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1. As Fermat’s Last Theorem Can Be Solved Like Pythagorean Theorem
(n = 2 → a2
+ b2
= c2
), why Mathematicians do not Admit Fermat
Made a Mistake, by Postulating just Integer (Z) Numbers to Solve it?
Why Mathematics Alone Cannot Explain Problems Involving Physics.
“Today’s scientists have substituted mathematics for experiments,
and they wander off through equation after equation and
eventually build a structure which has no relation to reality.”— Nikola Tesla
“Physics is mathematical not because we know so much about the physical world, but because we know so little; it is
only its mathematical properties that we can discover” _ Bertrand Russell
Dear Friends,
Please feel free to say what you really think, and don’t feel “intimidated” by this topic. I’m proposing this
subject, but I’ll not take part in the debate, so that to let you totally free to say what you wish, once you
know in advance my personal opinion.
Actually, the problem I’m proposing to debate is not so difficult, indeed. If you think: “ah…Fermat… it’s
not my field”, please, wait for a moment, because it takes only ordinary good sense and logic (it doesn’t
involve the knowledge abstract algebra, as someone could believe) to discuss the main points of this issue.
Even more important: the relationship between mathematics and physics (and other fields), is a point
that any researchers, in any fields, are expected to form an opinion, regardless of Fermat, Wiles, etc.
And yet, today’ scientific-academic castes are trying – as it frequently happens! – to silence the debate,
trying to make researchers challenging “the official proof” by Andrew Wiles seem like “cranks”, “ignorant
people”, etc., in a violent, offensive, intimidating and intolerable way.
Don’t believe them! Carl Friedrich Gauss – probably the most “naturally-gifted” mathematician ever
– refused to “prove” Fermat’s Last Theorem, saying that in his opinion it was the kind of “theorem” that
could be both “proved and disproved”.
(Source of image: Wikipedia US fair use)

2. A diplomatic way to say that the theorem seemed to him ill-posed and flawed in its assumptions.
Thus, the great Gauss “smelled a rat”, he understood that something was wrong with that ”theorem”
and did not waste his life in trying to prove it.
I published here a few days ago – as a physicist – a new study https://www.academia.edu/34525439/
showing that Fermat’s Last Theorem an
+ bn
= cn.
- whose solution is coincident with the old Pythagorean
theorem: a2
+ b2
= c2
– is actually a physical/mathematical problem referring to the measurement of
physical/real rectangular triangles of our real world.
Therefore, as Pythagorean theorem is satisfied by both integer (Z) a,b,c (3-4-5, 7-24-25, etc.) but above
all by real (R) a,b,c numbers such as a = 3.7, b = 4.4, c = 5.7, etc., the famous Wiles’ conjecture of
1995, purporting to “prove” FLT through integer numbers only and elliptical “non-exiting” curves
(“Frey curve”: y² = x ( x – A) ( x + B ) is simply a denial of Pythagorean theorem and real “physical”
world (where objects are always measured through R numbers). That’s reminiscent of the famous
Zeno’s paradox, of Achilles and the tortoise. For more than 2,000 years – from Zeno to Gregory of Saint
Vincent – mathematicians tried to explain Achille’s motion (a physical phenomenon) in a wrong way – as an
“abstract” mathematical problem of infinite series, forgetting that any steps of Achilles can be
mathematically seen as both converging to 1 (= ½ + ¼ + 1/8…+ 1/2n
) but also diverging to infinity (=
harmonic series: ½ + 1/3 + ¼ + 1/5…+ 1/n), and so it is impossible to solve the problem of motion in an
“abstract and merely mathematical way” through the infinite series. After XVII century and Newton, the
problem of motion of 2 bodies was correctly solved in the frame of physics, dynamics, and comparison
of velocities.
(Source of image: ibmathresource.com website )
In other words, no “theoretical mathematician” who cheered (many times even without understanding it!) the
famous “proof” of Andrew Wiles, can answer my simple number 3 question (the first 2 questions have
already been answered since 1637):
1) “Is FLT an
+ bn
= cn
satisfied by just the n index = 2 corresponding to Pythagorean theorem
a2
+ b2
= c2
?”
Answer: “Yes” (Fermat himself set this as the first fundamental postulate)

