“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. See Examples...
“…Math objects are abstract objects. They are not physical objects, but we think about them and talk about them as if they actually existed… [They] don’t move or change over time… [or interact] with the real world….
“…Our experience with [math objects] is repeatable. If you ask some mathematicians about a property of some particular mathematical object that is not too hard to verify, they will generally agree on what they say about it. When there is disagreement they commonly discover that someone has made a mistake or has misunderstood the problem. This is analogous to the way we deal with physical objects….
“…All you can know about a math object is its properties, the processes you can apply to it, and its relationships with other math objects. There is nothing else to know.”
Source: MATHEMATICAL OBJECTS, from AbstractMath.org, retrieved 10/3/2020. Bold lettering added to highlight what I believe is the most important part. Mathematical Object, from Wikipedia, also has some potentially useful information.
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
