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From: Archimedes Plutonium on 13 Aug 2010 14:58
Even geniuses slip. If I had it to do over again, looking at Goldbach,
I should first have wondered whether there are counterexamples in
Infinite Integers such as p-adics or AP-adics. There most certainly
are counterexamples.

A few counterexamples are these:
(a) ....191817161514131211109876543210
(b) ....888833338883338833830
(c) .....666666660

And come to think of it, my Galois Algebra proof of Goldbach has
restrictions as does all of Projective Geometry has restrictions. So I
do learn something new in all of this. The Galois Algebra of Goldbach
says that multiplication requires at least two prime factors for Even
Naturals >4. If we thus interchange multiplication with addition,
every Even Natural requires two prime Goldbach summands. But notice
that all of Projective Geometry is finite geometry of objects of lines
and points interchangeability. One theorem in projective geometry that
talks of points and then interchanges them with lines is that of
finite mathematics since points are finite and the lines are line
segments. The study of Projective Geometry never made that clear, and
only long after having taken the subject might someone, upon
reflection, realize that the subject was finite geometry.

So that the Galois Algebra proof of Goldbach is not a Goldbach to
infinity but a finite Goldbach to 10^500 or less. Goldbach is true for
N smaller than 1000 or 10,000, but Goldbach is not true for what "old
math called infinity" Goldbach is not true for "out to infinity"
unless we specify that 10^500 is the boundary of finite
and infinite.

This is the same situation for Fermat's Last Theorem and for the
Riemann Hypothesis.

Now there is going to be alot of carping and complaining by dull
people of mathematics, wondering that it appears as if 10^500 is too
artificial, since it seems as though Goldbach works just as well out
to 10^600 or 10^2,000 and that Fermat's Last Theorem or
Riemann Hypothesis are good for that distance also.

But the reason they are dullards, is because Physics is exhausted at
10^500 and especially its inverse of 10^-500.

Has anyone really, ever noticed that in mathematics, there is a huge
bias of theorems for the world at large, but seldom if ever a theorem
of the world at the small scale? It is not because of a lack of
interest in the microworld for mathematics, but more to do with our
inability to think small. And mathematics and mathematicians never
really payed attention to math at the small. Occasionally some math is
of the microworld such as Poincare Conjecture and the reason PC has
never been proven, well, because it too, like Goldbach, like Fermat's
Last Theorem and like the
Riemann Hypothesis, has run into the boundary between what is finite
versus infinite.

A long time back in this book which is approaching a thousand pages or
more, I gave a proof that you cannot have absolute betweeness in
geometry. That you cannot have a axiom that says between any two
points on a line there is a new third point. Where does that
breakdown? It breaks down at 10^-500. Poincare Conjecture is never
provable because the axiom of betweeness stops at 10^-500.

Another proof I gave was that if you have absolute betweeness, then
you have triangles in Euclidean Geometry whose angle sum is larger
than 180 degrees.

The point I am making with 10^-500, is that people, dullards in math,
look at Goldbach, FLT, RH and think, oh, why stop at 10^500 for those
seem to work at 10^600. And the answer to the dullards, is that as you
push beyond 10^500, you have to realize that you are pushing beyond
10^-500 in the microworld where you have triangles in that microworld
with angle sums larger than 180 degrees.

So I have been able to prove Infinitude of Twin Primes, the Polignac
conjecture, the Infinitude of Mersenne primes, the Infinitude of
Perfect Numbers, and a broad class of infinitude of primes proof,
conventionally. I was able to do this because I saw a flaw in the
history of mathematics with the inability to properly give a Euclid
Indirect method Infinitude of Regular Primes. I also was able to prove
that No Odd Perfect Number (except 1) exists by conventional means,
where the proof is a template of how square root of 2 is irrational
was proven.

But as for Goldbach, FLT, and Riemann Hypothesis and the Poincare
Conjecture, they are unprovable in their "old math format" because the
old-math never defined what it means to be finite-number versus
infinite-number.

Let me also add, that the Kepler Packing Problem is also unproveable
because of the silly ill-defined notion
of infinite tiling when packing requires a distinction between finite
number and infinite number. So that once KPP is embedded in 10^500, it
is instantly proveable that the hexagonal closed packing is not the
densest of packings but requires a mix of packings which includes the
oblong packing at the container walls.

In sum total, mathematics, from Ancient Greece times has built up alot
of poor definitions and misconceptions which has led to conjectures
that contain those poor-definitions and thus never proveable. And this
book is all about cleaning up the messy house of mathematics.

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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