p.96:
The facts of mathematics are verified and presented by the axiomatic
method. One must guard, however, against confusing the _presentation_ of
mathematics with the _content_ of mathematics. An axiomatic presentation
of a mathematical fact differs from the fact that is being presented as
medicine differs from food. It is true that this particular medicine is
necessary to keep the mathematicianat a safe distance from self-delusions
of the mind. Nonetheless, understanding mathematics means being able to
forget the medicine and enjoy the food.
p.142:
Nowhere in the sciences does one find as wide a gap as that between
the written version of a mathematical result and the discourse that
is required in order to understand the same result. The axiomatic
method of presentation of mathematics has reached a pinnacle of
fanaticism in our time.
...
This pretense of "identifying" mathematics with a style of exposition is
having a corrosive effect on the way mathematics is viewed by scientists
in other disciplines. The impenetrability of mathematical writing has
isolated the community of mathematicians. The mistaken identification of
mathematics with the axiomatic method has led to a widespread prejudice
among scientists that mathematics is nothing but a pedantic grammar,
suitable only for belaboring the obvious and for producing marginal
counterexamples to useful facts that are by and large true.
At 9:09 AM -0500 11/3/98, Daryn Lehoux wrote:
> > But it could also be true that Greek and modern mathematics are
> > the actual 'curiosity'. In fact, for example, the faith in
> > axiomatic-deductive procedures can be found in just two
> > historical-geographical 'enclaves': in ancient Greek mathematics
> > and in the last two centuries of our mathematics.
> > Even from Proclus to the XVIII century, nobody really thought useful
> > to 'prove' theorems: "rigor is for philosophers, not for mathematicians".
>
> A very good point. And one I think we can too easily lose track of: that
> if we look to history for semblances to modernity we will not be getting
> anything like the whole picture. It is arrogant to think that what is not
> like us is not 'real'.
>
> -Daryn
------------------------------------------------------------------------
Jerry Uhl juhl@ncsa.uiuc.edu
Professor of Mathematics 1409 West Green Street
University of Illinois Urbana,Illinois 61801
Calculus&Mathematica, DiffEq&Mathematica, Matrices, Geometry&Mathematica
http://www-cm.math.uiuc.edu and http://netmath.math.uiuc.edu
All that is human must retrograde if it does not advance.
-----Edward Gibbon