[cmath] Re: [Cmesg-l] Fwd: Good article for promoting pure math research

Mon Jul 18 12:34:35 EDT 2011

Hi Walter, 

we are on the same page. To add a further nuance: what does it mean to
'do' mathematics? does 'doing math' require some kind of
'awareness' of underlying math processes? 

of course, in the broadest sense,
we all have experiences in 'doing' math from earliest age on
(you can argue that playing soccer/baseball/etc is doing math, 
for instance geometry in 3d); 
also 'doing' research (digging a hole in the sand), or
engineering (building sand castles), or geology (throwing rocks), etc.

but then is a bee which 'uses'
polar coordinates (in human lingo) to convey the information
about the location of a food source, doing math? or a dog which
jumps into a lake to catch a ball and does it in a way that minimizes time
rather than distance?

miroslav

On Sat, 16 Jul 2011 20:36:53 -0400
 Walter Whiteley <whiteley at mathstat.yorku.ca> wrote:
> Miroslav
> 
> 	I think it is valuable to separate several factors here to generate a  more
> nuanced conclusion:
> 
> - unplanned impact:  this arises often within applied math as well and  many
> other areas.
>   	Unplanned impact is indeed a feature of human creativity in almost  
> every field.  This is an important point for funders and people making
>  decisions in every field (not specific to 'pure mathematics').  It is  also
> important for students in general - but part of the message is to  look for,
> even seek out, unplanned connections and impact.
> 
> - explorations of a  'pure mathematical nature' as done by many  stripes of
> mathematicians, in many settings, which is distinct from   the fields of
> "pure mathematics" as something done full time  (sometimes with pride at
> having no applications).
> 
> 	For example consider the discussion of topology in the article.   Topology
> is something young children explore (before they explore  straight lines,
> area, volume .... ) - what spaces can I 'reach' -  which door can I exit and
> then come back though another door ... .    Parts of topology are something
> Mobius explored (what we now call  oriented cell complexes) - while doing
> developing barycentric  coordinates to give a good exposition of statics,
> working out oriented  and non-oriented surfaces (signed volumes etc.), as
> well as doing  astronomy and other work.  Topology is something Poincare did
> - while  coming very close to publishing relativity theory at the same time
> as  Einstein.
> 	That subject of topology is not, never really was, purely abstract/
> theoretical non-applicable.
> Of course, people may wander into topics while not currently motivated  by
> applications (but still grounded, like all human thinking, in  experiences,
> in imaginative possibilities connecting/blending concepts  and samples,
> experienced over time.
> 
> 	I learned topology (homology) as 'pure mathematics' - and then  relearned it
> in several applied contexts.   My instructor actually  knew some of these
> areas of application - but chose not to offer that  added context which would
> have helped my learning (including the  techniques I memorized for a
> comprehensive exam then forgot!).
> 
>   	When talking with my students, I discuss the history of math.  My  
> understanding is that up to post 1900, everyone we talk about was  doing what
> is now called both pure and applied mathematics, and often  several other
> subjects as well.   To me, for anyone to do 'only pure  mathematics' is a
> temporary aberration within the larger flow of  mathematics with all its
> connections to human processes, as well as  connections to other puzzles
> across a range of activities we try to  solve with mathematics.
> 
> Walter Whiteley
> 
> On 14-Jul-11, at 10:51 PM, Miroslav Lovric wrote:
> 
> >
> >
> > Peter,
> >
> > thank you very much for this
> >
> > Some of the stories/case studies I know about, and always talk about  
> > them
> > to my students. Now I know more stories!
> >
> > Important message -- for students, as well as for teachers, math
> > curriculum people, etc. -- is that not every piece of math
> > needs to be (or can be) justified by some (present-day, "real life")
> > application.
> >
> > There is huge value in learning about (and researching) areas of  
> > math that
> > seem to be "purely abstract/theoretical" or "non applicable."
> >
> > Cheers
> > Miroslav
> >
> >
> >
> >
> >
> >
> >
> > On Thu, 14 Jul 2011 11:34:19 -0400
> > Peter Taylor <peter.taylor at queensu.ca> wrote:
> >> Steve La Rocque brought to my attention a commentary article in  
> >> Nature which
> >> came out today celebrating the unanticipated impact of mathematics  
> >> research.
> >> It's great to see such articles in Nature and it's certainly timely  
> >> for us
> >> in Canada(!)  At the bottom of the article there is a useful link  
> >> to the work
> >> of the British Society for the History of Math in collecting  
> >> interesting
> >> stories about applications.
> >> peter
> >>
> >> The unplanned impact of mathematics
> >> Nature 475, 166–169 (14 July 2011)
> >> <http://dx.doi.org/10.1038/475166a>doi:10.1038/475166a
> >> Published online 13 July 2011
> >>
> >> Nature url:
> >>
> >
>
<http://www.nature.com/nature/journal/v475/n7355/full/475166a.html>http://www.nature.com/nature/journal/v475/n7355/full/475166a.html
> >> Shortform url: <http://bit.ly/nbsY5B>http://bit.ly/nbsY5B
> >>
> >>
> >>
> >> Peter Taylor
> >> Professor
> >> Dept Math&Stats
> >> Queen's University
> >> Kingston ON K7L 3N6
> >> 613 533-2434
> >> http://www.mast.queensu.ca/~peter/
> >> -- 
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> >>
> >
> > * * * * * * ************************************************
> >  Miroslav Lovric
> >  Professor
> >  Department of Mathematics and Statistics
> >  McMaster University
> >  Hamilton, Ontario L8S 4K1, Canada
> >
> >  tel.: 905.525.9140.ext27362
> >  fax:  905.522.0935 (attn. M.Lovric)
> >  e-mail: lovric at mcmaster.ca
> >  http://www.math.mcmaster.ca/lovric/lovric.html
> > ************************************************************
> >
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> > .
> >
> 

* * * * * * ************************************************
  Miroslav Lovric 
  Professor
  Department of Mathematics and Statistics
  McMaster University
  Hamilton, Ontario L8S 4K1, Canada

  tel.: 905.525.9140.ext27362
  fax:  905.522.0935 (attn. M.Lovric)
  e-mail: lovric at mcmaster.ca
  http://www.math.mcmaster.ca/lovric/lovric.html
************************************************************