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Is math discovered or created?

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by

Zoe Cook

on 17 October 2013

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Transcript of Is math discovered or created?

Is math
discovered or created ?

Like other phenomena, mathematical principles are discovered using data. Just as, for example, localization of the brain was a discovered phenomenon, Pythagoras discovered the relationship of right triangles and Fibonacci discovered the endless, spiraling pattern using natural occurrences.
Math in Nature
Mathematical Realism
Mathematical realism is the idea that mathematical entities exist independently of the human mind. One famous mathematical realist, named Kurt Gödel, believed that mathematical reality could be perceived in a manner analogous to sense perception. Sense perception is an intrinsic method of processing external stimuli just like math.
Mathematical Empiricism
This idea started in the mid 19th century. It states that mathematical concepts are discovered by empirical research just as in other sciences. Mathematical empiricism explains that, because math is used to describe other concepts (like a value of gravity in physics), then math must intrinsically exist. Math, as the study of abstract entities, is being grouped together with other Areas of Knowledge: the sciences (Biology, Physics, and Chemistry).
If no humans exist to compute it, does math exist at all?
Mathematical Universe Hypothesis (MUH)
Our external physical reality is a mathematical structure.
How do we perceive math?
That is, the physical universe is mathematics in a well-defined sense, and "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".
By Jacob and Zoe
Mathematical anti-realism:

mathematical entities have no existence independent of the mind
C=2πr
sin^2 θ + cos^2 θ = 1
A=(1/2)bh
V=(1/3)bh
Two Major Forms:

Formalism
Fictionalism
x^2 + y^2 = z^2
f'(ln(x))= 1/x
Formalism
Fictionalism
Mathematics can be thought of as nothing more than a statement about the consequences of certain "string manipulation" rules.
The truths expressed are not really about numbers or right triangles or integrals; they aren't about anything at all. Not until we give them meaning.
Mathematical concepts and theories are about "abstract objects" (at least according to Platonism), but since these objects do not exist, mathematical truth does not exist. Mathematical sentences are inherently false.
The mathematical sentence "2+3=5" is false for just the same reason as "Elves work for Santa Claus" is false. While true within the constructed narratives, none of the elements actually exist.
Did mathematics exist before humans and will it outlive us?
Knowledge Issue Questions
Does the origin of math make it more or less valid?
Does the way we perceive knowledge affect what it "actually" is? Is it "actually" anything?
Is math worth "studying"? Is it "studying" if it is just created?
Do things like hurricanes form like this because of math?
Why this topic?
We chose this topic after struggling through numerous hours of HL Math homework. One has to question why you are doing it and what, if anything, it all means.
It should be noted that the majority of mathematicians believe that math is, in fact, discovered and not created. This bias may exist because many mathematicians use math to handle real world problems (e.g. engineering) or it may simply be because we believe things that things that are intrinsically true to be more valuable.
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