Mathematics is a very
convincing field to most people. However, many of these people do not have a
strong understanding of it. The field of mathematics relies on repeated use of
rules. This essay will focus on the reliability of mathematics against other areas
of knowledge. Mathematics is seen as
a very reliable area of knowledge because it uses reason and most of it is a
very logical and straightforward system. Mathematics is obvious and independent
of subjective experience. In most of the mathematics field, there is no argument
over the answer. If something in proved true, everyone accepts it. This is
because there is a formal proof with which nobody can dispute. For example, in
mathematics, we learned that the inside angles of a triangle, add up to 180
degrees. This is a proven fact and is accepted globally. Furthermore in math
recently we studied about plane geometry. 
During this topic, there were some ‘axioms’ that we had to just accept
without any formal proof. This made me wonder how it is possible that something
is regarded and globally accepted as being true without any actual proof.

Axioms are the basis for further proofs. With further research, I was finally
able to come to a logical understanding and accept what axioms really were. An
axiom is a proposition regarded as self-evidently true without proof. It can
either be accepted or rejected by each individual. So if I choose the
Pythagorean theorem to be true, but I say that the parallel postulate is false,
then I have a flawed mathematical system. This is due to the fact that both
these axioms are interconnected. The parallel postulate is an axiom indicating
that two lines can never intersect if they are in exactly the same direction.

For example, referring back to the proof that all the angles inside a triangle
add up to 180 degrees, the parallel postulate is a key axiom in making this
proof. On the other hand,
when using different mathematics systems it becomes possible for us to acquire
a different conclusion. When we look at the angles of a triangle in spherical
or hyperbolic geometry the interior angles do not necessarily add up to 180
degrees. It is therefore shown that mathematics is often showing something is
true within one fixed system. While researching I
came across this line, which I thought was a great way of explaining math as an
area of knowledge. “Mathematics is a playground of human abstraction and
critical thinking, and is at best inspired by the things we see around us.”
This quote is ideal for giving light to the many different concepts of mathematics
and how the same mathematics problem can have multiple answers. For example
1+1=? In regular mathematics it will equal to 2, but is mod p mathematics it is
equal to 0. This quote leads on to another question: Was mathematics invented
or discovered?When we look at
different areas of knowledge, they can be very subjective. History, arts, human
and ethics, are all examples of very subjective areas of knowledge. For
example, when I was studying history, I looked through two different books, one
written by an American author and the other by a Russian author, on the start
of the cold war. Both of these books have very different viewpoints and can
clearly be seen to be biased and subjective. This is a very natural process of
the brain, and in areas of knowledge where an opinion is key, there is always
going to be some bias. Furthermore, unlike in mathematics
paradigm shifts do occur every once in a while. A paradigm shift is a change in
paradigm and a shift, which attracts many people and leads to a basic and
revolutionary change. Due to the improvement of technology, and better research
and development, many of the old conceptions, which were always viewed to be
correct, have either been proved or disproved.  For example less then two hundred years ago
there was a major paradigm shift in the theory of evolution. Before 1859, most
people believed that humans were ‘created’ by God himself. When Darwin published
his book, it was given lots of criticism and most people did not accept it. Slowly
his ideas gathered steam, and eventually let to a paradigm shift. So this is a
great example of how the other areas of knowledge could be deemed less certain
than mathematics.

Overall, this entry shows how no area of
knowledge can be certain, as there will always be change. It could be argued
that in mathematics there is always an undisputed answer but as we explored
deeper into the realm of mathematics we see how much doubt there actually is.

This is also present in the other areas of knowledge but in my opinion it is less
prevalent in mathematics. However, as time goes on, there will be many more
discoveries and inventions that could lead to making mathematics uncertain and
there is always room for exploration.

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I'm Colleen!

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