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 |
|---|---|
| Diophantine equations | mathematical concept |
| Dedekind cut | mathematical concept |
| Dedekind ideal | mathematical concept |
| Dedekind number | mathematical concept |
|
Eilenberg–MacLane spaces
surface form:
Eilenberg–MacLane space
|
— |
| Culler–Vogtmann Outer space | — |
| Liouville function | arithmetic function |
|
Mellin transforms
surface form:
Mellin transform
|
mathematical concept |
|
Liouville numbers
surface form:
Liouville number
|
real number |
| Mordell curve | algebraic curve |
| GF(p) | integral domain |
| Itô–Taylor expansion | mathematical concept |
| Riccati equation | mathematical concept |
|
Stefan Machlup
surface form:
Onsager–Machlup function
|
mathematical function |
| Arf invariant | topological invariant |
| Arf rings | mathematical concept |
| Cassels–Tate pairing | mathematical concept |
|
Chebyshev distance (L-infinity metric)
surface form:
Chebyshev distance
|
mathematical concept |
| Gauss code | knot invariant |
| Fischer–Griess Monster | sporadic simple group |
| M | sporadic simple group |
| Fischer group Fi24′ | sporadic simple group |
| Held group | sporadic simple group |
| McLaughlin group | sporadic simple group |
| Thompson group Th | sporadic simple group |
| Janko group J4 | sporadic simple group |
| Kauffman polynomial | knot invariant |
| Khovanov homology | knot invariant |
| Stern–Brocot tree | — |
| Harada–Norton group | sporadic simple group |
| McL | sporadic simple group |
| Gauss sum | mathematical concept |
|
Patrick Michael Grundy
surface form:
Grundy number
|
mathematical concept |
| Alexander polynomial | knot invariant |
|
Jim Hoste
surface form:
HOMFLY-PT polynomial
|
polynomial invariant |
|
Józef H. Przytycki
surface form:
HOMFLY-PT polynomial
|
knot invariant |
| Kakutani–Rokhlin towers | mathematical concept |
|
Paweł Traczyk
surface form:
HOMFLY-PT polynomial
|
knot invariant |
| Fibonacci sequence | mathematical concept |
| Wigner 3j symbols | — |
|
Brillouin
surface form:
Brillouin function
|
mathematical function |
| Brillouin function | mathematical function |
| Turing degrees | mathematical concept |
| Big-O notation | mathematical notation |
| Hopf invariant | topological invariant |
|
Hopf algebra (concept named after him)
surface form:
Hopf algebra
|
mathematical concept |
| Coons patch | mathematical concept |
| Borel set | mathematical concept |
| Souslin operation | mathematical construction |
| Lévy–Prokhorov metric | mathematical concept |