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 |
|---|---|
| Grothendieck topology | mathematical concept |
| Grothendieck spectral sequence | mathematical concept |
| Grothendieck category | mathematical concept |
| Veblen hierarchy | mathematical concept |
| Atiyah–Hirzebruch spectral sequence | — |
| Serre spectral sequence | mathematical concept |
| Riemann–Stieltjes integral | mathematical concept |
| Kleinian group | — |
| Riemann sphere | — |
| Caputo derivative | mathematical concept |
| Weyl fractional integral | mathematical operator |
| Hadamard fractional integral | mathematical concept |
| Dirichlet conditions | mathematical concept |
| Catmull–Rom spline | mathematical concept |
| Markov semigroup | mathematical concept |
|
Dedekind zeta functions
surface form:
Dedekind zeta function
|
number-theoretic function |
| Teichmüller curve | — |
| Clebsch–Gordan coefficients | mathematical concept |
|
Clebsch diagonal surfaces
surface form:
Clebsch diagonal surface
|
projective variety |
|
Galois
surface form:
Galois group
|
mathematical concept |
| Yang monopole | object in gauge theory |
| Dehn’s decision problems in group theory | mathematical concept |
| Dehn invariant | mathematical quantity |
| Dehn complex | — |
| Dehn function | mathematical concept |
| Milnor fibration | mathematical concept |
| Pascal's triangle | — |
| Deligne cohomology | mathematical concept |
| Gelfand transform | mathematical concept |
|
Venn
surface form:
Venn diagram
|
mathematical concept |
| Wightman functions | — |
| Snell envelope | mathematical concept |
| Wightman correlation functions | — |
| C*-algebras | operator algebra |
|
Plücker
surface form:
Plücker coordinates
|
mathematical concept |
| Plücker coordinates | mathematical concept |
| Wiener measure | mathematical concept |
| Gaussian integral | mathematical concept |
| construction of the regular 17-gon with straightedge and compass | straightedge-and-compass construction |
| Gaussian integers | — |
| Gauss’s constant | mathematical constant |
| Noetherian module | mathematical concept |
| Conway notation for knots | mathematical notation |
| Conway groups | family of sporadic simple groups |
| Conway polynomial | knot invariant |
| Look-and-say sequence | combinatorial object |
| Conway’s topograph | mathematical visualization |
| Stratonovich integral | mathematical concept |
| Noetherian space | topological notion |
| Chebyshev functions | arithmetic function |