Mathematical object

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A mathematical object is an abstract concept arising in mathematics.

In the usual language of mathematics, an object is anything that has been
(or could be) formally defined, and with which one may do deductive reasoning
and mathematical proofs.

Typically, a mathematical object can be a value that can be assigned to
a variable, and therefore can be involved in formulas.

Commonly encountered mathematical objects include numbers, sets, functions,
expressions, geometric shapes, transformations of other mathematical objects,
and spaces.

Mathematical objects can be very complex; for example, theorem, proofs,
and even theories are considered as mathematical objects in proof theory.

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A good rule of thumb, is a mathematical object is something you would label.
The point p, the line AB, the number n, the function f, the matrix A,
the group G, the manifold M, ...

Not everything is an object. When you say 2x3=6, the multiplication isn't really an object.
Here it's more like an action - a verb.

https://math.stackexchange.com/quest...matical-object

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Mathematical objects are what we talk and write about when we do math.

Numbers, functions, triangles, matrices, groups and more complicated things
such as vector spaces and infinite series are all examples of mathematical objects.

Math objects are abstract objects. They are not physical objects,
but we think about them and talk about them as if they actually existed.

Math objects have certain properties that other kinds of abstract objects may not have.

In particular, unlike other kinds of abstract objects, math objects are inert.
Math objects don't move or change over time.
Math objects don't interact with other objects or with the real world.

For the purposes of doing math, what we need to understand is (among other things)
how mathematicians think about them, not what they "are".

https://abstractmath.org/MM/MMMathOb...maticalobjects

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List of mathematical objects by branch 1

Combinatorics
permutations, derangements, combinations

Set theory
sets, set partitions
functions, and relations

Geometry
- points, lines, line segments,
- polygons (triangles, squares, pentagons, hexagons, ...),
circles, ellipses, parabolas, hyperbolas,
- polyhedra (tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons, ),
spheres, ellipsoids, paraboloids, hyperboloids, cylinders, cones.

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