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From: Archimedes Plutonium on 22 Jul 2010 17:45
We can use the Fall, 2009 Mathematical Intelligencer article Prime
Simplicity to showcase
how slow the math community operates. The reason Twin Prime Infinitude
was never proven
is because of a fault or error in doing the Euclid proof via Indirect.
That no-one could see that
P-1 and P+1 are necessarily new primes in the Indirect Method. So when
no-one could do a
proper Indirect Euclid IP, well, Twin Primes will remain unproven. It
was pointed out to the
Logic journal editor at Notre Dame University in the early 1990s that
a Twin Primes proof exists the moment that the error in Indirect is
corrected. The lady editor dismissed my
claim and proof of the Infinitude of Twin Primes telling me that, much
like Chandler Davis
with Mathematical Intelligencer, telling me that Euclid's proof was a
closed, ended proof.

So here we have two historical math references, one of the ill-defined
finite-number concept. It
has been assumed as long as mathematics was around, that finite-number
was understood by all and that no-one needed to formally define what
finite-number meant. So that when Wiles
chased after FLT in the 1990s, he just assumed like everyone else what
finite-number meant
and that his use of p-adics in his offerings were not finite-numbers.
Peano axioms never defines finite versus infinite number.

I should not say that the concept of finite-number versus infinite-
number was ill-defined. For it was not even given a initial
definition. There were no definitions and it was left up to every
individual person to "think what is a finite number."

In the case of Euclid's Infinitude of Primes proof IP, there was the
problem of mixing up methods of Direct and Indirect. To the point
where everyone was doing the same proof steps
and calling it willy nilly either direct or indirect.

The parallels of these two case studies of finite number and Euclid's
IP is that conjectures remain open so long as concepts are ill
defined. To define finite number versus infinite number you need to
have a boundary
number that says 10^500 is the boundary between finite and infinite.
Then conjectures like
FLT or Riemann Hypothesis have proofs, otherwise they are never
proveable. In the case of Euclid's IP, if you leave the Indirect
method in a mess, then you cannot prove the Twin Primes
conjecture and slews of other conjectures about infinite set of
primes.

And here it is clear why math is the slowest moving of the sciences.
Math needs judgement
calls to tell if correct or wrong. Those judgement calls are often
faulty and erroneous. Whereas
physics, chemistry, biology never need judgement calls to arrive at
truth, because it is
experiment driven that decides on truth or falsity.

Math is still doing Ancient Greek problems of Twin Primes, whereas
physics, chemistry, biology have no ancient Greek questions open on
their subject.

The slowness of math is seen by the fact that I published on sci.math
the Twin Primes proof
by 1993-1994 and showed the correction to Euclid's IP Indirect, yet by
2009 some 15 years later in a math magazine, Mathematical
Intelligencer, we still see flawed Euclid Indirect IP claims. If
physics moves at the speed of a jet airplane, then math moves at the
speed of
a crawling snail. And the reason is that math does not have experiment
as its arbiter.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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