1-AP's 6th published book WORLD's FIRST VALID PROOF OF FERMAT's LAST THEOREM, and exposing the shoddy fake proof of Euler in exp3 and the con-artist fake Wiles offering.

AP is revisiting and revising his World's First Valid Proof of Fermat's Last Theorem and giving a detailed account of the fake and con-artist offering by Andrew Wiles. Andrew Wiles cheated AP of the prizes awarded for the proof of Fermat's Last Theorem. And this was a huge huge problem of science journalism publishing. Those that had access to publishing had a dreadful tendency of cheating scientists who had no direct access to publishing. So that Andrew Wiles achieved fame for FLT not on merits of truth, but only because he controlled as editor of a math journal out of Princeton Univ. All that AP had was Usenet, sci.math and sci.physics and other newsgroups. The old old way of doing science with publication became fraught with cheating and error and outright stealing of scientists working in the field without that access to publication.

And it was about 1993, when the Usenet and Internet started to Free the World, Give Liberty to scientists in the Field, who had no direct access to publishing and were prone to being stolen from and cheated of their work.

6th published book

World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 29Apr2021. This is AP's 6th published book.

Preface:
Real proofs of Fermat's Last Theorem// including the fake Euler proof in exp3 and Wiles fake proof.

Recap summary: In 1993 I proved Fermat's Last Theorem with a pure algebra proof, arguing that because of the special number 4 where 2 + 2 = 2^2 = 2*2 = 4 that this special feature of a unique number 4, allows for there to exist solutions to A^2 + B^2 = C^2. That the number 4 is a basis vector allowing more solutions to exist in exponent 2. But since there is no number with N+N+N = N*N*N that exists, there cannot be a solution in exp3 and the same argument for higher exponents. In 2014, I went and proved Generalized FLT by using "condensed rectangles". Once I had proven Generalized, then Regular FLT comes out of that proof as a simple corollary. So I had two proofs of Regular FLT, pure algebra and a corollary from Generalized FLT. Then recently in 2019, I sought to find a pure algebra proof of Generalized FLT, and I believe I accomplished that also by showing solutions to Generalized FLT also come from the special number 4 where 2 + 2 = 2^2 = 2*2 = 4. Amazing how so much math comes from the specialness of 4, where I argue that a Vector Space of multiplication provides the Generalized FLT of A^x + B^y = C^z.

Cover Picture: In my own handwriting, some Generalized Fermat's Last Theorem type of equations.

As for the Euler exponent 3 invalid proof and the Wiles invalid FLT, both are missing a proof of the case of all three A,B,C are evens (see in the text).
Length: 156 pages

File Size: 1503 KB
Print Length: 156 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PQKGW4M
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled 

Euler was shoddy with his fake Fermat's Last Theorem, FLT, Proof for exponent 3, shoddy and failed to give a proof. But Andrew Wiles is a con-artist fraud, more than just shoddy on FLT.

Euler made a mistake in his fake proof, for he assumed that x,y,z all three even numbers cannot be a solution set in FLT. As Wikipedia entry quoted below says "One of the three must be even, whereas the other two are odd."

And it is true Euler provided a proof of the case of exponent 3 provided two of x,y,z are odd and the last, even. However, that is not a proof for the entire exponent 3. Euler was shoddy in his proof for to be a mathematics proof, it has to be complete. And what Euler missed was the case in which all three x,y,z are even numbers.

Now we can see this important missed case of Euler by just running through a few numbers.

So we have

2^3 = 8 and 4^3 = 64 and we have 8 + 8 =/= 64 but far from it.
6^3 = 216, and we have 64 + 64 =/= 216, but we are narrowing the gap.

So let us jump out to 100^3 and 98^3 and we have
98^3 = 941,192
100^3 = 1,000,000
And instantly you can see and recognize that 98^3 + 98^3 far far exceeds 1,000,000 and telling you, that Euler cannot Assume a FLT in exp 3 must only be two odds with one even. Euler shoddily miss the fact that he had to prove no three even numbers for x,y,z can hold true for FLT.

Now, steps into the picture Andrew Wiles around 1993 with his elliptic curves attempt at proving FLT. And Andrew is reliant, is dependent on Euler's exponent 3 proof for his elliptic curves to work. Trouble is, well, Andrew Wiles seems to have no logical brains in even spotting the fact that Euler had no proof of FLT for exponent 3. Because to prover FLT is true in exponent 3, meant, Euler had to prove not only two odds with one even cannot be a solution, but meant that all three evens could not be a solution.

