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# Why Fermat's Last Theorem is half-true/half-false (Gauss)

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WHY WILES’ “PROOF” OF FERMAT’S LAST THEOREM IS JUST A “MATHEMATICAL PARADOX”

(and why the great Carl Gauss was  right )

I don’t like to waste neither my time, nor yours. I’m not a “crankpot”,  but a serious physicist. All my papers are based on classical physics and quantum mechanics, the most sound theories of physics, all experimentally proved. You can disagree on my results - of course - but my method is correct.

The first person that  can prove  me   I’m wrong – if he/she can –wins a 4 days FREE stay at Grand Hotel Villa Serbelloni Hotel (Como Lake). http://www.villaserbelloni.com/

I already chellenged 50 (but the number will be extended)  university full professors (in physics/mathematics) to find an error in my thesis. None of them could reply.

“Cranckpots” don’t put at stake their money, I do!

So, please, read carefully what I’m writing, it’s worth it!  Also because the main  CONCEPT is very easy to be understood even by a high-school student , no complex or “strange” equation.

The point is that we can summarize the truth about Fermat’s Last Theorem (that I tried to show in my last papers)

as follows:

Wiles’ famous “proof” of 1995 is just a “mathematical paradox”, because FLT – as the great Carl Gauss suspected (but without deepening his assertion)  – can be both “proved and disproved”.

I very simply tried to  prove why Gauss was right, whereas  Wiles/Fermat were wrong.

The point is that  the solution of FLT ( a^n + b^n = c^ n) is coincident with the old Pythagorean theorem, namely a^2 + b^2 = c^2, n index cannot be larger/different  than 2, and this is the CORRECT premise/assumption by Pierre de Fermat.

And yet, Pythagorean theorem refers to the PHYSICAL MEASURE of rectangular triangles, to calculate/measure  hypotenuses. It was discovered by making physical measurements of physical triangles, by ancient land surveyors, mathematicians, etc.

The point is that NO  theorem/algorithm involving the measurement of a physical/geometrical entity can be performed through integer Z numbers only.

Any physical measures of physical entities always   need REAL NUMBERS!

Please, read the list of the 17 most important math equations by Ian Stewart https://i.pinimg.com/originals/25/6a/45/256a453c8ff909eb47eec42bf57019c1.jpg

All of them are related to a physical phenomenon, all of them need real numbers (or sometimes complex numbers = again a  real + imaginary number), all of them involve (from logarithms to E = mc^2, from calculus to Maxwell equations, from Fourier transforms to wave equations, etc.) the measurement of a physical entity.

Only as an APPROXIMATE  way of simplification (for elementary/middle  school children)   we use to  describe Pythagorean theorem through integer triples: 3-4-5, 5-12-13, 8-15-17, etc., as the ancient Babylonians and  Greeks were doing, instead of using triples of real numbers, such as: a = 3.7, b= 4.4, c= 5.7 etc.

Thus,  the correct way to describe Pythagorean Theorem is through REAL NUMBERS, such as in the trigonometric identity: sin α^2 + cosα^2 = 1, where sinus and cosine are of course REAL NUMBERS, not integers.

So, the error by Fermat and Wiles was in not realizing that the premise/assumption of proving  a physical/geometrical theorem involving PHYSICAL MEASUREMENTS through Z integers only - and not through real R numbers - is FALSE/INCORRECT.

That’s the reason why Fermat’s Last Theorem is someway  “half-true/half-false”, it can be both “proved and disproved” as the great Gauss was suspecting, and I showed.

Proving FLT just through integer numbers is like proving calculus (which by definition needs infinitesimals (dx)) through just integer numbers, it makes no sense, it could be just a “mathematical paradox”.

So, Wiles’ “proof” of 1995 is just a “mathematical paradox”

But what is more exactly  a “mathematical paradox”?

It is a FALSE/UNPHYSICAL - “purely mathematical proof” -  of a phenomenon linked to the PHYSICAL WORLD, that “forgets” a physical and  necessary parameter/assumption/premise.

For instance, ZENO’s paradox of Achilles and  tortoise’s motion, in a purely abstract mathematical way (through infinite series)  is a mathematical paradox, because it “forgets” physical velocity (v = s/t) of Achilles and the tortoise,  and examines only mathematical spaces. But this leads to a paradox, because the steps by Achilles, in a “purely mathematical way” – without any connection with time and velocity -  can be interpreted as both an infinite series converging  to 1 (1/2 + ¼ + 1/8…+ ½^n) , so Achilles will manage in reaching  the tortoise, AND an infinite series diverging to infinity ( = ½ + 1/3 + ¼ + 1/5 + …1/n) and this way Achilles NEVER reaches the slow tortoise.

And also, BANACH-TARSKI  paradox, “forgets” that in our physical world points and segments ALWAYS possess physical dimensions/sizes. And so – by setting the false and unphysical  premise/assumption that points have no dimension, you can derive 2 IDENTICAL SPHERES from 1 = the mathematical “miracle” of multiplication of spheres!

And also, you can mathematically “prove” that  a few centuries ago Earth was overpopulated by TRILLIONS of inhabitants, through the mathematical paradox of ancestors.

As any of us has 2 parents, 4 grandparents, 8 great-grandparents, etc., you can calculate that in the past, in  just 10-20 generations, our Earth was overpopulated thousands, millions, etc. times more than today.

It is a mathematical paradox that “forgets” the empirical/physical and necessary  premise that we are all RELATED to  other persons, the more we look back  to the past, the more people and their families  were related each other, we all have common ancestors.

So, Fermat and Wiles “FORGOT” that it is impossible to measure physical/geometrical entities through integer Z numbers only, we need R REAL NUMBERS.

Any physical objects are made up  by atoms, whose sizes can be measured just through REAL NUMBERS, and this is well known by calculus and quantum mechanics.

Sorry for Wiles, he didn’t prove anything, he just described  a mathematical/unphysical paradox.

Please, show me that  I’m wrong, if you can. I admit my mistakes.  I offered a FREE 4 days’ stay    at Grand Hotel Villa Serbelloni, (Como Lake) to the first person proving that we can measure physical/geometrical entities (including rectangular triangles)  in our real world  ONLY through integers, and WITHOUT real numbers.

I think I’ll have to wait for a long time….

Alberto Miatello

September 24, 2017.

p.s.: please, don’t tell me that other mathematicians used abstract algebra to prove their theorems. I showed here https://www.academia.edu/34326285/ (see section 4)  that  Grigori Perelman used Ricci-flow with surgery to prove the “Poincarè conjecture”. But his proof is totally sound and  correct, as it is based on physics (Ricci flow is an operator that  was derived from heat equations, 2nd law of thermodynamics, etc.) and it is topologically undisputable. On the contrary Wiles “proof” is totally unphysical, simply because Fermat’s Last Theorem was unsound (half-correct = index 2, and half-incorrect = “solvable” just through integer Z numbers, and not through real R numbers)

False mathematical “proofs” are unphysical, they are  just “mathematical paradoxes”.