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 |
|---|---|
| Lefschetz number | topological invariant |
| Veech surface | — |
| Kontsevich–Zorich cocycle | — |
| Galois correspondence | mathematical concept |
| Galois connection | mathematical concept |
| Teichmüller space | mathematical concept |
|
Hurwitz surfaces
surface form:
Hurwitz surface
|
compact Riemann surface |
| Steklov operator | mathematical operator |
| Steklov function | mathematical concept |
| R-matrix | — |
| Hecke algebra | object in representation theory |
| 4-sphere S^4 | differentiable manifold |
| Fisher zeros | — |
|
Seifert fibered spaces
surface form:
Seifert fibered space
|
mathematical concept |
| Cayley graph | — |
| Gromov hyperbolic group | mathematical concept |
| Markov partition | mathematical concept |
| Sharkovsky ordering | mathematical concept |
| Godbillon–Vey invariant | topological invariant |
| Burger–Iozzi–Wienhard inequalities for higher rank groups | mathematical concept |
| Grassmann manifolds | mathematical concept |
|
Fatou sets
surface form:
Fatou set
|
mathematical concept |
| Tits building | — |
|
mixed Hodge structures
surface form:
mixed Hodge structure
|
mathematical concept |
| Frey curve | — |
| Frey curve construction | mathematical construction |
| GNS construction | mathematical construction |
|
Young diagrams
surface form:
Young diagram
|
combinatorial object |
| Eisenstein series | — |
| Cayley surface | projective variety |
| Hurwitz zeta function | meromorphic function |
| Bernstein–Gelfand–Gelfand resolution | mathematical construction |
| Bernstein center in representation theory | — |
| Bernstein–Sato polynomial | — |
| Bernstein center | — |
| Fox n-coloring of knots | knot invariant |
| Carleson measure | mathematical concept |
|
Christoffel
surface form:
Christoffel symbols
|
mathematical concept |
| Schwarz–Christoffel mapping | mathematical concept |
| Christoffel words | combinatorial object |
| Knuth’s up-arrow notation | mathematical notation |
| Rogers–Ramanujan-type identities | mathematical concept |
| Wigner distribution function | mathematical concept |
| Grothendieck universe | mathematical concept |