Re: WHY ARE WE CONCERNED? I

["Reinhard Boerger" <reinhard.boerger@FernUni-Hagen.de>]

Hello,

just a few remarks.
Jim Stasheff wrote:

> F W Lawvere wrote:
> > WHY ARE WE CONCERNED? I
> >
> > 	"Dumbing down" is an attack not only on school children and on
> > undergraduates, but also one taking measured aim at colleagues in
> > adjacent fields and at the general public. The general public is
> > thirsty for genuinely informational articles to replace the science
> > fiction gruel served constantly by journals like the Scientific
> > American and the New York Times "Science" section.
>
> so far so good
>
>   Those journals have never published anything
> > resembling a mathematical proof
>
> why should they?

Because otherwise the readers do not learn what mathematics is about.

> a math proof is hardly necessary to explain a scientific subject in a
> usable way.
>
> now for a mathematical subject a math proof is sometimes but not
> always necessary

That depends on what you mean by explaining a subject. Of course, many
people know what a prime is, and if a journal reports that some larger
(Mersenne) prime has been found, or if the journal contains some nice
pictures of fractals, they may either admire this or ask "so what?" In any
case they do not see what a mathematical result is. I met several people
with an academic education in another field. When I told them that I am a
mathematician, some of them replied: "I always liked maths - except
proofs." If this misconception is so wide-spread among educated people -
at least in Germany, Canada and the United States - I think it is more
important that these people see easy proofs of mathematical results (e.g.
Euclid's proof for the existence of infinitely many primes) than that they
see mysterious mathematical statements, which they don't understand.
Mathematics is thinking rather than computation, and if one does not know
what a proof is, one does not know what mathematics is. So for which
subject do you think that a proof is not necessary?


Greetings
Reinhard