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Re: Brainstorming about STEM (was About Functions)
Posted:
Dec 24, 2011 10:45 PM
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My point was that the entire discussion - although of its own
esoteric interest - has almost nothing to do with mathematics
research and absolutely nothing to do with mathematics teaching, at
least not at the K-16 level.
Wayne
At 09:23 AM 12/24/2011, Joe Niederberger wrote:
>Wayne said:
>- ---------------------------------
>I like geometry. Let's start with Hilbert's axioms for Euclidean
>geometry and prove a couple theorems and a couple statements that
>look like they are theorems but are demonstrably false.
>- -----------------------------------
>
>I have no idea why this is a response to what I wrote, unless you
>like Dan and Kirby think that finding proofs and generating proofs
>are the same problem. They are not.
>Generating proofs *is* like the flip side of the coin to automated
>proof checking, however, if the topic is truly "formal" theories
>(please note that qualification). This whole silly sub-thread
>started when I simply was trying to point that out to Dan.
>
>It is either slightly ironic or intentional that you bring up
>Hilbert's Geometry axioms. It was shown relatively recently (2001)
>by Meikle & Fleuriot, that Hilbert's system, when truly formalized
>in computer code, cannot handle some of the proofs by Hilbert
>himself that relied on geometric intuition rather than the formalism
>(i.e., these particular proofs of Hilbert's were decidedly "non-Hilbertian".)
>
>For those interested, here is a link to a paper which can be read
>free online, and gives a glimpse as to some recent thinking on the
>topic: http://rsta.royalsocietypublishing.org/content/363/1835/2377.full
>
>Therein is mentioned the ironic observation on Hilbert's
>geometry and also the famous "V-E+F = 2" of Euler that Kirby likes
>so much, and how such "proving" might itself be automated.
>
>Merry Christmas,
>Joe N
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