Instead, Euler shoddily overlooked the fact that he had to prove x,y,z, all three evens could not solve FLT.

And Andrew Wiles, being so logically dumb in mathematics, could not even spot the shoddy fake proof of Euler.

--- Quoting Wikipedia on Euler's error ridden FLT, where he never proves in the case of x, y, z integers all three being even ---

n = 3

Leonhard Euler by Jakob Emanuel Handmann.
Fermat sent the letters in which he mentioned the case in which n = 3 in 1636, 1640 and 1657. Euler sent a letter in which he gave a proof of the case in which n = 3 to Goldbach on 4 August 1753. Euler had the complete and pure elementary proof in 1760. The case n = 3 was proven by Euler in 1770. Independent proofs were published by several other mathematicians, including Kausler, Legendre, Calzolari, Lamé, Tait, Günther, Gambioli, Krey, Rychlik, Stockhaus, Carmichael, van der Corput, Thue, and Duarte.

Chronological table of the proof of n = 3
date result/proof published/not published work name
1621 none published Latin version of Diophantus's Arithmetica Bachet
around 1630 only result not published a marginal note in Arithmetica Fermat
1636, 1640, 1657 only result published letters of n = 3 Fermat
1670 only result published a marginal note in Arithmetica Fermat's son Samuel published the Arithmetica with Fermat's note.
4 August 1753 only result published letter to Goldbach Euler
1760 proof not published complete and pure elemental proof Euler
1770 proof published incomplete but elegant proof in Elements of Algebra Euler

As Fermat did for the case n = 4, Euler used the technique of infinite descent. The proof assumes a solution (x, y, z) to the equation x^3 + y^3 + z^3 = 0, where the three non-zero integers x, y, and z are pairwise coprime and not all positive. One of the three must be even, whereas the other two are odd. Without loss of generality, z may be assumed to be even.

Since x and y are both odd, they cannot be equal. If x = y, then 2x^3 = −z^3, which implies that x is even, a contradiction.

Since x and y are both odd, their sum and difference are both even numbers

2u = x + y
2v = x − y
where the non-zero integers u and v are coprime and have different parity (one is even, the other odd). Since x = u + v and y = u − v, it follows that

−z^3 = (u + v)^3 + (u − v)^3 = 2u(u^2 + 3v^2)
Since u and v have opposite parity, u^2 + 3v^2 is always an odd number. Therefore, since z is even, u is even and v is odd. Since u and v are coprime, the greatest common divisor of 2u and u^2 + 3v^2 is either 1 (case A) or 3 (case B).

Proof for Case A
In this case, the two factors of −z^3 are coprime. This implies that three does not divide u and that the two factors are cubes of two smaller numbers, r and s

2u = r^3
u^2 + 3v^2 = s^3
Since u^2 + 3v^2 is odd, so is s. A crucial lemma shows that if s is odd and if it satisfies an equation s^3 = u^2 + 3v^2, then it can be written in terms of two coprime integers e and f

s = e^2 + 3f^2
so that

u = e ( e^2 − 9f^2)
v = 3f ( e^2 − f^2)
Since u is even and v odd, then e is even and f is odd. Since

r3 = 2u = 2e (e − 3f)(e + 3f)
The factors 2e, (e–3f ), and (e+3f ) are coprime since 3 cannot divide e: If e were divisible by 3, then 3 would divide u, violating the designation of u and v as coprime. Since the three factors on the right-hand side are coprime, they must individually equal cubes of smaller integers

−2e = k^3
e − 3f = l^3
e + 3f = m^3
which yields a smaller solution k^3 + l^3 + m^3= 0. Therefore, by the argument of infinite descent, the original solution (x, y, z) was impossible.

Proof for Case B
In this case, the greatest common divisor of 2u and u^2 + 3v^2 is 3. That implies that 3 divides u, and one may express u = 3w in terms of a smaller integer, w. Since u is divisible by 4, so is w; hence, w is also even. Since u and v are coprime, so are v and w. Therefore, neither 3 nor 4 divide v..

Substituting u by w in the equation for z^3 yields

−z^3 = 6w(9w^2 + 3v^2) = 18w(3w^2 + v^2)
Because v and w are coprime, and because 3 does not divide v, then 18w and 3w^2 + v^2 are also coprime. Therefore, since their product is a cube, they are each the cube of smaller integers, r and s

18w = r^3
3w^2 + v^2 = s^3
By the lemma above, since s is odd and its cube is equal to a number of the form 3w^2 + v^2, it too can be expressed in terms of smaller coprime numbers, e and f.

