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 |
|---|---|
| Hecke characters | mathematical concept |
| Shafarevich group of a torus | arithmetic invariant |
| Stiefel–Whitney classes | topological invariant |
| Ulam stability | mathematical concept |
| Busemann function | mathematical concept |
| Busemann space | mathematical concept |
|
Chern–Simons forms
surface form:
Chern–Simons form
|
— |
| Seiberg–Witten curve | algebraic curve |
| Seiberg–Witten differential | — |
| Haar measure | mathematical concept |
| Weil–Deligne group | — |
| idèle class group | — |
| Tate pairing | mathematical concept |
| Fock model | mathematical construction |
| Maslov index | topological invariant |
| Seiberg–Witten invariants | topological invariant |
| Möbius function | arithmetic function |
| Jack polynomials | — |
| q-Selberg integral | mathematical concept |
| Ulam spiral | mathematical visualization |
| Einstein notation | mathematical notation |
| Siegel modular form | — |
| Siegel upper half-space | — |
| Beilinson regulator | arithmetic invariant |
| Harish-Chandra c-function | object in representation theory |
| Plancherel measure | mathematical concept |
| Hodge star operator | mathematical operator |
| Lebesgue spaces | mathematical concept |
|
Banach spaces
surface form:
Banach space
|
mathematical concept |
| Dini derivative | mathematical concept |
| Courant–Friedrichs–Lewy condition | mathematical concept |
| Tate cohomology | mathematical concept |
| Cartan–Eilenberg spectral sequence | mathematical concept |
| Drinfeld modules | object in arithmetic geometry |
| Cantor normal form | mathematical concept |
| Hitchin connection | mathematical concept |
| Moore–Penrose inverse (precursor ideas) | mathematical concept |
| Tate curve | algebraic curve |
| Lubin–Tate formal groups | — |
| Stieltjes transform | mathematical concept |
| Ginibre ensemble | mathematical concept |
| Wigner matrices | — |
| Lebesgue measurable set | mathematical concept |
| Liouville surface | mathematical concept |
| Grünwald–Letnikov derivative | mathematical concept |
| Riemann–Liouville derivative | mathematical concept |
| Caputo–Fabrizio derivative | mathematical operator |
|
Michele Caputo
surface form:
Caputo fractional derivative
|
mathematical concept |
| Hurwitz numbers | topological invariant |
| Hurwitz group | mathematical concept |