Fermat's Last Theorem

I've realized loose connections in this owing to my lack of mathematical nomenclature.  I endevour to study the necessary linguistics to eloquate the revelation Fermat had.  I've had the same revelation in sight, I lack only the right way to describe it.  The goal is a fields medal (obviously) atop other projects currently underway.  And, yes, we can multi-task beyond belief.



This is the current draft of my future one-page proof for Fermat's Last Theorem.

Fermat's Last Theorem proof outline (draft 1), by Rene Helmerichs ~ http://talk2dream.com

22 Sept 2018, 8:30pm.

In a shower, I thought to revisit the initial problem.

Fermat was a Genius, clearly.  His proof would suffice for public display to verify the thinking of an acclaimed genius.  350 years it was left unproven?  What was he saying, again?

a^0=b^0+c^0 is not possible because x^0=1, therefore 1=1+1, and that violates conventional math.

His theorem was that n can only be 1 or 2, not more, not less, not negative, and no decimal or imaginary number.   a^n=b^n+c^n

In the case of n=1, there is the line.  We call it y=x+b, with a slope of one, that is able to shift up or down depending on the value of "b".

Sure, but for n=1, the slope is also assumed to be 1, and there is no horizontal shift.  So for the case of n=1, it's actually a special case of a line, but a regular line nonetheless.

In the case of n=2, there is a circle.  We call it r^2=x^2+y^2 nowadays, but the idea is the same.  There is no shift along x or y this time, so previous shifting of "y" with "b" in the equation of the line has actually been eliminated.  There is also no distortion.  A distortion would turn the circle into an ellipse, sort of like a slope on a line would change the basic line to be more flat or steep.

The case of n=2 is then a "special" case that shows only a basic circle with radius, r, that is centered about the origin (where x and y are 0), and has not distortion (is not an ellipse).

And then I thought why the ability would end at 2.  And I "saw" it.

For n>2, the shapes become more theoretical but the principal law remains the same.  The number of n represents the "power".  When y or x is a two, there is curve involved.  When x and y are both three, there is an obligatory sphere involved.  However, there is not the ability to represent the sphere as a definitive object.  If it cannot be expressed definitively, it remains undefined, and, therefore, not existent.

The proof is actually simple.  A circle requires a radius value to fix the object with a size.  A sphere requires the same, which necessitates at least four terms in the equation.  Since a fixed point in three-space (for a sphere) requires three different axis, and a separate radius value for a definable size, the absence of any of those leaves the sphere without a definite size (visualization, actuality).

The same is true for every shape of any order greater than 3.  Therefore, the only valid positive integers for "n" in Fermat's Last Theorem are 1 and 2, such that, "n" cannot be greater than 2. 

And THAT proof is a LOT shorter than the current 129-page proof, which Fermat himself could not possibly have envisioned when he scrolled his famous remark that the proof he did envision was simply too much to fit into the margin, but implying that it was not too much for any current 11th grade advanced (normal-level) math student to understand.