Galois life story and insolvability of polynomials higher than fourth degrees generally by radicals

http://www-groups.dcs.st-and.ac....

Actually, I don’t know why I sense that such a historical story about a genius boy regarding great theorems in mathematics was quite forged and purely fabricated by old professional mathematicians for many untold reasons up to our current dates, especially that Galois had a record of failures in school and a very tragic life story

Usually, you would certainly find many similar interesting stories (mainly in the history of mathematics) about many genius boys whom their life’s were too short and were full of so miserable sad events to so unbelievable degree

Just imagine in those old days where a genius school student as (Galois) was writing his so famous important script about group theory just the night before he died in a quarrel for a girl, wonder!, where his brother and friends took it immediately after his sad death and submitted it to an academy authority in mathematics in the second day! Wonder!

Where at later and as usual (in the history of mathematics), may be after 14 years the professional experts in those days found it so thrilling and true discovery where they publish it ultimately , and since then it became a true knowledge that is not in doubt anymore!

But frankly, and even in our current days I find so many educated people with highest degrees in mathematics are suffering a lot in understanding it fully, but generally believe in its truthiness as the case now a days with the century proof of Fermat’s last theorem since quarter a century (by Wiles and Taylor)

So, what makes me suspect such a historical story that seems to me like a Good Hindi Drama Film that followers would feel so sympathy to accept it so blindly by the way it was prepared or cooked up neatly after many years of the genius death? Wonder!

And why do I say or even claim that with complete confidence is because I had truly discovered more solid reasons that are much more simpler to easily understand by generally a clever student or a mature or generally by an educated layperson, but so unfortunately and rarely with a professional specialized mathematician, for so many other physiological reasons that never counts to the absolute facts

So, here is again my reasoning that is too simple to understand.

Simply consider this Diophantine Equation, ([math] n^5 = nm^4 + m^5 [/math]), where ([math] n, m [/math] are two coprime natural numbers

It follows from the first look only by any number theorist or a clever school student or a mature or even a layperson that this above mentioned Diophantine Eqn. had no integer solution at all, (How?)

Simply by noticing that the integer ([math] m [/math]) divides exactly the Right hand side of the Equation, but never divides the left hand side of the same Eqn., since we have [math] \gcd(m, n = 1) [/math], hence a very clear contradiction of solvability of such Eqn. (Finished)

But observe carefully how the old alleged historical genius professional mathematicians refused to let go as easily as it is indeed, and insisted to make illegally the real solution beside many other four solutions that are strictly associated with that alleged fictional and non-existing real root solution

But, how is that being possible? Wonder! (So easy cheat indeed)

See here please: Wolfram|Alpha: Making the world’s knowledge computable

How do they try to obtain an approximate ratio of an alleged non-existing real root but at their fake Paradise named Infinity, once the add the so meaningless notation of ellipses denoted by (…), after some number of digits that make you feel you are near and nearer to a real solution

By dividing the whole (non-solvable Diophantine Eqn.), by the term ([math] m^5 [/math]), you so simply get the following Eqn.

([math] (\frac{n}{m})^5 = (\frac{n}{m}) + 1 [/math]), then denoting the ratio as ([math] x = \frac{n}{m} [/math], and then substitute, you get this wonderful irreducible quintic or fifth degree polynomial, that is a very well known example of impossibility of solution by radicals as this:

([math] x^5 – x – 1 = 0 [/math])

That must have at least one real root and another four complex roots in accordance with the well designed and fabricated fundamental theorem of algebra

See here please: Wolfram|Alpha: Making the world’s knowledge computable

How did they manage to create a real root from nothing as ([math] x = 1.167303978… [/math])

Please don’t let the decimal notation con you anymore and note the progressive endless approximation carefully as it is truly only a ratio of two integers:

[math] x \neq \frac{11}{10} [/math], since the later is rational number, similarly

[math] x \neq \frac{116}{100} [/math],

[math] x \neq \frac{1167}{1000} [/math],

[math] x \neq \frac{11673}{10000} [/math],

… …………………………………………….

………………………………………………..

