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Mathematical Truths

  1. Nov 3, 2014 #1
    Ok, so I don't doubt that this discussion has been had on these forums hundreds of times, but I want to take part in it rather than just read old threads, so here is the (admittedly trite) question: do you think that mathematical truths are discovered or are they merely invented?
     
  2. jcsd
  3. Nov 3, 2014 #2

    Danger

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    If they're truths, then they must have always existed, so the former would hold true (in my opinion).

    It's like... Ohm's law and all others have always been true, but someone had to realize that and put them to use.
     
  4. Nov 3, 2014 #3
    Not sure how to answer that. Mathematical truths can be axioms or lemmas or theorems, you name it. The axioms are agreed upon to be true without proof. Anything else needs to be proved. I would say that the truths are invented, but at the same time they also exist if they are true, however, none can be certain of a truth's existence, unless there is a problem posed and proved, hence inventors are required.
     
  5. Nov 3, 2014 #4
    I tend to agree with you...but just to play devil's advocate could someone not use a different way (besides mathematics) to describe Ohm's law? In a sense isn't mathematics just a set of invented tool's used to solve a certain problem? Could some civilization in another galaxy have reached the same conclusion (Ohm's law) using a different set of invented tools?
     
  6. Nov 3, 2014 #5

    Danger

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    Perplexing viewpoint. I would argue against you only in that mathematics itself (at least the verified parts thereof) consists of truths that also had to be discovered and articulated. It's like asking if water existed before the English called it "water" or the Russians called it "vody" (sorry, PopChar is acting up, so I couldn't use the proper Cyrillic letters).
     
  7. Nov 3, 2014 #6
    Good point, also I suppose that even if someone discovered a certain truth using a different set of tools, the truth itself was still always there, giving validity to the belief that such truths are discovered not invented....although after reading a bit about the subject I found out that some guy called Einstein believed that certain truths are invented...
     
  8. Nov 3, 2014 #7

    Danger

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    Well, he was getting on in years... :p
     
  9. Nov 3, 2014 #8

    russ_watters

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    Sure, but If a different method could also work, that doesn't say anything at all about Ohm's law. Ohm's law would still be true.
     
  10. Nov 3, 2014 #9
    a video of Stephen Wolfram discussing this topic for anyone who may be interested...
     
  11. Nov 4, 2014 #10
  12. Nov 4, 2014 #11
    Invented
     
  13. Nov 4, 2014 #12
    Why do you feel that way? I'm curious to here your POV because I tend to believe they are discovered
     
  14. Nov 4, 2014 #13

    Doug Huffman

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    An entertaining and freighted on-point novel is A Certain Ambiguity: A Mathematical Novel by Gaurav Suri and Hartosh Singh Bal (2010 Princeton).

    Were Sirinivasa Ramanujan's mathematics, not even imagined until his notes were understood, invented or discovered? Ramanujan invented his maths from whole cloth.
     
  15. Nov 4, 2014 #14
    Becouse I believe human race has unlimited inventive potential.
     
  16. Nov 4, 2014 #15

    Pythagorean

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    Mathematics is a language, both invented and discovered as well as naturally emerging like more qualitative languages are,

    Sometimes as a way to represent things observed in the universe, sometimes just to extend the abstract language system itself.
     
  17. Nov 4, 2014 #16
    Somewhere on several occasions I've heard of math described as the "universal language". Assuming the laws of physics are constant throughout the universe, constants such as pi and c as well as theorems like pythagoras' (a2+b2=c2) are universal and could be used as a "Rosetta stone" to translate the language.

    No one is responsible for round objects rolling or light travelling at the speed it does, we simply invent ways to describe and utilize these facts.
     
  18. Nov 4, 2014 #17

    Pythagorean

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    I've always wondered how valid that was. Maybe aliens, evolving a different brain structure, would come up with a different logic system that doesn't utilize distance or time (and thus, no pi or c emerge in their system) and our attempts to communicate through the physical constants discovered in our set of axioms would be found vulgar and offensive and Earth would be destroyed.
     
  19. Nov 4, 2014 #18
    Perhaps their existence might be in a pure energy state where our technology imprisons and/or destroys their lifeforms. Our language of mathematics would be terrorism!
     
  20. Nov 4, 2014 #19

    Pythagorean

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    I mean, why not? We're already basically terrorists to game in the wild while our cows and corn live a very Orwellian life.
     
  21. Nov 4, 2014 #20
    While the Pythagorean theorem is a discovered "mathematical truth," the right triangle it applies to is a pure human invention. The significance of a right angle only exists in the human mind. Humans invented and developed an ideal right angle, not discovered anywhere in nature, on which to perform calculations. Saying mathematical truths are discovered is like saying chess truths are discovered. Both statements ignore the fact you're making discoveries about a human mental invention and falsely imply you're making discoveries about nature.
     
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