From: Alexander Chislenko (alexc@firefly.net)
Date: Thu Jan 02 1997 - 15:40:34 MST
When at school, I tried to estimate the chances that it can be
disproven assuming random distribution of primes. The chances,
after a certain [low] threshold N, are virtually nil.
All my friends told me that probability methods should not be
applied here as they are 1) not cool and 2) there may be some
regularities there that we do not know that make probability
considerations non-applicable. I ignored 1) and remarked to 2)
that in everything there can be hidden regularities, and that
there is no practical difference between applying probability
theory methods to areas where there are no inherent regularities
and areas where we just do not see them. I am still unconvinced.
The results of such "proofs" are surely uncertain. But is it
such a big deal to have a mathematical "fact" that is not
*exactly* proven, but is certain to 99.9999999999999999999999% ?
How sure are we anyway that our "certain" proofs are correct?
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