[math] x \neq \frac{116730397}{100000000} [/math],

………………………………………………

So [math] x \neq \frac{A(n)}{10^{n - 1}} [/math], because it is always and forever rational number, hence

[math] x = Nothing [/math] as per our original insolvable Diophantine Eqn.,

However this generalization applies strictly to assumed numbers being with endless significant (terms or digits), in particular for real non-constructible numbers decimal and symbolic representation as the alleged real (algebraic and transcendental) numbers

Also applicable for only the endless decimal expansion of constructible numbers , since real constructibe numbers exists independently from their ghost endless decimal representations

And because Infinity doesn’t exist but merely a pure mind fiction, since natural numbers are truly an endless chain of successive integers with no largest integer existing, so the endless approximation methods or Dedekind cuts, Cauchy sequences, Intermediate theorem, limits, convergence or else can never substitute the exact meaning of exactness sign denoted by (=) in pure mathematics, (but never mind for little carpentry works that is not any mathematics, for sure)

Where the solution form (say for simplicity in 10base number system) would be as this form [math] \frac{A(n)}{10^{n – 1}} [/math], where [math] n [/math] are positive integer and [math]A(n) [/math] is positive integer but with [math] n [/math] sequence number of digits, which represent always a rational number approximation solution, where at the same time can’t consider [math] n [/math] as integer tending to infinity for that irrational root existing only in their minds, because this is actually impossible to achieve, and impossible to exist since natural numbers are endless with no largest integer, and also impossible acceptance in the holy grail rules of principles of mathematics itself (for being undefined and also not accepted integers with endless digits)

Where they claim that the real root is irrational number (but at a Paradise called Infinity), where at the same time it is strictly impossible to construct the real root exactly on the real number line as the case with those irrational numbers that are exactly constructible and also proved rigorously from the Pythagorean theorem itself (such as the only valid square root operation)

But someone might be so shocked about other complex numbers with imaginary parts, and then this is truly another very big issue that was so simply decided, fabricated or invented deliberately to comply with the well-designed fundamental theorem of algebra at later stage

Just remember the following three basic polynomials, and how did they so simply decided (but never discovered) their solution, since they haven’t any meaning full solution, especially that after fabricating or deciding the unreal integer “Zero” as real integer as any other existing integer, despite the fact that it represents “nothingness” and has no definitive inverse like any other natural integer

And then they expanded the functionality of mathematics in all directions with lots of misusing it for the sake of so easy business mathematics, by defining the multiplication operation on polarity sign as [math] (+1)(+1) = (+1) [/math], where then, adopting the same for negatives as [math] (-1)*( -1) = (+ 1) [/math] as a an artificial false and illogical symmetry, just to create the current coordination system, where if you draw a function, then must cross the (X-Axis) at an alleged real root, neglecting also the fact of impossibility of proving the continuity in order to justify all that obvious cheat of non-existence of such an alleged real root with endless operation at their alleged non-existing and meaningless and fictional Infinity,

1) A first polynomial degree of this form [math] x + 1 = 0 [/math], where negative numbers weren’t adopted yet, so the solution came after a decision but never as a real discovery, as let there be negative integers, where simply the problem was so easily solved as (x = -1), despite the fact that negative integers are mainly mirror image of natural numbers, hence truly unreal numbers

Here is some thought about it

https://www.quora.com/How-would-...

2) Where later they decided (but never discovered) and adopted the imaginary unit as a solution for a non-solvable polynomial ([math] x^2 + 1 = 0 [/math]) in real numbers

Where this was another fictional paradise that immediately allowed mathematics to expand indefinitely in the wrong direction and killing almost the physical sciences to very high degree

You may kindly see the silly tricks here:

https://www.quora.com/Did-the-mi...

But imagine nowadays with all the facilities of world fast and opened communication and supercomputer age that hundreds of genius armature boys as Galois are writing theorems and so many puzzles publically to the world professional mathematicians for day and night, then do you think truly that they would even look at them or even feel good to learn from them? Wonder!

So, did you realize exactly how many tons of fictional mathematics that had been built on false decisions over many centuries that this only simple Diophantine Eqn. can uncover? Wonder!

Can’t you make now very easy examples of many other similar Diophantine Eqns. to discover alone and only by yourself the impossibility of general solution by true radicals of polynomials of degree higher than two?

Did you realize that even the quadratic polynomials solutions are generally invalid when having imaginary parts?

Did you realize that Infinity itself can’t help in creating any real existing solution because it is merely a pure fiction?

So, no wonder that people even on the top levels of mathematics confess truly and publically that they don’t realize everything, but generally tend to be merely stubborn dogmatic believers and blind defenders of all ignorance sources in mathematics especially if the invader is mainly a hoppiest armature outsider

So to say, this is truly the tragedy of a genius in all the times that usually can’t go the same way as the vast majorities of the mainstream always do, they are simply the same inhabitants of those old centuries, for sure

If you truly get the theme, please help others to understand it better

And finally, we do understand that new visions with rigorous proofs based on solid numerical examples wouldn’t be appreciated for the many contradictions it hunts together in our current mathematics, and most likely would be strictly resisted for many other non mathematical reasons mainly by the professionals, so we do request them at least to keep it for generation to come, since the absolute facts only that must be realized and raised above all lies and fictions that had been illegally and so hugely established in our current modern mathematics

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Regards

Bassam Karzeddin

March, 11, 2018