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 |
|---|---|
| Dirichlet eta function | mathematical function |
| Dirichlet kernel | — |
| Dirichlet boundary conditions | mathematical concept |
| Riemann integral | mathematical concept |
|
Riemann surfaces
surface form:
Riemann surface
|
mathematical concept |
| Riemann–Liouville integral | mathematical operator |
| Riemann sums | mathematical concept |
| Riemann zeta function | complex-valued function |
| Bernstein polynomials | mathematical concept |
| Fourier series | mathematical concept |
|
Markov processes
surface form:
Markov process
|
mathematical concept |
| Henselian ring | algebraic structure property |
| Fuchsian differential equation | — |
| Fuchsian group | mathematical concept |
| Fuchsian singularity | mathematical concept |
|
Hermitian forms (work on quadratic forms)
surface form:
Hermitian form
|
mathematical concept |
| Hermite constant | mathematical constant |
| Klein quartic | algebraic curve |
|
semisimple Lie groups
surface form:
semisimple Lie group
|
mathematical concept |
| Weyl denominator | mathematical concept |
| Weyl vector | — |
| Moyal product | mathematical concept |
| Mittag-Leffler function | complex-valued function |
| Blum integer | mathematical concept |
| Pfaffian form | mathematical concept |
| Witten–Reshetikhin–Turaev invariant | topological invariant |
| Donaldson invariants | topological invariant |
| Thurston norm | topological invariant |
| Leray–Schauder degree | topological invariant |
| Lindelöf space | mathematical concept |
| Gibbs dividing surface | mathematical construct |
| Carmichael number | mathematical concept |
| Pythagorean triples | mathematical concept |
| Fermat surface | projective variety |
| Galois representations | mathematical concept |
| Whitney stratification | mathematical concept |
| Cartan–Killing form | — |
| Borel subalgebras | mathematical concept |
| Iwasawa decomposition | mathematical concept |
| Euler’s totient function φ(n) | arithmetic function |
| Bourgain spaces | mathematical concept |
| Euler’s polyhedron formula | topological invariant |
| Kähler identities | mathematical concept |
|
Dolbeault cohomology classes
surface form:
Dolbeault cohomology class
|
— |
| Hodge filtration | mathematical concept |
| de Rham cohomology | topological invariant |
| Erdős number concept | mathematical concept |
|
Poisson
surface form:
Poisson bracket
|
mathematical concept |
| Poisson equation | mathematical concept |
| Poisson bracket | mathematical operator |