When the math history books of the future are written, Andrew Wiles will be in that history as a tiny footnote in passage. Andrew Wiles will be mentioned as to math history of how corrupt was the "business of science publication". Where managing editors of science journals could easily -- steal and hornswaggle the world public with their own fake con-artist offerings.

Andrew Wiles will not be mentioned for any math success on his part, for he had none to offer. Andrew will be mentioned as a dinosaur of science where journals of publication corrupted the true history of math progress.

AP proved FLT for the first time in math history around 1991-1993, with the simple statement-- FLT is true because the Pythagorean Theorem is true due to a fantastic numbers 2 and 4 where 2+2= 4 and where 2x2=4, allowing for solutions to x^2 + y^2 = z^2. If no number exists with the property of 2 and 4, then the world would not have a Pythagorean Theorem. Likewise, if the world had a special number of N+N+N= M and where NxNxN= M, then the world would have solutions to x^3 + y^3 = z^3. Same goes for exponent 4 and higher.

AP's proof in 1991-1993 is easily generalized to proving the Generalized Fermat's Last Theorem of a^x + b^y = c^z.

Andrew Wiles was so dumb in mathematics, he could not spot the error of Euler's incomplete proof and therefore invalid exp3 of FLT. Andrew could not spot that Euler missed proving in the case of all three integers being even, and that makes Andrew Wiles's offering using Elliptic Curves all washed down the toilet bowl, for his technique is dependent on Euler's exp3. And, also, Wiles's fake proof uses Reductio Ad Absurdum which AP wrote a book about showing that Reductio Ad Absurdum is not a deductive proof method but only probability of being true. RAA cannot be used in math for a proof. And this explains why Andrew Wiles's fake FLT could never even touch the Generalized FLT, for it was a sham from the get go.

But notice, that AP's proof of regular FLT from 2+2= 2x2 = 4 , not only proves regular FLT but proves the Generalized FLT.

The trouble with Wiles is he was a victim of history of an old corrupt way of doing mathematics reporting while the age of computers and opening up the Publication Presses of Science became available to all scientists. All scientists can openly and freely publish their work, no longer tied to having some corrupt journal to cater to.

AP
King of Science, especially Physics

Now AP is not suggesting the FBI be called in and investigate corruption of Andrew Wiles and his fake FLT proof that garnered him fame and fortune but never the truth of mathematics. No, I realize that Andrew Wiles actions and behavior were never criminal in nature, just psychological delusion of seeking fame and fortune. But these issues need investigation due to the nature of Science reporting in the future.

1) Andrew Wiles publishing his own alleged proof of FLT in a journal that he controlled as managing editor. And being a famous math problem, knowing that he would have a spotlight in math. The reasonable action would have been to have a different journal publish his offering. We see this in judicial systems were judges recuse themselves.

2) When the gap in Wiles offering was discovered and then Wiles brought on board a graduate student at Princeton, Mr. Taylor, was the gap really filled or was the Taylor on board a smokescreen to push the fakery on down the line.

3) The installing of Simon Singh, not a mathematician himself, to wrote a flowery book on Wiles fakery. Was there money or favors passed between Singh and Wiles? Did Wiles write a text for Singh to be the crux of Singh's flowery praise of Wiles?

4) The knighthood of Andrew Wiles, for if he so easily can pull the wool over the eyes of mathematicians, would be a cinch to have him knighted by the general public who is lucky to not make mistakes in sums or percentage, let alone a proof of mathematics. So how does Andrew hornswaggle a knighthood from a fake math proof, so fast and so easily.

5) To look into how Andrew Wiles was able to convince NOVA science tv shows to do a 1 hour praise praise praise when probably no-one in the NOVA production team even knows what Fermat's Last Theorem was. So if anyone wants to call Wiles a genius, he should be called a genius of manipulation for a math fakery that bowls almost the entire Earth's math community and then the general public. And yet, Andrew Wiles could never spot the flaw in Euler's fake FLT for exponent 3, on top of that, Andrew Wiles was oblivious to math's most worrisome and deeply rooted most important problem in all of mathematics-- a geometry proof of the Fundamental Theorem of Calculus. It is as if moron Andrew Wiles never realized that calculus was geometry, and hence-- the most important problem of math was deliver a geometry proof of Fundamental Theorem of Calculus.

