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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 objects, transformations of other mathematical objects, and spaces. Mathematical objects can be very complex; for example, theorems, proofs, and even theories are considered as mathematical objects in proof theory.

The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.^{[1]}

**^**Burgess, John, and Rosen, Gideon, 1997.*A Subject with No Object: Strategies for Nominalistic Reconstrual of Mathematics*. Oxford University Press. ISBN 0198236158