The Nature of Math

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Posted by: JohnnySaber
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I was inspired by the following Calvin and Hobbes comic to start thinking about the nature of mathematics:


http://farm1.static.flickr.com/2/1869299_a96476631c.jpg


While his point about addition seems more like an excuse to get out of doing homework, what about order of operations?  Wouldn't we have dramatically different results if we had decided to do math in a different order than what is accepted nowadays?


Was this entirely arbitrary, or are there sound reasons for the way we do math?  In other words, is math an undeniable and provable truth, or is it only so concrete because we have made it so?

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