AP
King of Science, especially Physics

"Are you the same Archimedes Plutonium being mentioned on this old blog post?:

https://freethoughtblogs.com/pharyngula/2013/01/31/where-have-all-the-usenet-kooks-gone/

If so, then wow! You've basically wasted your life in a sense.

I suppose in another sense the stamina is quite impressive and you might get logged in some future internet historian's notes on this kind of behaviour (is that the goal, a kind of thin residual abstract immortality?).

John Gabriel can only fantasize about earning such a historical footnote at this point. He'd be better off trying to save up for a module or two at the Open University, but you can only help people that want to be helped I guess."

Ross implores Google to have a Fair Balanced Search hits on Andrew Wiles, not that 1m-hits of gold plated praise, but a CounterPoint and Balanced hit list with this thread appearing on 1st page of Andrew Wiles Google Search.

On Saturday, May 29, 2021 at 1:28:03 PM UTC-5, ross.pro...@gmx.com wrote:
>Open University, but you can only help people that want to be helped I guess."

AP's 6th published book WORLD's FIRST VALID PROOF OF FERMAT's LAST THEOREM, and exposing the shoddy fake proof of Euler in exp3 and the con-artist fake Wiles offering. AP is revisiting and revising his World's First Valid Proof of Fermat's Last
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1-AP's 6th published book WORLD's FIRST VALID PROOF OF FERMAT's LAST THEOREM, and exposing the shoddy fake proof of Euler in exp3 and the con-artist fake Wiles offering.

AP is revisiting and revising his World's First Valid Proof of Fermat's Last Theorem and giving a detailed account of the fake and con-artist offering by Andrew Wiles. Andrew Wiles cheated AP of the prizes awarded for the proof of Fermat's Last Theorem. And this was a huge huge problem of science journalism publishing. Those that had access to publishing had a dreadful tendency of cheating scientists who had no direct access to publishing. So that Andrew Wiles achieved fame for FLT not on merits of truth, but only because he controlled as editor of a math journal out of Princeton Univ. All that AP had was Usenet, sci.math and sci.physics and other newsgroups. The old old way of doing science with publication became fraught with cheating and error and outright stealing of scientists working in the field without that access to publication.

And it was about 1993, when the Usenet and Internet started to Free the World, Give Liberty to scientists in the Field, who had no direct access to publishing and were prone to being stolen from and cheated of their work.

6th published book

World's First Valid Proofs of Fermat's Last Theorem, 1993 & 2014 // Math proof series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 29Apr2021. This is AP's 6th published book.

Preface:
Real proofs of Fermat's Last Theorem// including the fake Euler proof in exp3 and Wiles fake proof.

Recap summary: In 1993 I proved Fermat's Last Theorem with a pure algebra proof, arguing that because of the special number 4 where 2 + 2 = 2^2 = 2*2 = 4 that this special feature of a unique number 4, allows for there to exist solutions to A^2 + B^2 = C^2. That the number 4 is a basis vector allowing more solutions to exist in exponent 2. But since there is no number with N+N+N = N*N*N that exists, there cannot be a solution in exp3 and the same argument for higher exponents. In 2014, I went and proved Generalized FLT by using "condensed rectangles". Once I had proven Generalized, then Regular FLT comes out of that proof as a simple corollary. So I had two proofs of Regular FLT, pure algebra and a corollary from Generalized FLT. Then recently in 2019, I sought to find a pure algebra proof of Generalized FLT, and I believe I accomplished that also by showing solutions to Generalized FLT also come from the special number 4 where 2 + 2 = 2^2 = 2*2 = 4. Amazing how so much math comes from the specialness of 4, where I argue that a Vector Space of multiplication provides the Generalized FLT of A^x + B^y = C^z.

Cover Picture: In my own handwriting, some Generalized Fermat's Last Theorem type of equations.

As for the Euler exponent 3 invalid proof and the Wiles invalid FLT, both are missing a proof of the case of all three A,B,C are evens (see in the text).
Length: 156 pages

File Size: 1503 KB
Print Length: 156 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PQKGW4M
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled 

Euler was shoddy with his fake Fermat's Last Theorem, FLT, Proof for exponent 3, shoddy and failed to give a proof. But Andrew Wiles is a con-artist fraud, more than just shoddy on FLT.

Euler made a mistake in his fake proof, for he assumed that x,y,z all three even numbers cannot be a solution set in FLT. As Wikipedia entry quoted below says "One of the three must be even, whereas the other two are odd."

