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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.


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

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.

Associated Topics:
High School History/Biography

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