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Do you know the right book for me?

  1. Aug 5, 2005 #1
    Hi,

    I need such a book which could teach mathematics emphasizing most on philosophy on second place the history of a concept, And on third place its implementation.


    Regards.

    Waheed.
     
    Last edited: Aug 5, 2005
  2. jcsd
  3. Aug 5, 2005 #2

    matt grime

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    i think you're asking in the wrong place. few mathematicians care about the philosophy of mathematics. try asking in the philosophy area for better responses. And when you refer to mathematics do you mean any particular area?

    http://www-groups.dcs.st-and.ac.uk/~history/


    is widely considered to be a good resource for the history of mathematics
     
  4. Aug 5, 2005 #3
    Hi,

    Regarding why i'm putting this question here is because, I thought that there might be a conceptual book of mathematics(basic) which not written by philosophers, But discussing philosophy, the advantage is that one can digest such material and things don't go too much abstarct and difficult to understand.

    Regards.

    Waheed.
     
  5. Aug 5, 2005 #4

    matt grime

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    One thing you need to realize is there isn't *a* philosophy of mathematics, there are many, and none has any appreciable effect in the slightest on mathematics. (ok, that's a strong view, and I ought to say what I mean, but think on this: it doesn't matter what philosophical view you have, as long as you can do maths.)

    here's another link for you.


    http://www.dpmms.cam.ac.uk/~wtg10/philosophy.html

    have you even considered just googling for philosophy of mathematics and seeing all the different views out there for you to cherry pick? I mean just googling for those words gave me this page:

    http://print.google.com/print?q=philosophy+of+mathematics&oi=print
     
    Last edited: Aug 5, 2005
  6. Aug 5, 2005 #5

    EnumaElish

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    You may want to look at Everything and More: A Compact History of Infinity by David Foster Wallace; also Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein. Both are from W. W. Norton's Great Discoveries series. I might add Zero: The Biography of a Dangerous Idea by Charles Seife (Penguin) and The Nothing That Is: A Natural History of Zero by Robert Kaplan (Oxford University Press).
     
    Last edited: Aug 5, 2005
  7. Aug 5, 2005 #6

    robphy

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    What is your target audience?
    Here are some, with varying levels of difficulty and scope.

    Mathematics, Form and Function (by MacLane) (you can follow the Amazon links to related titles)
    Mathematics and the Physical World (by Kline)
    Mathematics for the Nonmathematician (by Kline)
    Foundations and Fundamental Concepts of Mathematics (by Eves)
    Mathematics: Its Content, Methods, and Meaning (by Aleksandrov et al.)
    What Is Mathematics?: An Elementary Approach to Ideas and Methods (by Courant)
    A panorama of pure mathematics, as seen by N. Bourbaki (by Dieudonné) (not easy reading)
     
  8. Aug 6, 2005 #7

    EnumaElish

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  9. Aug 6, 2005 #8
    Hi,


    Thanks to all of you, I think I'll surely find some good books out of these.

    Thanks..


    Regards.

    Waheed.
     
  10. Aug 6, 2005 #9

    arildno

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    Hi, waheed:
    I urge you to consider very carefully what the others have aid, in particular matt grime.
    You should ask yourself the following question:
    WHY do you want to learn primarily about the "philosophy" of mathematics, rather than its "implementation"?

    Do you think to learn the "philosophy" behind maths enable you to understand math without learning how to actually practice it?
    Do you believe that there exist deep, philosophical ideas lurking behind definitions, theorems&proofs, ideas that are only imperfectly rendered by definitions,theorems&proofs?

    If you believe any such thing, you are sorely mistaken.
     
  11. Aug 7, 2005 #10

    matt grime

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    and also bear in mind that there is a technical distinction between philosophy of mathematics (which is often not interesting to mathematicians, much to the amazement of the lay person) as opposed to foundations of mathematics which is much more about the practical nature of what we base mathematics on. for instance what are the benefits of accepting the axiom of choice (all vector spaces have a well defined notion of basis, for example) versus its implications that contradict our views on what ought to be true (banach tarski paradox). i remember a title, though not the contents, of course called "how well founded is well founded set theory" for instance.
     
  12. Aug 10, 2005 #11
    Hi All,

    Actually what i want to know is what exactly is mathematics, and I think implementation can't tell this totally, thats why philosophy is required, But I'm not totally ignoring the implementation it has its own importance.

    Regards

    Waheed.
     
    Last edited: Aug 10, 2005
  13. Aug 11, 2005 #12

    arildno

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    That one's easy:
    Mathematics is what mathematicians judge to be mathematics.
     
  14. Aug 11, 2005 #13
    well said. :approve:
    but philosophy is the root of mathematics and implementation its goal.
    o:) :smile:
     
    Last edited: Aug 12, 2005
  15. Aug 11, 2005 #14

    arildno

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    Well, to be honest:
    I don't know about any less inaccurate definition of mathematics than the one I suggested.
     
  16. Aug 12, 2005 #15
    The universe is a labyrinth made of labyrinths. Each leads to another.
    And wherever we cannot go ourselves, we reach with mathematics.
     
  17. Aug 18, 2005 #16
    knowledge of mathematics makes mathematician, and mathematician judges mathematics, it is circular, Like A is opposite to B, and B is opposite to A gives no clue to where A and B are situated.
     
  18. Aug 19, 2005 #17

    arildno

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    Of course it's circular.
    Perhaps you should consider it to be a comment that basically ridicules any attempt once and for all to define and delineate what mathematics truly is about.
     
  19. Aug 19, 2005 #18

    mathwonk

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    mathematicians do not consciously have any philosophy, they are motivated by the desire to solve problems and understand phenomena in a precise way.

    so studying the philosophy of mathematics is a bit like reading movie reviews instead of actually watching movies.

    Perhaps various mathematicians have a philosophy, but they do not all have the same philosophy, so there is no universal philosophy of mathematics.

    of course i could be wrong. but i am occasionally a mathematician.
     
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