributed free of charge by four researchers.
Bertrand's postulate
Bertrand's postulate, also called the Bertrand–Chebyshev theorem, states that for every n > 1 there is a prime between n and 2n; conjectured in 1845 by Joseph Bertrand and first proved by Chebyshev in 1850.
Beta function
The beta function, also called the Euler beta function, is a special function B(a, b) defined by an integral and equal to Γ(a)Γ(b)/Γ(a + b).
Bézout domain
A Bézout domain is an integral domain in which every finitely generated ideal is principal; examples include the ring of entire holomorphic functions and the ring of all algebraic integers.
Bézout's identity
Bézout's identity, also called Bézout's lemma, is a theorem of elementary number theory stating that the gcd of two integers is an integer linear combination of them.
Bézout's theorem
Bézout's theorem is a result in algebraic geometry stating that two projective plane curves of degrees m and n intersect in exactly mn points, counted with multiplicity.
Bfloat16
Bfloat16 (Brain Floating Point, BF16) is a 16-bit floating-point format for machine learning, introduced by Google Brain on TPUs, with FP32's range but lower precision.
BGG category O
BGG category O is a subcategory of modules over a complex semisimple Lie algebra serving as the standard setting for highest weight representation theory, introduced by Bernstein and the Gelfands in the 1970s.
Bhāskara I
Bhāskara I, also known as Bhaskara the First, was a 7th-century Indian mathematician and astronomer whose 629 commentary on Āryabhaṭa's Āryabhaṭīya is the earliest detailed prose exposition of mathematical astronomy in India.
Bhāskara II (भास्कर)
Bhāskara II, also called Bhāskarāchārya or Bhaskara the Learned, was an Indian mathematician and astronomer (1114–1185) who led the Ujjain observatory and wrote the Lilavati.
Bialgebra
A bialgebra (also bigebra) is a vector space with both an algebra structure and a compatible coalgebra structure, the common ancestor of Hopf algebras and quantum groups.
Bicategory
A bicategory is a weak 2-category in which composition of morphisms is associative and has identities only up to invertible 2-morphisms, introduced by Jean Bénabou in 1967.
Bicomplex number
A bicomplex number is a four-dimensional generalization of the complex number, written with two independent imaginary units; unlike quaternions it is commutative but has zero divisors.
Bidual
The bidual (second dual) of a vector space X is the dual of its dual, X = (X), containing X via a canonical embedding; reflexivity means this embedding is onto.
Bilinear form
A bilinear form is a function on a vector space that is linear in each argument separately, generalizing the dot product and underlying quadratic forms.
Billion
Billion, also called one billion, is the number 1,000,000,000 (a thousand million) in American and British English, though older European usage gives it the value 10^12.
Bimodule
A bimodule is an abelian group carrying a left module structure over one ring and a right module structure over another, with the two actions commuting.
Binary arithmetic
Binary arithmetic is arithmetic in base 2 using only the digits 0 and 1, the arithmetic of electronic computers, first described by Leibniz around 1679.