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Thread: What is mathematics?

  1. #1
    MHF Contributor alexmahone's Avatar
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    What is mathematics?

    I'm a math major and therefore need to be able to define "mathematics" in a sentence. A few years ago, I would've said "the study of numbers", but with topics like "Set Theory" that have little to do with numbers, that definition seems inadequate.
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  2. #2
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    Re: What is mathematics?

    Quote Originally Posted by alexmahone View Post
    I'm a math major and therefore need to be able to define "mathematics" in a sentence. A few years ago, I would've said "the study of numbers", but with topics like "Set Theory" that have little to do with numbers, that definition seems inadequate.
    I the area known as the philosophy of mathematics it is generally agreed that mathematics is the science of patterns.

    For a longer exploration of this topic, I recommend What is Mathematics Really by Reuben Hersh.
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  3. #3
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    Re: What is mathematics?

    I wouldn't use the word "science" but the study of patterns, certainly. It might be slightly better to say the "study of relationships" as a little more general.
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    Re: What is mathematics?

    Quote Originally Posted by HallsofIvy View Post
    I wouldn't use the word "science" but the study of patterns, certainly. It might be slightly better to say the "study of relationships" as a little more general.
    Actually I agree with you there. But I was a student of the philosopher Micheal Resnik who was a Quine PhD. That was his definition.
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    Re: What is mathematics?

    "Study of relationships" is awfully broad - study of relationships among what? This sounds like something a genealogist would claim, or a family psychologist. A quick google search suggests "the science that deals with the logic of shape, quantity and arrangement."
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    Re: What is mathematics?

    Quote Originally Posted by ChipB View Post
    "Study of relationships" is awfully broad - study of relationships among what?
    That's actually the whole point- NOT relationships among specific things but just "relationships" in the abstract.
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    Re: What is mathematics?

    Quote Originally Posted by HallsofIvy View Post
    That's actually the whole point- NOT relationships among specific things but just "relationships" in the abstract.
    Maybe, "The study of abstract and concrete relationships".
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    Re: What is mathematics?

    Are there other kinds of relationships, that are neither "abstract" nor "concrete"? If not how is "abstract and concrete relationships" different from "relationships"?
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    Re: What is mathematics?

    Quote Originally Posted by HallsofIvy View Post
    Are there other kinds of relationships, that are neither "abstract" nor "concrete"? If not how is "abstract and concrete relationships" different from "relationships"?
    In common English, the word "relationship" has connotation that is implied when not modified by any adjectives. By adding adjectives, it becomes more clear that the connotations normally associated with the word may not apply. Even this phrase is not necessarily clear, and could likely be improved upon.
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