in 1637, Pierre de Fermat,
a judge at the French Parliament of Toulouse, wrote in the margin of a book on
Diophantine equations that he had devised a marvelous proof that there are no
positive whole number solutions to the equation

**x**for^{n}+ y^{n}= z^{n}**n**greater than two. His proof, for n = 4 is known, but his general proof for all n greater than two was never found.
It is an interesting aside that Fermat was not a professional
mathematician. He did not publish his findings, he simply conveyed them in
letters to other mathematicians, and thus was considered an amateur. The less than modest French mathematician and philosopher Rene Descartes tried to discredit
Fermat by proclaiming that he
was “a troublemaker who owed his reputation to a few lucky guesses”. However, in one dispute after another, e.g.
their derivations of the sine law for the refraction of light, Fermat proved to
be right and Descartes wrong. While Descartes clearly considered himself to be the
superior intellect of the day, a comparison of their works reveals the fact
that Fermat was the better scientist and mathematician of the two.

Descartes’ arrogance
shines out in the following statement: “I hope that posterity will judge me kindly, not
only as to the things which I have explained, but also to those which I have
intentionally omitted so as to leave to others the pleasure of discovery.” Implying
that he could have explained much more. This is analogous to a classmate of
mine who liked to say “I’m not conceited, I’m actually twice as smart as I say
I am!”

*Against the Gods*, states that Fermat "was a mathematician of rare power. He was an independent inventor of analytical geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."

Regarding Fermat's work, Sir Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."

Speaking of Fermat's
work in number theory, Mathematician Andre Weil says that: "what we
possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the
modern theory of such curves. It naturally falls into two parts; the first one
... may conveniently be termed a method of ascent, in contrast with the method
of descent which is rightly regarded as Fermat's own. … With his gift for
number relations and his ability to find proofs for many of his theorems,
Fermat essentially created the modern theory of numbers.

Never-the-less, popular history
has treated Rene Descartes very well, while ignoring Fermat. The name Descartes
is well known to every student of mathematics and science, while Fermat’s name
is virtually unknown except for in relation to Fermat’s Last Theorem, -and most
modern mathematicians openly doubt that he actually proved it! Why? Because for more than 300 years, professional mathematicians tried
to find a proof, and failed.

The power of Fermat’s math
lies in his method of infinite descent, and the principle of “efficient purpose in nature”, and in 1964-5, while teaching high school
mathematics, using the same simple principles used by Pierre de Fermat, I
produced a proof which I first submitted to a professional mathematician in
1966. Because my proof was completed in 1965, I call it FLT65.

To see FLT65 as it was submitted to the first
reviewer on January 25 1966, copy the link below and paste it into your web
browser.

This link will take you to a lengthy discussion
of FLT65. To see the original submitted version, scroll down to Appendix C.

I have submitted FLT65 to more than 50
mathematicians over the years, and only a few of them who responded actually
offered any mathematical arguments attempting to disprove FLT65. And while a
precious few have admitted it, none of them were able to produce a valid
refutation of FLT65. Because I believed it would eventually be recognized as a
valid proof, I have carefully documented the submittals and responses.

You might well ask: if no one has refuted
FLT65, why hasn’t it been accepted? The answer to this is an interesting story
by itself. To learn the details of the history of the odyssey of FLT65, copy
the link below and paste it into your web browser.

I believe that the time for Fermat to become a household name
has come, because his simple methods of Diophantine analysis are totally
appropriate and exactly what is needed for application to quantum physics. It
is time to go beyond the calculus of Newton and Leibniz and apply the Calculus
of Distinctions to TRUE quantum equivalence units to produce a better
description of multi-dimensional reality. See details in the posts of TDVP and www.BrainVoyage.com.

Because of excessive academic specialization, and the fact that
modern thinking has lost its metaphysical basis in Infinite Intelligence, science
has gone astray and adopted atheistic materialism as its metaphysical basis.
The result is a world society that is morally adrift. This lack of meaning and
purpose is so dangerous that, if not corrected, it could spell the demise of
the human race. It is time to revisit the simple infinite descent and principle of “efficient
purpose in nature”, of Pierre de Fermat.

Edward R. Close August
4, 2017

Referring to my last comment, Ed, I'm sure the Ultimate Force has already adequately catered for Pierre de Fermat's continuing future, ad infinitum - As I trust it has for us, without us necessarily becoming so-called household names! IJN!

ReplyDeleteI quite agree, except that it's time for mathematicians and scientists to wake up to the potential of Fermat's methods and see the short-comings of the current paradigm.

ReplyDelete