Xref: utzoo comp.edu:1823 sci.math:5318
Path: utzoo!attcan!uunet!lll-winken!ames!xanth!nic.MR.NET!umn-d-ub!rutgers!att!whuts!homxb!genesis!odyssey!gls
From: gls@odyssey.ATT.COM (g.l.sicherman)
Newsgroups: comp.edu,sci.math
Subject: Re: the why of math
Message-ID: <783@odyssey.ATT.COM>
Date: 10 Jan 89 16:04:08 GMT
References: <605@ucrmath.EDU> <6578@killer.DALLAS.TX.US>
Organization: AT&T Bell Laboratories, West Long Branch, NJ
Lines: 48

In article <6578@killer.DALLAS.TX.US>, elg (Eric Green) writes:
> in article <605@ucrmath.EDU>, marek@ucrmath.EDU (Marek Chrobak) says:
> > Xref: killer comp.edu:1858 sci.math:5231 sci.physics:5475
> > a proof. In Herman's terms, the question WHY does not cross
> > their mind. They just want to know HOW. ...
> > It would be silly to blame the students for this. This is the
> > way they have been taught in school, it's no wonder this is
> > what they expect from college. 
> 
> Sounds like you're blaming the teachers. You shouldn't. They're doing
> the best they can, with what little knowledge they have. Blame college
> curriculums which do not include any "Basics of Mathematics" courses,
> only tons of courses in equation manipulation (Algebra, Trig, ...

I don't see any reason to cast blame.  Engineers are by far the
biggest "consumers" of mathematics, and they need techniques rather
than derivations for nearly all their work.  If they are interested
in the derivations, they can take "honors" mathematics.  But I would
rather cross a bridge built by an engineer who knows the formulas
thoroughly than by one who knows some of the formulas and can derive
the rest!

There is also a philosophical issue here.  What we call "foundations"
of mathematics are really built on top of practical mathematics, by
cumulative abstraction.  Indeed, an application of mathematics may have
alternative foundations; for example, calculus can be founded on Weier-
strass logic or on nonstandard arithmetic.  It's something like the
physicist's alternatives of Maxwell's equations or Lorenz's transform;
either will serve as a model.  But mathematicians should beware of
believing in their models!  There is no "why" of mathematics except
in the art of the mathematician.  For example, why when you add two
numbers does the order not matter?  A typical schoolteacher would
answer "because addition is commutative." That's not an answer!

> Is it any wonder why your typical bright and impatient student hates
> "math"? It's BORING!

Patience is an effect of typographic culture.  As has been pointed out
here and in comp.society, new methods are being developed for elec-
tronic culture.  The real "new math" is yet to come!

-:-
	"This rock, for instance, has an I.Q. of zero.  Ouch!"
	"What's the matter, Professor?"
	"It bit me!"
-- 
Col. G. L. Sicherman
gls@odyssey.att.COM