rhersh at math.unm.edu
Mon Feb 22 20:05:13 EST 1999
I agree that Tarski can give a first-order proof of everything
in Euclid's Elements.
Nevertheless, mathematicians use geometric proofs, even
if you claim you can prove they aren't proofs.
There's "Visual Complex Analysis," I forget the author's name,
it should be in your library.
There's Arnold's books on ordinary differential equations.
Mathematics magazine for years has published "proofs without words."
Recently a collection of proofs without words was published
as a book entitled "Proofs without words." If it's not in
your library, just look at some issues of Math Magazine.
Why do mathematicians do this?
Because a geometric proof is often more convincing, more perspicuous,
more inteeesting, more memorable.
You can say it isn't a proof, but it is recognized as a proof by
people whose business is proving theorems.
You can take a tree branch and chop is into bits, and then
say you've proved it was really a tree branch.
To what end?
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