Was Mathematics Invented or Discovered?
From: John Mergendoller Date: Wed, 17 May 95 18:58:58 -700 Subject: Is mathematics invented or discovered? I am not a k-12 student, but I have a math question I've wondered about ever since I was. I hope you will address it. Is mathematics invented or discovered? Seems like mathematicians ponder and invent, and yet, the book of nature . . . Any light you can shed on this is appreciated. john
From: Dr. Ken Subject: Re: Is mathematics invented or discovered? Date: Sun, 21 May 1995 10:23:05 -0400 (EDT) Hello there! You've hit on what I think is one of the coolest aspects of Mathematics. Here's what I think about it. Mathematics is created through both invention _and_ discovery, and they work hand-in-hand to do it. You may have the sense that there is some huge body of mathematical knowledge that's just sitting out there, partially discovered, waiting patiently for us to come along and chisel it out like bones on an archaeological dig. Well, that's certainly somewhat the case; nobody is ever going to invent any mathematics that wasn't already true. I mean, no matter how hard you try, you're never going to be able to prove that 1+1=4, or prove the necessity of the Euclidean Parallel postulate. So in this sense, that body of yet-to-be-seen mathematics might be called "things that are true" or "things that are provable." In a very real sense, though, mathematics reflects the spirit of the times in which it is created and studied. One neat definition I've seen of mathematics (not my favorite one, but one I like anyway) is "mathematics is whatever mathematicians are doing at the time." I think this really captures the sense that mathematics is a dynamic body of knowledge, and it has areas that fall in and out of fashion, areas that die as other areas are created. Also, there's the issue of notation and how that affects mathematical thought. It's often said that in order to create any body of mathematics, you first have to have the right notation, and then the rest just comes without much effort. So in this sense, notation (a human construction which isn't necessarily inherent in the math itself) has a huge impact on what we perceive as mathematics, and what math gets created. All in all, though, this is kind of a tough issue. I like to use a nice weak verb when I talk about math: people _do_ mathematics, they don't discover or invent it. But that's pretty much a matter of personal taste. -K
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