The beauty of abstraction in mathematics

摘要

This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones, seven fish, and seven trees represent in some sense one entity, in this case all united by the number seven. That in itself is an abstraction. We will discuss abstraction and the different beautiful properties of mathematics in relation to some examples, where we describe the connection between algebra and geometry. Modern technological tools enable and encourage us to perform mathematical investigations of a kind that was once considered difficult.