Re: Where do mathematical ideas come from?
- From: "Jiri Lebl" <jirka@xxxxxx>
- Date: 16 Sep 2005 08:36:48 -0700
mzafrullah@xxxxxxx wrote:
> It is conceivable that divorcing Mathematics completely from other
> Sciences would result in other Scientists developing their own
> Mathematics, which has already happened so often. It is also
> conceivable that when Mathematicians try to swallow this half digested
> material they do not have a first hand knowledge of what is going on,
> so their model may not be adequate. But should it matter? If there is a
> need there would be someone else who would improve the model.
It would be more interesting to look at examples. There was a lot of
mathematics that comes from say physics. For example physicists came
up originally with things which we now call distributional derivatives,
but in an informal way. It was mathematicians that took those ideas
and made them precise and applied these ideas to other parts of
mathematics. I think scientists use or create the mathematical tools
that they need at the moment. Mathematicians are primarily interested
in these tools and their abstractions, rather then their exact
application. For example most primality testing routines ASSUME the
Riemann hypothesis as true, while we (mathematicians) still don't know
if it's true. Even if we knew that the Riemann hypothesis was true
"far enough" for all practical purposes, it still wouldn't satisfy
mathematicians, but crytanalysts would not care one bit about it.
> On the other hand it always helps to know more and to know that all the
> branches of Mathematics originated in efforts to explain some Natural
> or Mathematical phenomena or to meet some computational need. So when
> we are trying to teach a topic in Mathematics we should bring in the
> practical/intellectual/scientific origins of the topic. If this means
> including introduction to some physics and some other sciences in the
> Math Curriculum, so be it.
> Muhammad
A common misconception. Mathematics DID NOT originally arise from
scientific applications. The ancient greeks were the original pure
mathematicians (they also did some applied mathematics, but they
clearly didived the two). Most western mathematics before 1700's was
based around geometry and number theory. And number theory was only
applied most recently.
Since people are quoting famous mathematicians, I should too:
Before creation God did just pure mathematics. Then He thought it
would be a
pleasant change to do some applied.
-- J. E. Littlewood
Jiri
.
- References:
- Where do mathematical ideas come from?
- From: david petry
- Re: Where do mathematical ideas come from?
- From: mzafrullah
- Where do mathematical ideas come from?
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