Ian Halliday wrote:
> UNORTHODOXIES: Most mathematicians have had the following experience
> and those whose activities are somewhat more public have had it often:
> an unsolicited letter arrives from an unknown individual and contained
> in the letter is a piece of mathematics of a very sensational nature.
[snip interesting bit of stuff]
I've had this experience, myself, and I'm not even a professional
mathematician. I once had this experience with a guy who purported
to prove that the function
f(z) = z
is NOT ANALYTIC. He used a convoluted contour integral[*] in the
complex plane, neglecting to note that he crossed over branch
cuts when doing the integration. He had published a little booklet
entititled "A Demonstration that the Function F(Z) = Z Is Not
Analytic, Along With Some Consequences, Of Which the Mathematical
Community Remains Wilfully Ignorant" or something similar. He was
convinced that simply because he did not have a math degree,
mathematicians refused to listen to, or believe, or accept his
evidence and proof.
I spent weeks in exchanging e-mail with this person, showing him how
to do the contour integral properly (after which, of course, the
singularities are no longer present).
Up until this point we had had convivial, if somewhat unusual,
correspondence, mostly because I patiently listened to what he
had to say. But when the axe finally fell, I suddenly became one
of "them", and he started denouncing me using if not precisely vile
language, certainly pejorative language. Suddenly, our weeks long
correspondence became merely a subterfuge on my part, lulling him into
thinking I could be trusted, when I was really just a part of the Vast
Mathematical Conspiracy devoted to insisting that f(z) = z is analytic,
in face of the fact that he had himself personally proven that it
has singularities.
I finally realized that this man was not just ignorant of the mistakes
he had made, but was actually mentally ill, and that no amount of
rational discussion could make progress with him, since his delusions
and emotional attachment to being right, in the face of all us, if
not quite evil, certainly self-protective and exclusionary
mathematicians, were paramount.
[*] In effect, he was using a contour integral to compute
f(z) = arctan tan z, and not noting that arctan has branch cuts
which must be taken into account when doing the integration
to compute it, which the periodicity of tan nullifies. It took
some work to disentangle the mess, and do the contour integral
correctly, after which he went ballistic, thinking I had "led
him down the garden path" with all my mathematical mumbo-jumbo.
Mike
--
p="p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}
This message made from 100% recycled bits.
You have found the bank of Larn.
I can explain it for you, but I can't understand it for you.
I speak only for myself, and I am unanimous in that!
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