Mathematical Abstraction
Mathematical abstraction is the process of simplifying complex concepts by focusing on their essential features while ignoring irrelevant details. This allows mathematicians to create general principles and theories that can be applied to various situations. For example, the concept of a number can represent different quantities, whether it's counting apples or measuring distances.
Through abstraction, mathematicians can develop structures like sets, functions, and algebraic systems that help in understanding relationships and patterns. This approach not only aids in problem-solving but also fosters the development of new mathematical ideas and fields, such as geometry and calculus.