Subject: categories: Re: cracks and pots and Mac Lane

From: "Mamuka Jibladze" <[email-masked]>
Date: Sun, 2 Apr 2006 12:36:16 +0500

> Eduardo quotes Mac Lane as saying
> (paraphrased) If it hasn't been proved, it isn't mathematics
>
> Much as I admire Mac Lane and owe much to him,
> that's rather at odds with what most of us do
> even those who insist on getting a proof ultimately.
>
> case in point:
>
> http://www.oxfordtoday.ox.ac.uk/2005-06/v18n2/04.shtml
>
> if that isn't math, what is it?
> (perjorative adjective of your choice) mathematics?
>
> Was Newton doing *only* physics?
>
> jim

In fact standards of proof and rigor have undergone quite some
transformation in time, so why could they not change drastically in future?
Again lacking proper knowledge I want to ask those who know more history to
confirm or reject something I've been told. Namely, seemingly in times of
Euler and Bernoullis, to be able to prove one's statements was just a matter
of honour, but nobody was obliged to accompany announcement of a theorem
with a proof - you could keep the latter to yourself and should only present
it if somebody would challenge you by expressing doubt; which probably did
not happen that often.

So how do we know that what we consider a rigorous proof today will not be
viewed as something insufficient or even irrelevant in a couple of
centuries? For example, if mathematics would develop my way, I would give a
fact the status of being established only after seeing its validity does not
require any serious effort or expertise from an average mathematician (maybe
even a student). This would not necessarily mean waiting much more time - in
case mathematicians would continue to learn *seeing* more and more. I mean,
if you have to explain to a person in the street how to reach some place,
the amount and kind of explanation you need depends critically on whether
the person is blind or not.

Mamuka