ON THE VIRTUE OF
PATIENCE, FERMAT’S LAST THEOREM AND SURVIVAL
©
Edward R Close 2019
“…at
length, the truth will out.” – Shakespeare, The Merchant of Venice.
Dear Reader, I want
to ask you to use your imagination. Please imagine that Pierre de Fermat, a Jurist
who worked in the Parliament of Toulouse France in the middle of the 17th
century (1630-1665) is speaking:
“From childhood, I was
fascinated by numbers, and mathematical propositions often came to me quite as naturally
as breathing! But, alas, it was not my fate to become a professional academic.
My father, Dominique Fermat, prevailed upon me to study law in order to have a
vocation that would enable me to support my family. While my law degree did enable
me to become a productive member of society, I was often bored with legal work,
and turned to musings about numbers when not occupied with my duties as a juror.
I had studied Greek and Latin while at University, which allowed me to have
access to the works of natural philosophers and mathematicians of the past. Around
1625, I began working in my spare time on reconstructing the works of the Greek
geometer Apollonius, having to do with loci and planar surfaces.
Because
I was not an academic, I had no ready institutional support to publish my
findings, so I saved my mathematical musings in the back of my desk and tried
to correspond with professional mathematicians as I could, on occasion. Rene
Descartes, the recognized genius of the day, dismissed me as an amateur, derided
my use of “obscure notation” and called my demonstrations “lucky guesses” when
I proved to be right. I was able to calculate areas and volumes under various
curves using the process of diminishing infinitesimals, something which Descartes
declared to be “impossible”. We also had disagreements about the mathematics
and geometry of the refraction of light and the construction of tangents to
curves, and even though he was wrong, his inflated ego would not allow him to
see the truth! Later, I found more favorable reception of my ideas with the eminent
philosopher of natural sciences, Blaise Pascal, especially regarding the
calculation of probabilities, but it was number theory that was my first love;
especially Diophantine equations and infinite descent. The acme of my
mathematical musings was my proof of the following proposition:
Xn
+ Yn cannot equal Zn, when X, Y and Z are integers
and n is an integer larger than 2.
It was well-known
from the time of the Greek mathematician Pythagoras that the sum of the squares
of two whole numbers can equal a larger whole number squared. In fact, there
are an endless number of such triads, XYX, such that X2 + Y2
= Z2, as is demonstrated in the Pythagorean Theorem. But no one was
able to produce a set of numbers satisfying this requirement when n is
larger than 2. In 1637 I found an elegant proof that the equation Xn
+ Yn = Zn has no whole-number solutions when n
is greater than 2. I penned a statement to this effect in the margin of my copy
of the book Diophantus’ Arithmetica, but the proof was a little too
long to include in the note. However, the whole proof scarcely covered a single
page, and I placed it among some other short notes in a cubbyhole of my desk
for safe keeping.”
▬ ▬ ▬ ▼▲▼ ▬ ▬ ▬
Now, as the reader may
know, Pierre de Fermat’s proof that Xn + Yn ≠ Zn,
when X, Y, Z and n are integers and n > 2 became famous as “Fermat’s
Last Theorem”, because Fermat’s proof was never found and the world’s best mathematicians
were unable to prove or disprove it to their satisfaction for more than 300
years. Because of that, mathematicians came to believe that Fermat was probably
mistaken about having a proof. What the reader may or may not know, is that I
proved Fermat’s Last Theorem in 1965, 30 years before Andrew Wiles’ proof was finally
accepted in 1995. My proof was short, unlike Wiles’ proof of more than 200
pages, and in Fermat’s notation it would probably fit on a single page.
All attempts
to refute my proof, which I call FLT65, over the past 50 plus years have failed,
but it still has only been accepted by a few mathematicians because of the
general belief that a “simple” proof of FLT is simply impossible. The whole
history of my attempts to get it accepted and several of the attempts to refute
it are posted on this blog. Just search for ‘FLT65’ if you want to see them.
Fermat’s Last
Theorem proved to be important in the development of the quantum mathematics I developed,
called the Calculus of Dimensional Distinctions, which Dr. Vernon Neppe and I applied
in our Triadic Dimensional Vortical Paradigm (TDVP), a shift to consciousness
based science. However, the TDVP does not rely on my FLT65 proof at all, because
it only requires the the validity of FLT for values of n from 3 to 9, and it
has been known that FLT is valid for n=3 to a much larger value than 9 for a
very long time.
It would be nice to
be recognized for being the first to prove FLT since Fermat, and it would restore
Fermat’s honor and reputation as a first-rate mathematician, but I’m not
holding my breath. I’ve learned to be patient because I believe at
length, the truth will out!
On a deeper level, I
was beginning to feel depressed about the loss of the physical presence of my
soulmate Jacqui. I am fortunate to have evidence in the form of a meticulous
double-blind experiment that she still exists as a conscious entity, able to
communicate with me and help me as she did while alive. But that evidence is of
an indirect nature. I would like the communication to be more direct and personal,
just between the two of us. I am becoming impatient for that to happen, and
impatience leads to disappointment and disappointment breeds depression.
Today is
Black Friday, the seventh anniversary of the day Jacqui suffered acute kidney
failure in Tucson Arizona, and I had to rush her frantically to the ER at St. Joseph's Hospital,
ERC 11/29/2019
