Abstraction in Mathematics
Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
The advantages of abstraction in mathematics are:
- it reveals deep connections between different areas of mathematics
- known results in one area can suggest conjectures in a related area
- techniques and methods from one area can be applied to prove results in a related area.
The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.
Read more about this topic: Abstractedly
Famous quotes containing the words abstraction and/or mathematics:
“When truth is nothing but the truth, it’s unnatural, it’s an abstraction that resembles nothing in the real world. In nature there are always so many other irrelevant things mixed up with the essential truth. That’s why art moves you—precisely because it’s unadulterated with all the irrelevancies of real life.”
—Aldous Huxley (1894–1963)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)