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Math is invented?

  1. Aug 29, 2014 #1
    Hi everyone, I'm new here so, hello. I guess for my first thread, I'd like to ask whoever thinks math is invented, how do they define "invented"?
     
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  3. Aug 29, 2014 #2

    berkeman

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    Welcome to the PF.

    What is your background in math? What year are you in school? Are you familiar with Peano's Axioms?

    http://en.wikipedia.org/wiki/Peano_axioms

    That's a good place to start to understand the basis of mathematics IMO.
     
  4. Aug 29, 2014 #3
    I guess you can say I'm pretty rusty. Highest math I know or "used to know" was diff eq and linear algebra.
     
  5. Aug 29, 2014 #4
    In this context "invented" means created by humans for humans, but based on principles existing in nature.

    The simple act of counting is an invention. Things aren't counted in nature, they aren't assigned a number between zero and whatever upper limit is operative. The whole notion of keeping a tally is a human one.
     
  6. Aug 29, 2014 #5
    Thanks for the response. Is there a context in which you think "mathematics" leans more towards discovery than a human creation?
     
  7. Aug 29, 2014 #6

    SteamKing

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    IMO, all knowledge is a human creation.

    By using a few axioms or propositions, one can create a mathematical structure, which may or may not mimic nature. The ancient Greeks, in particular Euclid, started with a handful of propositions, postulates and definitions and constructed a geometry which was thought to describe the earth and the measure of all earthly things.

    One of Euclid's postulates, the Fifth, or Parallel, Postulate, caused trouble from the start, almost as soon as the ink was dry on Euclid's 'Elements'. Centuries later, mathematicians like Gauss, Bolyai, and Lobachevsky, were able to show that by altering Euclid's Fifth Postulate, whole new geometries could be derived.

    http://en.wikipedia.org/wiki/Non-Euclidean_geometry

    By showing that whole new mathematical structures could be derived after changing a few key aspects, mathematicians got to thinking in more depth about the nature of mathematics.
     
  8. Aug 29, 2014 #7
    Only in the sense you could say Edison "discovered" that sound could be recorded.
     
  9. Aug 29, 2014 #8
    So basically, correct me if I'm wrong (it's late), what I'm seeing here so far is that math is merely a set a tools and curiosities created by humans.
     
  10. Aug 29, 2014 #9
    Well, your opening post asks for responses from people who think it's an invention.
     
  11. Aug 29, 2014 #10
    I'm just trying to sum up a basic definition based off of the responses so far.
     
  12. Aug 29, 2014 #11
    I actually should have made the opening post, "Math is invented because _______."
     
  13. Aug 30, 2014 #12

    phinds

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    I think your attempt to categorize math as discovered or invented is just an exercise in semantics and not particularly helpful. Those words tend to get very fuzzy sometimes.
     
  14. Aug 30, 2014 #13
  15. Aug 30, 2014 #14

    micromass

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    The axioms and definitions are invented, the rest is discovered :tongue:
     
  16. Aug 30, 2014 #15

    phinds

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    That's a pretty one-sided view of the article you linked to since the first sentence in it is
     
  17. Aug 30, 2014 #16
    Mathematics is logic represented in formal language. Obviously, the formal language is man-made. The logic is with any intelligent form, not just with humans. The prey decides to defend or escape based on the number of predators. It must be able to do the "<", ">" logic in some primitive way .
     
  18. Aug 30, 2014 #17
    Basic logic, distinguishing up to (about) five objects, and being able to distinguish "none" and "many", give us some numbers and basic operations. These, and a few other basic abilities, are given to us by evolution, and give us the beginning of mathematics. You need to start with something!

    From most animal films I've seen, the prey doesn't usually act based on *number* of predators. One lion will get you running just as fast as two! Maybe an elephant needs to distinguish "number of lions". Above a few it might decide to amble away. The evolution of being able to distinguish instantly between (say) 4 and 6 objects must (surely) have many causes. It might be caused through gathering activities, as much as prey avoidance.

    For instance, if you see a number of apple trees to the left, and a similar number to the right, it might be useful to know six trees from four. If there are many trees, I guess the ability to see that one wood is significantly bigger than another wood, is also useful. But we can't see that there are exactly (say) 67 trees, so I guess the ability to distinguish (say) 65 from 67 just wasn't useful in biological evolution.
     
    Last edited: Aug 30, 2014
  19. Aug 30, 2014 #18
    I don't think it's an exercise in semantics. It's very easy to feel that Nature is built on mathematics, that the fundamental relationship of everything to everything else is mathematical. I believe it was Galileo who concluded (something like): "God is a mathematician!" Newton seemed to agree.

    There are plenty of examples of things that would make people think this way. Take the fact that musical overtones automatically take the form of integer multiples of the fundamental.

    http://en.wikipedia.org/wiki/Pythagoras
     
  20. Aug 31, 2014 #19
    What does mathematics have to do with feeling?

    The Inquisition were famous for torturing inane statements out of Galileo.

    Leopold Kronecker: "God made the integers; all else is the work of man".

    Here, I think, Kronecker is making ironic use of the "God concept", and simplifying the actuality, somewhat, to counter Galileo with an equally simple sentence. In that sentence, replace "God" by "evolution" and "the integers" by "between 5 and 9 integers, and a few other simple concepts" and this statement appears reasonable.
     
  21. Aug 31, 2014 #20
    My post was about what semantics has to do with feeling, not mathematics.
     
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