3. 2) “Is the Pythagorean theorem a2
+ b2
= c2
satisfied with both numbers and integers ?”
Answer: “Yes” Actually sizes of sides of ALL physical triangles we see are not precisely Z
integers, they are R numbers (e.g. 3.51 meters, 15.6 cm., 3.8 inches, 7.65 yards, etc. etc.)
3) “And so, why FLT should not be satisfied through numbers too?”
Answer: “…………..”
I can wait for the answer – to paraphrase the US Ambassador Adlai Stevenson - “until the hell freezes
over”!
Final question: Instead of wasting a life in trying to demonstrate that Fermat’s Last Theorem can be proved
by JUST integer Z numbers, why mathematicians don’t admit that maybe (or better definitely!) Pierre de
Fermat made a mistake, purporting to prove his theorem with just a,b,c, Z integer numbers, and discarding
a,b,c R real numbers ?
Who was Pierre de Fermat? Superman? Spiderman?
Because the problem is quite simple: either Pythagoras is right (he is!), as his theorem can be proved through
both integer and real numbers as sizes of sides, or Fermat is wrong, purporting to prove Pythagorean theorem
through integer numbers a,b,c only.
Pierre de Fermat was the kind of person that sometimes was joking, and used “to talk big”.
It is time we admit his theorem was his greatest joke to generations of mathematicians…
And in addition, Fermat’s Last Theorem and today’s attitude of scientific establishment, is disclosing
another thorny problem:
DIVORCE BETWEEN MATHEMATICS AND PHYSICS
We all know that – at the end of XIX century – mathematicians set – as unique scientific criterion – the
logical coherence of axioms and postulates, without any need to look for the physical, or experimental,
confirmation of mathematical theorems.
Riemann and Lobacevskij invented the new elliptical and hyperbolic geometries that – contrary to the
physical “parabolic” Euclidean geometry and the V Euclidean Postulate - are contradicted by our physical
experience.
Moreover, we all know that mathematics “proved” theorems and paradoxes – such as the Banach-Tarski
paradox – that are totally contradicted by our physical experience. According to Banach-Tarski paradox, if
we admit - as a postulate – that a sphere is made by “points” having neither size, nor volume, we can
logically and mathematically deconstruct it, and make 2 “new spheres”, identical to the first one, a true
“miracle”!.
As the remarkable quantum physicist Jack Sarfatti said in an interview: “…Theoretical physics is
monopolized by string theory, that became a sort of church, a religion. All we have is mathematics, quite
fascinating. Mathematicians are trying to deal with physics, and they produced interesting data, but they
couldn’t squeeze any predictions from string theory corresponding to empirical observations. They did not
shed any light on today’s scientific enigmas.”

4. However, in recent years a sort of little “turnaround” came from studies and theories such as those by Max
Tegmark (MU mathematical universe, or CUH computable universe hypothesis) trying again to link
mathematics to the physical world and reality.
After all, once Gödel (but also Tarski) proved how incomplete are all formal systems such as mathematics,
the naïve and too enthusiast attitudes of the end of XIX century- beginning of XX century toward the
“power” of mathematics (and the unrealistic and arrogant claim to find just in mathematical reasoning the
explanation of the physical world) began to decline.
Many scholars and scientists pointed out that the attitude of today’s scientific establishment in trusting too
much in mathematics – even to the point of despising experiments and physics – is not at all “modern”. It
resembles the attitude of philosophers of dark centuries of Middle Age. In my other recent paper
https://www.academia.edu/34326285/ I just wanted to remember that ALL the most important discoveries of
mathematics (from Archimedes’ quadrature of parabola, to Boolean algebra, formalism of quantum
mechanics, Mandelbrot’s fractals, etc.) and physics in the history came from the patient observation of
physical world, and NOT from “theoretical and abstract mathematical reasoning” alone. As the great
mathematician Bertrand Russell used to say: physics is mathematical, thus the “despise” (or at least the
disregard) of physical world by many mathematicians is simply unreasonable and incoherent.
Feel free to say what you think about.
Thanks.
Alberto Miatello
September 14, 2017