FOM: Re:

[Michel Eytan]

Thus spake Reuben Hersh at 22-2-99 re ():

> 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.

Also "Anschauliche Geometrie" by none less than Hilbert, if I remember
correctly. Aim is to make things 'obvious', not to prove them. Cf the
Indian mathematics where you (supposedly) decompose a problem into pieces
small enough to be able to say "Look!" and the property to prove leaps at
your eyes...

>
> 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?
>
> Reuben Hersh


--
Michel Eytan                                       eytan at dpt-info.u-strasbg.fr
                                       "I say what I mean and mean what I say"