Re: cracks and pots and Mac Lane

Re: cracks and pots and Mac Lane

[Colin McLarty]

I am not sure I understand this.  Jim, do you mean to say that these
people are using some mathematical statments that are not proved?  The
article seems to me to say the opposite:  They are using numerical
calculations, which I suppose can be routinely verified as such, but
with novel applications in biology.

Colin

----- Original Message -----
From: jim stasheff <jds@math.upenn.edu>
> 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

Re: cracks and pots and Mac Lane

[jim stasheff]

No, guess I was too telegraphic
I meant to ask
if
They are using numerical
 > calculations, which I suppose can be routinely verified as such, but
 > with novel applications in biology.

but they themselves are not *proving* anything
then they are not doing mathematics???

jim



Colin McLarty wrote:
> I am not sure I understand this.  Jim, do you mean to say that these
> people are using some mathematical statments that are not proved?  The
> article seems to me to say the opposite:  They are using numerical
> calculations, which I suppose can be routinely verified as such, but
> with novel applications in biology.
>
> Colin
>

Re: cracks and pots and Mac Lane

[Mamuka Jibladze]

> 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

Re: cracks and pots and Mac Lane

[jim stasheff]

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