Re: What is understanding?

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Hi Jack:
I will be waiting for what you have to say (see below).
For the time being I will stick to my belief that IN PURE
MATHEMATICS, as opposed to its practical applications,
understanding can be described as "an ability of a human
being to generate syllogistic derivations from already
accepted statements". A mathematical theorem must be
proven to be accepted; an agreement with some real data
is not a convincing argument in pure math.

Mathematicians do other things, such as eating, playing
musical instruments, learning physics and enjoying situations
in which fruits of their labor are used by practical people.
They are probably still inspired by what happens outside
of their discipline but the basic rule of their game, I was told,
is to logically justify statements (before they become accepted
as the mathematical truth).

But I am not a mathematician and I may be incorrect. Let me
end with a sentence Gary Kashner used today: "I think I have
stated more then I know, so I will shut up."
Ludwik Kowalski

Jack Uretsky wrote:
> ................. I have just arrived at a slap the forehead kind of
> understanding of a problem that I will describe at some other
> time. I think that I totally disagree with what you say, because
> I think that you incorrectly perceive the role of mathematics,
> and your definition of "understanding" is so circumsribed as
> to lack utility.