Examples of Poor Definitions of Mathematics for Essay Assignment 1
The following statements have been made by previous students who have taken this class with me on
their 1st essay assignment. All of them received an F on essay assignment 1 because their definitions of
mathematics were too ambiguous. What do I mean by ambiguous? Here are some of the worst ones:
Mathematics is everywhere… Mathematics is in everything… Mathematics is everything … or
Everything is mathematics.
Far too vague… Some things we regard as NOT mathematics… What are the qualities that separate math
from things which are “not math”?
Mathematics is something that…
Any definition that uses the phrase “something that” is automatically too vague. What kind of thing is
it? Is it actually a thing? You must classify what thing it is.
Mathematics is numbers and distance / quantity and space.
While this may be true (or not!!!), it does not explain what kind of things are numbers/distance
quantity/space. Also, this may not comprehensively describe everything that is mathematics. You must
describe the qualities of ALL objects of mathematics, not just list the objects of mathematics.
Mathematics is indefinable.
It is true that it is difficult to pin point a definition for mathematics. It is NOT IMPOSSIBLE. That is the
whole point of your essay… to narrow definition to the specific qualities that you believe are true of all
mathematics and defend your definition from the various points of view that we have covered in class.
Anyone who uses any of the previous definitions will be guaranteed an F on their essay assignment.
