From: "Joyal, André" <joyal.andre@uqam.ca>
To: "Ronnie Brown" <ronnie.profbrown@btinternet.com>,
"Graham White" <graham@eecs.qmul.ac.uk>
Cc: <categories@mta.ca>
Subject: Re: Explanations
Date: Mon, 25 Apr 2011 09:51:59 -0400 [thread overview]
Message-ID: <E1QEVqB-0002b6-Gb@mlist.mta.ca> (raw)
In-Reply-To: <E1QE9Hl-00070T-1X@mlist.mta.ca>
I cannot resist adding my grain of salt.
Maybe we should distinguish between a human proof and a mechanical proof.
The goal of a human proof is to convince other peoples of the truthfulness
of a proposition.
It is by nature explanatory and it can lead to new insights.
A mechanical proof can be checked by computer but may not produce new insights.
It is establishing a fact. Of course, it is better than none.
Mathematics is above all a human activity.
The value of a proof depends very much on its method.
A new proof may suggest a new method.
A method is a kind of toolbox for proving a large class of propositions.
Commutative algebra is a method in geometry
Category theory is a method in mathematics.
proofs --->methods ----> proofs ----> methods .......
André
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-04-25 13:51 UTC|newest]
Thread overview: 25+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-04-22 13:55 Explanations Graham White
2011-04-23 20:27 ` Explanations David Yetter
2011-04-23 21:29 ` Explanations Ronnie Brown
2011-04-25 13:51 ` Joyal, André [this message]
2011-04-26 0:52 ` Explanations jim stasheff
2011-04-26 13:45 ` Explanations William Messing
[not found] ` <4DB6CC7D.40407@math.umn.edu>
2011-04-26 22:05 ` Explanations Ronnie Brown
2011-04-23 21:52 ` Explanations Dusko Pavlovic
2011-04-25 13:17 ` Explanations ClemsonSteve
2011-04-26 5:55 ` Explanations Timothy Porter
2011-04-27 7:53 ` Explanations Uli Fahrenberg
[not found] ` <17617_1303861705_4DB759C9_17617_39_1_E1QEryD-0006dq-7k@mlist.mta.ca>
2011-04-27 13:20 ` Explanations Marta Bunge
[not found] <654PeBPnq2496S01.1304350816@web01.cms.usa.net>
2011-05-02 18:22 ` Explanations peasthope
-- strict thread matches above, loose matches on Subject: below --
2011-05-01 21:27 Explanations peasthope
[not found] <609PDdViw1024S04.1304197762@web04.cms.usa.net>
2011-05-01 21:00 ` Explanations peasthope
2011-04-30 21:09 Explanations Fred E.J. Linton
[not found] <BANLkTi=XhOM=FKajXUA6pyOq575fm_N=PQ@mail.gmail.com>
2011-04-29 19:56 ` Explanations peasthope
2011-04-30 19:58 ` Explanations Charles Wells
2011-05-02 17:01 ` Explanations Clemson Steve
2011-05-01 12:50 ` Explanations F. William Lawvere
2011-04-28 13:12 Explanations Ellis D. Cooper
2011-04-27 8:16 Explanations Mattias Wikström
2011-04-20 17:22 Explanations Fred E.J. Linton
2011-04-21 19:09 ` Explanations peasthope
2011-04-19 23:37 Explanations Jean-Pierre Marquis
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