Mathematical objects are abstract entities that arise in the study of mathematics. They include numbers, shapes, functions, and sets, among others. Each of these objects has specific properties and relationships that can be analyzed and manipulated using mathematical rules and operations. For example, the number 3 can be added to 5 to yield 8, while a circle can be defined by its radius and center. These objects serve as the foundation for various branches of mathematics, such as algebra, geometry, and calculus. They help mathematicians formulate theories, solve problems, and understand complex concepts. By studying these objects, one can gain insights into patterns and structures that exist in both mathematics and the real world.