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When we do physics and have a problem, we invariably start with a
Newtonian worksheet. We do it because it is convenient and fast and our
minds work well in this system. But we know that our answer in
Newtonian Mechanics is a close approximation and is not the true
answer. Sometimes the Newtonian answer is altogether 180 degrees wrong
and opposite the Quantum Mechanics answer such as that the electron in
orbit will lose energy and fall into the nucleus of the atom.
Mathematics after 1993 is in a similar Revolution. A revolution that
says most of everything in present day mathematics is wrong or vastly
wrong or slightly wrong. The Revolution is that Natural Numbers are not
what they appear or seem to be. There is no "finite integers" out to
infinity. That is the problem. The Natural Numbers are really the
Adics. And that similar to Newtonian Mechanics in Physics is just a
convenience but nothing to take serious, likewise in mathematics, that
Natural Numbers are not Finite-Integers but are Infinite Integers.
The reason mathematics at present has these unsolved problems:
(1) Riemann Hypothesis
(2) Fermat's Last Theorem
(3) Infinitude of Twin Primes
(4) Infinitude of all Even Numbered Spaced Primes (generalization of
Twin Primes)
(5) Infinitude of Perfect Numbers
(6) Goldbach Conjecture
and I am probably forgetting or missing several hundred more unsolved
problems.
The reason none of the above is solved is because Natural Numbers are
Infinite Integers.
Newtonian Mechanics was marvellously successful for Physics when Newton
devised it in the 1600s and was pretty for 300 years, until problems
arose about the physics of the atom. And those problems accumulated as
bad as the list above in mathematics accumulated. Finally, Quantum
Mechanics had to scrapp Newtonian Mechanics.
I am the first person to start this major revolution in Mathematics.
When I first appeared on the Internet in 1993, I offered a proof of
Fermat's Last Theorem by saying that if there existed a Pythagorean
Triple for exponent 3 there has to exist a base-triple and it has to
have the number "2" involved. Because in exponent 2 the smallest
P-triple is 3,4,5 and one can easily see that this is 2+1, 2+2, 2+2+1
and one knows that 2+2 is the same as 2x2 where multiplication is the
same as addition. So my argument was, that if there exists a valid
proof of Fermat's Last Theorem, it has to involve this "base-triple"
that employs the fact that 2+2 is equal to 2x2. In 1993 as I posted
this to sci.math with several responses, it was determined that such an
attack on Fermat's Last Theorem was not going to produce anything. But
it should have produced the proof. So what does that tell us. It tells
us that Fermat's Last Theorem is nothing what mathematicians ever
thought it was. That there is some huge-flaw in our understanding of
Natural Numbers. That when they become large, they no longer are what
we dream or imagine them to be. This is where the Newtonian Mathematics
becomes the Quantum Mathematics.
The resolution to Fermat's Last Theorem is that it is false. That there
exists P-triples for all exponents. One such P-triple is this:
.....8212890625
.....1787109376
.....0000000001
The resolution to Riemann Hypothesis is that the primes do not lie on a
straight line of the 1/2 straight line. The Primes and the Natural
Numbers begin to curve when they get large. In fact they spiral,
geometrically. So that when the Natural Numbers get to say
...2222222222 and the interval between say .....33333333333 is a new
and different layer of infinity. And where the Natural Numbers have
become no longer a straight line but a huge curve.
When I took a vacation from sci.math in the 1990s and up until recently
I sort of bunched together those unsolved problems into two
categories-- one being totally in the sphere of Natural Numbers = Adics
such as the Riemann Hypothesis, Fermat's Last Theorem, Goldbach, and
the other category that perhaps, just a tiny perhaps the old
mathematics way of doing things may still prove some of these unsolved
problems. The No Odd Perfect Number conjecture, the infinitude of Twin
Primes and the several geometry conjectures like Poincare and 4-Color
Mapping.
But after today I am going to have to throw Infinitude of Twin Primes
onto the same pile as Riemann Hypothesis and Goldbach Conjecture and
Fermat's Last Theorem.
I thought that perhaps with the correction of Euclid's Infinitude of
Primes that since W+1 and W-1 are necessarily a new prime, would be
enough of a key to prove the assertion. Finding out that the Direct
Method is never viable for it can never force a proof. And finding out
that the correction of Euclid is not enough to give a Indirect Proof.
That I am convinced it is a proof in the realm of Natural Numbers =
Adics. And there is one other feature that I am struggling with in this
conclusion. The feature of Direct Method versus Indirect. Physics
should answer this question. Can you have a valid proof of mathematics
if there is only a Direct Method proof available? Or is a valid proof
of mathematics arise only when a Direct Method and Indirect Method are
available? Physics has it that a electron or proton exists but also its
reverse of a antielectron and a antiproton. So in mathematics, if one
can only find a Indirect Method proof, perhaps they are only 1/2 way
there in having a proof. This is deep subject for which I should spend
more time on, but I know the answer will come from Physics, not
mathematics.
As for the Infinitude of Twin Primes using Natural Numbers = Adics. I
am going to use the 10-adic representatives but when I say Adics I mean
every infinite string leftward, the flip side of the Reals.
Proof of the Infinitude of Twin Primes: the first pair of Twin Primes
is {3,5}. The last pair of Twin Primes are {....9999995 and
.....99999997} This is a new method of proving infinity of a set of
numbers. The Number ....9999999 is the "point at infinity" It is the
last number in existence and it is still an infinite set. Since the
pair of numbers ....999995 and .....999997 are at the point of infinity
and since they are twin primes means that the set of Twin Primes is
infinite.
This above method works also for Infinitude of Perfect Numbers,
provided one can get a number like ....9999999xyz that fulfill the
requirements of Perfect Number.
Summary: like in 1993 when my base-P-triple could not work, yet should
have worked means that the concept of Natural Numbers is at fault and
when you make the claim Natural Numbers = Adics, then the problem is
solved. Likewise, here in December of 2006 with a new fresh attack on
Infinitude of Twin Primes where W+1, W-1 in reductio ad absurdum
guaranteeing that these are necessarily new primes should have worked,
but could not work. That means the conjecture is in the realm of
Natural Numbers = Adics, just like Newtonian Mechanics would always
have the electron fall into the nucleus.
Archimedes Plutonium
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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