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 |
|---|---|
| Co1 | sporadic simple group |
| Co2 | sporadic simple group |
| Monster group | sporadic simple group |
| Jones polynomial | knot invariant |
| Farey tessellation | object in hyperbolic geometry |
|
Dyson’s transform in number theory
surface form:
Dyson’s transform
|
tool in additive number theory |
| Co3 | sporadic simple group |
| Legendre symbol | number-theoretic function |
| Noether field | — |
| B-splines | mathematical concept |
| HOMFLY-PT polynomial | knot invariant |
| Alexandrov–Čech cohomology | topological invariant |
| Pauli matrices | — |
| Lyapunov exponents | mathematical concept |
| Lyapunov fractal | — |
| Lyapunov vector | mathematical concept |
| Jacobi symbol | number-theoretic function |
| Jacobi last multiplier | mathematical concept |
| Jacobi operator | mathematical operator |
| Koblitz curves | — |
| Fresnel integrals | mathematical function |
| Dirac delta function | mathematical concept |
|
Menger
surface form:
Menger sponge
|
— |
| Menger sponge | — |
| Penrose tilings | — |
| Hasse invariant | arithmetic invariant |
| Hasse–Weil zeta function | object in arithmetic geometry |
|
Fresnel
surface form:
Fresnel integrals
|
mathematical function |
| Gröbner basis | mathematical concept |
| Euclidean space | mathematical concept |
| Levi-Civita connection | mathematical concept |
| Kähler manifold | complex manifold |
| Reverse Polish Notation | mathematical notation |
| Boltzmann collision operator | mathematical operator |
| de Bruijn sequence | combinatorial object |
| de Bruijn graph | mathematical concept |
| de Bruijn–Newman constant | mathematical constant |
| Riemann–Siegel theta function | mathematical function |
| Hardy Z-function | mathematical function |
| Cauchy sequence | mathematical concept |
| Cauchy problem | mathematical concept |
| Cauchy principal value | mathematical concept |
| Chern classes | topological invariant |
| Witten index | topological invariant |
| Weil group | object in number theory |
| Weil divisor | — |
| Weil pairing | mathematical concept |
| Weil representation | object in representation theory |
| Harish-Chandra isomorphism | isomorphism |
| étale cohomology | mathematical concept |