1.0   The definitions used in Mathematics have no rigor

    The mathematicians routinely boast that Mathematics is a discipline of rigorous definitions:

    “ math is about making definitions”  [1]

    “ mathematics requires more precision than everyday speech. Mathematicians
       refer to this precision of language and logic as ‘rigor’.”   [2]

    This would truly be a noble pursuit if it didn't amount to false advertising. The mathematicians rarely if
    ever define any of their words unambiguously, especially the strategic words that make or break their
    theories. Two words that they have given up on are point and line.

    “ Points, lines, and planes are the foundations of the whole system of geometry…
       But point, line, and plane are all undefined terms.”   [3]

    The mathematicians allege that they don't define these enigmatic words for fear of ending up with circular
    arguments:

    “ In mathematics, it becomes the requirement that we only use words that are
       previously defined or intentionally left undefined. We must have some undefined
       words in order to avoid an infinite process of definitions or a circular chain of
       definitions.”  [4]
    “ mathematics may be defined as the subject in which we never know what we are
       talking about, nor whether what we are saying is true.”  [5]

    By leaving the crucial words that make or break their presentations undefined, they guarantee that they
    have not communicated with the audience.


    2.0   A mathematician says that he is intelligent, but that he doesn't know what a line is

    A line is one of the simplest geometric figures known to Man. Why would a mathematician have so much
    trouble with it? Don't you know what a line is? If I ask you to draw a straight line for me, would you know
    what to do? What would you draw? Would you confuse it with an elephant or with a rocket? Do you think
    you could identify a line in a multiple choice question where the options are a horse, a house, a tree, a
    line, and all of the above (Fig. 1)?
The Primitive Line
Adapted for the Internet from:

Why God Doesn't Exist

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    So what are the mathematicians referring to when they claim that a line should remain primitive, meaning
    undefined? Why would they prefer to leave this simple geometric figure undefined for 3000 years?

    Before we investigate the infamous line of Mathematics, let me state up front that relativists aren’t overly
    concerned about definitions because they are in the habit of amending them retroactively. If a definition
    doesn't suit their purposes, the mathematicians simply borrow another one from the list and continue as if
    nothing. If you point this inconsistency out to them, they brush aside your objection by saying that you
    raise a philosophical matter. These are the same people that also urge you to set aside your intuition and
    common sense and to trust their logic when they arrive at fantastic conclusions as a result of undefined
    words.

    The fact that there are several definitions of the word line in the literature shows that the mathematicians
    really don't believe that it is indefinable. There is something more subtle going on.  Let’s explore these
    definitions, test whether any of them have the much touted ‘rigor,’ and find out why the mathematicians
    have conveniently chosen to argue that a line is undefined.

Fig. 1   Choices, choices!

The mathematicians say that
they don't know what a line
is. Do you think you could
help Dr. Einstein identify the
line in his difficult multiple
choice quiz?
What a savage! He
confuses a line for a
stick and a point for a
dot. Will the masses
ever come up to
speed?
Mmmh. Long stick mean line. And
black smudge mean point on line.
To think tribes in city say line
primitive! Ha, ha, ha!
It's piece of cake!