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Opinions: was Mathematics invented or discovered? watch

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  • View Poll Results: Was mathematics invented or discovered?
    Mathematics was invented
    49.18%
    Mathematics was discovered
    50.82%

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    (Original post by LaurenLovesMaths)
    Yeah I suppose, but there are certain parts of maths that you can't change no matter what, and, in my opinion, basic maths is very important for the foundations of life


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    Really? What parts of maths can't you change no matter what? All the mathematical knowledge you've currently got is only something that applies under a certain model/universe/set of axioms, so you could certainly change the 'universe' you're working in. Mind giving an example to clarify?
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    I think Mathematics was invented. If we go back to its very origin, they were used as an instrument for counting things.

    Mathematics was first a way of expressing something as natural as geometric shapes. In ancient Greece, Pythagoras used them to describe the arche (origin, essence) of the universe. He thought the arche were the unity, which he associated to a point. He thought everything can be reduced to a group of points making a geometrical figure (as shown in the next photograph, which is in Spanish, but really easy to understand).

    Name:  Pythagoras.png
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    This is, therefore, the first Physical approach to the arche in a mathematical way. Pythagoras was the first physicist (if we consider physics as something purely mathematical; if not, Thales of Miletus would be the first physicist).

    Since the Enlightenment and with the establishment of Galilean and Newtonian Mechanics, Mathematics and Physics can be differentiated between each other. Mathematics is a tool that can be applied in so many different fields. Physics, on the contrary, is an empirical science, the main aim of which is to understand the rules governing nature.

    Being Mathematics a tool, makes it something really adaptable to our daily needs. Is something that can be improved, developed or simply changed. Are tools discovered or invented? I definitely think the latter is the case, not only for Mathematics, but also for any other tool we might think of.

    The same applies to the Laws of Physics. They are not discovered, neither are invented. They are described! And how can we describe them? Using the tool we have to do so: Mathematics.

    Imagine interchanging the plus and minus signs and after that, rewriting all the equations that describe the way nature works. Will they still describe with the same accuracy the way we the universe behaves? Of course they will. But, will the way the world behaves changed in the same way as the signs used to describe it? Obviously not, so Mathematics is not something absolute, but a way of understanding something as absolute (or maybe not, as we have a limited knowledge of it) as the laws governing nature.
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    (Original post by Aph)
    Discovered. Just to prove it think about Pythagoras, he didn't just decide that a^2+b^2=c^2 but discovered that that way the case.
    That's not a proof...
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    (Original post by Zacken)
    Really? What parts of maths can't you change no matter what? All the mathematical knowledge you've currently got is only something that applies under a certain model/universe/set of axioms, so you could certainly change the 'universe' you're working in. Mind giving an example to clarify?
    I don't know.. F=ma; angles in a quadrilateral adding to 360 degrees - even though we invented the 'degree' itself as a measurement, that is always fact and can't be changed.. But yeah, a lot of maths does come from a certain set of axioms


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    (Original post by LaurenLovesMaths)
    I don't know.. F=ma; angles in a quadrilateral adding to 360 degrees - even though we invented the 'degree' itself as a measurement, that is always fact and can't be changed.. But yeah, a lot of maths does come from a certain set of axioms


    Posted from TSR Mobile
    Angles in a quadrilateral adding up to 360 degrees is something that only occurs in Euclidean geometry though, try that in spherical geometry and it's easily changed. Why don't you take an orange and draw a triangle/squadrailateral on the peel in marker and then measure how the angles add up to more than 180/360. :-)

    F=ma only applies for constant mass/etc... doesn't apply for relativistic scenarios or rockets for example, etc...

    What d'you mean we invented the degree? Isn't a degree part of maths and maths discovered, according to you? If so, why can't we simply change what a degree means, what's stopping us from doing that?
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    (Original post by alegonperez)
    x
    Is your argument \text{maths} \in \{\text{tools}\} and \text{tools} \in \{\text{invented stuff}\} and hence \text{maths} \in \{\text{invented stuff}\}
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    Both. The mathematical principles always have and always will be there. We've just but physical numbers and meanings to it all in order to make sense of it.
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    Axioms are invented. The theorems resulting from them are discovered.
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    (Original post by Zacken)
    Is your argument \text{maths} \in \{\text{tools}\} and \text{tools} \in \{\text{invented stuff}\} and hence \text{maths} \in \{\text{invented stuff}\}
    Well that wouldn't be true, because not all tools are invented.
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    (Original post by Zacken)
    Is your argument \text{maths} \in \{\text{tools}\} and \text{tools} \in \{\text{invented stuff}\} and hence \text{maths} \in \{\text{invented stuff}\}
    It wasn't really an argument, but a way of illustrating what I was saying. Had I used it as an argument, I would have included a fallacy in my short dissertation, as generalizing is always a fallacy.
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    (Original post by Student403)
    Well that wouldn't be true, because not all tools are invented.
    Precisely.
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    Foundations invented, the rest discovered.
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    (Original post by hassassin04)
    Foundations invented, the rest discovered.
    If that is indeed the case, then damn (imo) this is the most beautiful thing man has ever invented
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    (Original post by StrangeBanana)
    Axioms are invented. The theorems resulting from them are discovered.
    I agree


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    I think it depends on how you define "Mathematics" but the way we think about Mathematics was certainly a human invention.
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    Despite being a maths grad, I have never stopped to think about this question. You could argue it either way, but there's no definite answer.

    All I know is that maths is awesome and it makes life easier
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    (Original post by Zacken)
    Does it matter?
    Lmao this is so true.
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    (Original post by Indeterminate)
    Despite being a maths grad, I have never stopped to think about this question. You could argue it either way, but there's no definite answer.

    All I know is that maths is awesome and it makes life easier
    Precisely this! :-)
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    (Original post by Louisb19)
    Lmao this is so true.
    The mathematicians do the maths, the wishy washy philosophers do the "is maths invented or discovered" thing.
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    (Original post by Student403)
    I see..

    I think if it was invented, that would imply there are infinitely more things to find out (aka invent ourselves) about the subject. Whereas if it was discovered, that could imply there is a finite number of things left for us to discover!
    I think it's pretty clear that there are infinitely many more things to discover/invent regardless.
 
 
 
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