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Is this a fair description of mathematics (in one sentence)?

  1. Mar 14, 2016 #1

    tgt

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    Mathematics is a vast subject with a very long and rich history divided into many branches that usually begins by making precise and defining new intuitive rational concepts (often inspired by the perceived world or from existing mathematical or scientific theories) and develops by employing logically sound and consistent rules and methods, producing results that are often interesting, interconnected, surprising and useful.

    How does that sound (for one sentence) to this big topic?
     
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  3. Mar 14, 2016 #2

    jedishrfu

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    I think your sentence is very hard to read.

    To me, mathematics is beautiful. Mathematics is about studying patterns in all forms. It is about making provable assertions that can lead to new mathematical discoveries.

    Even my sentence doesn't do justice to what mathematics is.

    What are you writing about?
     
  4. Mar 14, 2016 #3
    There are so many descriptions of Mathematics - where did you come up with this? -- I prefer to think of mathematics as a language, it is just a tool we use to understand the world (universe) around us - as well as many man made systems, like finance, etc. It seems you are trying to use a lot of vague wooring to describe something that is by nature - not vague.
     
  5. Mar 14, 2016 #4

    micromass

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    Mathematics is like porn, hard to define but you recognize it immediately when you see it.
     
  6. Mar 14, 2016 #5

    tgt

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    Many people have asked me the question 'what is mathematics'? Even I asked this question seriously in first year uni and read many books on the subject. I've now studied maths for over a decade at uni and now have a much better idea of what mathematics is about. I just want to give a non biased, and a working rather than a philosophical description of what maths is about. I also want to make it very brief in one sentence but as informative as possible.
     
  7. Mar 14, 2016 #6

    tgt

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    I've studied mathematical logic before and many of the ideas described came from there. You seem to come from an applied maths background?
     
  8. Mar 14, 2016 #7

    jedishrfu

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    This is why I like the use of patterns in describing mathematics as it covers geometry, number theory and pretty much whatever discipline you throw at it.

    However, Micro's post really hits the point but you'd have to be careful where you'd use it.
     
  9. Mar 14, 2016 #8
    Well - yes I am an engineer, but what does that have to do with the reply. You did not ask us to critique a statement like "this is what mathematics is to me" - or a personal narrative as your reply implies. Your topic statement is pretty neutral, as applying to everyone - and in that case the answer, IMO - should be more fundamental. I can say modern art is "a vast subject with a very long and rich history divided into many branches that usually begins by making precise and defining new intuitive rational concepts" - but Modern art is subjective and interpretive - two words that are NOT what mathematics is about. Using the Def of Language - I can not see how my statement is off base. We use English to communicate - yet through poetry for example it can be used to "produce(ing) results that are often interesting, interconnected, surprising and useful." - So this language can be precise AND it can be beautiful.

    I do not, at all, disagree with your description, but it would not be the first, or single sentience description. So perhaps your query is out of context - who is your audience ?
     
  10. Mar 14, 2016 #9

    Mark44

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    Content aside, an editor would have a field day with this. For one thing, the sentence is waaaaaay too long with a number of ideas jumbled together that don't make sense, as written.
    • "very long and rich history divided into many branches..." -- the history is divided into many branches?
    • "divided into many branches that usually begins ..." -- the clause starting with "that usually begins" desperately needs a comma. This clause modifies "history," but without the comma, seems to modify "branches," thereby disagreeing in number between "branches" (plural noun) and "that ... begins" (singular verb).
    • "making precise and defining new intuitive rational concepts" -- making precise what? This would sound better and flow better in the opposite order. You have to define things first before you can make them precise.

    Indeed, mathematics is a vast subject, so what's the point of trying to define it in one sentence?
     
  11. Mar 15, 2016 #10

    Svein

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    Mathematics is a study of
    1. What is true and can be proved true
    2. What is false and can be proved false
    Unfortunately, since Kurt Gödel proved his famous theorem, we have to deal with two inconvenient categories
    • What is true, but cannot be proved true
    • What is false, but cannot be proved false
    And so we end up with Shakespeare:

    There are more things in heaven and earth, Horatio,
    Than are dreamt of in your philosophy.
    - Hamlet (1.5.167-8), Hamlet to Horatio
     
  12. Mar 15, 2016 #11

    micromass

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    I'm sorry. I see your point but I do not accept your definition. Consider the following neat deductive system from Underwood's "Mathematical Cranks"

    Here we have defined a very rich deductive system and proved theorems to be rigorously true. Is this mathematics? You might stick to your guns and say that yes, this is mathematics. I say no, this isn't mathematics. Mathematics is supposed to be about something. It's not just meaningless deductions like these. There is supposed to be a goal, interrelations, connections with some reality. None of this is to be found here. No mathematician would want to study his system.
     
  13. Mar 15, 2016 #12

    tgt

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    Or the old mathematics is like love, the idea is simple but it can get complicated.
     
  14. Mar 15, 2016 #13

    tgt

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    My audience are beginners and math undergraduates at most.
     
  15. Mar 15, 2016 #14

    tgt

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    But Godel constructed very 'unnatural' scenarios. I'd be much more impressed if there was a 'genuine' maths problem that falls into Godel's category.
     
  16. Mar 15, 2016 #15

    micromass

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    The axiom of choice and the continuum hypothesis are not unnatural at all!
     
  17. Mar 15, 2016 #16

    tgt

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    I only wish someone had written something like this when I was an undergraduate. I loved maths but didn't know what I was studying.
     
  18. Mar 26, 2016 #17

    mathwonk

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  19. Mar 26, 2016 #18

    pwsnafu

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    See Goodstein's[/PLAIN] [Broken] theorem and Paris-Harrington theorem.

    Can't forget this thread:
     
    Last edited by a moderator: May 7, 2017
  20. Mar 27, 2016 #19

    Ssnow

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    I believe that your description is complex to read. I don't know an exact definition but Mathematics, as the poetry, uses the essentials to say much and I think also the definition must respect this feature ...
     
  21. Mar 28, 2016 #20

    Svein

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    Have you ever read the axiomatic definitions of a first-order system?
     
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