Another advantage of abstraction is that it reveals a deeper connection between different fields of mathematics. Results in one field can suggest concepts and ideas to be explored in a related field.

Tracy Goodson-Espy, The Roles of Reification and Reflective Abstraction in the Development of Abstract Thought: Transitions from Arithmetic to Algebra, Educational Studies in Mathematics, Vol. 36, No.

Yet mathematics has undergone tremendous changes, especially during the twentieth century, when it pushed ever deeper into the realm of abstraction.