mathematical object
C3507
concept
A mathematical object is an abstract entity, such as a number, function, set, or space, defined by precise properties and relations within a formal mathematical system.
All labels observed (72)
| Label | Occurrences |
|---|---|
| mathematical concept | 236 |
| mathematical object canonical | 73 |
| topological invariant | 23 |
| sporadic simple group | 16 |
| mathematical function | 15 |
| mathematical notation | 14 |
| knot invariant | 11 |
| mathematical constant | 11 |
| mathematical operator | 10 |
| algebraic curve | 9 |
| mathematical construction | 8 |
| number-theoretic function | 8 |
| combinatorial object | 7 |
| arithmetic function | 6 |
| complex number | 6 |
| arithmetic invariant | 5 |
| real number | 5 |
| Hurwitz surface | 4 |
| algebraic structure property | 4 |
| class of polyhedra | 4 |
| complex manifold | 4 |
| differentiable manifold | 4 |
| integral domain | 4 |
| multiplicative function | 4 |
| polynomial invariant | 4 |
| projective variety | 4 |
| compact Riemann surface | 3 |
| complex-valued function | 3 |
| mathematical construct | 3 |
| mathematical curve | 3 |
| mathematical visualization | 3 |
| meromorphic function | 3 |
| object in arithmetic geometry | 3 |
| object in number theory | 3 |
| object in representation theory | 3 |
| abstract object | 2 |
| complex algebraic curve | 2 |
| one-dimensional complex manifold | 2 |
| operator algebra | 2 |
| real-valued function | 2 |
| C*-algebra | 1 |
| analytic space | 1 |
| constructible polygon problem | 1 |
| definite integral | 1 |
| family of sporadic simple groups | 1 |
| graphical representation of binary quadratic forms | 1 |
| imaginary unit | 1 |
| isomorphism | 1 |
| lattice in 24-dimensional Euclidean space | 1 |
| lattice in the complex plane | 1 |
| mathematical quantity | 1 |
| mathematical set | 1 |
| measure-theoretic notion | 1 |
| named mathematical concept | 1 |
| notion in real analysis | 1 |
| number theoretic object | 1 |
| number-theoretic constant | 1 |
| number-theoretic object | 1 |
| object in abstract algebra | 1 |
| object in dynamical systems theory | 1 |
| object in functional analysis | 1 |
| object in gauge theory | 1 |
| object in harmonic analysis | 1 |
| object in hyperbolic geometry | 1 |
| object in kinetic theory | 1 |
| object in real analysis | 1 |
| object of mathematical physics | 1 |
| objective function | 1 |
| representation of natural numbers | 1 |
| straightedge-and-compass construction | 1 |
| tool in additive number theory | 1 |
| topological notion | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: mathematical object
Generated description
A mathematical object is an abstract entity, such as a number, function, set, or space, defined by precise properties and relations within a formal mathematical system.
Instances (494)
| Instance | Via concept surface |
|---|---|
| Euler products for automorphic L-functions | mathematical concept |
| Galois group | mathematical concept |
| KKT conditions | mathematical concept |
| Lagrangian function | mathematical concept |
| Monge–Ampère equation | mathematical concept |
|
Hadamard matrices
surface form:
Hadamard matrix
|
combinatorial object |
| Gell-Mann matrices | — |
| golden ratio | mathematical constant |
| Lucas sequences | mathematical concept |
| Pisano period | mathematical concept |
| Penrose graphical notation | mathematical notation |
| Itô integral | mathematical concept |
| Ramanujan tau function | arithmetic function |
| Ramanujan theta function | mathematical function |
| Ramanujan prime | mathematical concept |
| mock theta functions | mathematical concept |
|
highly composite numbers
surface form:
highly composite number
|
mathematical concept |
| Ramanujan’s sum | number-theoretic function |
|
L-functions
surface form:
L-function
|
— |
| Platonic solids | class of polyhedra |
|
Riemannian manifolds
surface form:
Riemannian manifold
|
— |
| Born expansion of Green’s function | mathematical concept |
|
Khinchin
surface form:
Khinchin's constant
|
mathematical constant |
| Khinchin's constant | mathematical constant |
| Khinchin–Lévy constant | mathematical constant |
| Schmidt decomposition | mathematical concept |
| Cauchy functional equation | mathematical concept |
| Fredholm operator | mathematical concept |
| Chern character | mathematical concept |
| Todd class | topological invariant |
| Cartesian coordinate system | mathematical concept |
| Laplacian spectrum | mathematical concept |
| Peano curve | — |
| Eratosthenes spiral | mathematical visualization |
| Sobolev spaces | mathematical concept |
| Schauder basis | mathematical concept |
| Lefschetz fibration | mathematical concept |
| Banach–Mazur distance | mathematical concept |
| Banach limit | mathematical concept |
| Bailey chains | mathematical construction |
| affine Lie algebras | mathematical concept |
| Kleene numbering | mathematical concept |
| Shunya (void) | mathematical concept |
| Cesàro summation | mathematical concept |
| Szegő kernel | — |
| Neumann boundary conditions in potential theory | mathematical concept |
| Hilbert class field | mathematical concept |
| Dirichlet characters | mathematical concept |
| Du Bois-Reymond function | mathematical function |
| Kummer congruences | mathematical concept |