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:
“By “object” is meant some element in the complex whole that is defined in abstraction from the whole of which it is a distinction.”
—John Dewey (1859–1952)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)