##### Definition

A *mathematical object* is a concept or a structure that is defined and studied in mathematics. It is an abstract idea that can be represented and manipulated using mathematical language and symbols.

Mathematical objects can be simple, such as *numbers*, or more complex, like *functions* and *spaces*. Other examples are *sets*, *groups*, *points*, *lines*, *vectors*, *maps*, and so on.

They can be used to model real-world phenomena, express *mathematical relationships*, and solve mathematical problems. The study of mathematical objects often involves proving *theorems*, making *deductions*, and exploring their *properties* and *relationships*.