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### Math Invented or Discovered?

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Date: 10/26/1999 at 09:39:31
From: Tom Demarco
Subject: Origin

Did man create all math? If not, what did? If man created math, then
all math can be manipulated, and there is no higher 'power'
controlling math, right? It is whatever we want it to be, right?
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Date: 10/26/1999 at 18:02:01
From: Doctor Rick
Subject: Re: Origin

Hi, Tom.

This is related to the age-old question, "Is math discovered or
invented?" My answer has to be both. We invent new kinds of math by
setting the "rules of the game." After we have done this, we discover
all kinds of consequences that follow from these rules.

Thus, we do have a certain freedom in inventing new kinds of math.
However, once we have done this - set the rules - then only certain
things are true and other things are false, within the system we have
set up.

It's like asking, "Since man invented baseball, doesn't anything go?
Can't I get a fourth strike?" The answer is: "If you want to start
your own league with different rules (designated hitter, for
instance), go ahead. But it won't be the same game that I play. As
long as we're playing in the same game, we have to play by the same
rules!"

Earlier this year I wrote an answer to another question that might be
coming from the opposite perspective to yours. My correspondent asked
whether the existence of unproven and unprovable statements (called
postulates and undefined terms) in geometry demonstrates that every
human system must be built upon faith. Take a look at my answer in our
Archives -- I think it is relevant to your question too.

Unproven Fundamentals of Geometry
http://mathforum.org/dr.math/problems/han.05.18.99.html

You will see from this that as long as we're talking about pure math,
we are free to try any set of rules and see where they lead. Some
interesting things can come out of this sort of exploration. But
freedom ends - and both science and faith begin - when we try to say
that our brand of math describes the real world.

just to set up a basis for dialog.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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