And it is true Euler provided a proof of the case of exponent 3 provided two of x,y,z are odd and the last, even. However, that is not a proof for the entire exponent 3. Euler was shoddy in his proof for to be a mathematics proof, it has to be complete. And what Euler missed was the case in which all three x,y,z are even numbers.

Now we can see this important missed case of Euler by just running through a few numbers.

So we have

2^3 = 8 and 4^3 = 64 and we have 8 + 8 =/= 64 but far from it.
6^3 = 216, and we have 64 + 64 =/= 216, but we are narrowing the gap.

So let us jump out to 100^3 and 98^3 and we have
98^3 = 941,192
100^3 = 1,000,000
And instantly you can see and recognize that 98^3 + 98^3 far far exceeds 1,000,000 and telling you, that Euler cannot Assume a FLT in exp 3 must only be two odds with one even. Euler shoddily miss the fact that he had to prove no three even numbers for x,y,z can hold true for FLT.

Now, steps into the picture Andrew Wiles around 1993 with his elliptic curves attempt at proving FLT. And Andrew is reliant, is dependent on Euler's exponent 3 proof for his elliptic curves to work. Trouble is, well, Andrew Wiles seems to have no logical brains in even spotting the fact that Euler had no proof of FLT for exponent 3. Because to prove FLT is true in exponent 3, meant, Euler had to prove not only two odds with one even cannot be a solution, but meant that all three evens could not be a solution.

Instead, Euler shoddily overlooked the fact that he had to prove x,y,z, all three evens could not solve FLT.

And Andrew Wiles, being so logically dumb in mathematics, could not even spot the shoddy fake proof of Euler.

--- Quoting Wikipedia on Euler's error ridden FLT, where he never proves in the case of x, y, z integers all three being even ---

n = 3

Leonhard Euler by Jakob Emanuel Handmann.
Fermat sent the letters in which he mentioned the case in which n = 3 in 1636, 1640 and 1657. Euler sent a letter in which he gave a proof of the case in which n = 3 to Goldbach on 4 August 1753. Euler had the complete and pure elementary proof in 1760. The case n = 3 was proven by Euler in 1770. Independent proofs were published by several other mathematicians, including Kausler, Legendre, Calzolari, Lamé, Tait, Günther, Gambioli, Krey, Rychlik, Stockhaus, Carmichael, van der Corput, Thue, and Duarte.

Chronological table of the proof of n = 3
date result/proof published/not published work name
1621 none published Latin version of Diophantus's Arithmetica Bachet
around 1630 only result not published a marginal note in Arithmetica Fermat
1636, 1640, 1657 only result published letters of n = 3 Fermat
1670 only result published a marginal note in Arithmetica Fermat's son Samuel published the Arithmetica with Fermat's note.
4 August 1753 only result published letter to Goldbach Euler
1760 proof not published complete and pure elemental proof Euler
1770 proof published incomplete but elegant proof in Elements of Algebra Euler

As Fermat did for the case n = 4, Euler used the technique of infinite descent. The proof assumes a solution (x, y, z) to the equation x^3 + y^3 + z^3 = 0, where the three non-zero integers x, y, and z are pairwise coprime and not all positive. One of the three must be even, whereas the other two are odd. Without loss of generality, z may be assumed to be even.

Since x and y are both odd, they cannot be equal. If x = y, then 2x^3 = −z^3, which implies that x is even, a contradiction.

Since x and y are both odd, their sum and difference are both even numbers

2u = x + y
2v = x − y
where the non-zero integers u and v are coprime and have different parity (one is even, the other odd). Since x = u + v and y = u − v, it follows that

−z^3 = (u + v)^3 + (u − v)^3 = 2u(u^2 + 3v^2)
Since u and v have opposite parity, u^2 + 3v^2 is always an odd number. Therefore, since z is even, u is even and v is odd. Since u and v are coprime, the greatest common divisor of 2u and u^2 + 3v^2 is either 1 (case A) or 3 (case B).

Proof for Case A
In this case, the two factors of −z^3 are coprime. This implies that three does not divide u and that the two factors are cubes of two smaller numbers, r and s

2u = r^3
u^2 + 3v^2 = s^3
Since u^2 + 3v^2 is odd, so is s. A crucial lemma shows that if s is odd and if it satisfies an equation s^3 = u^2 + 3v^2, then it can be written in terms of two coprime integers e and f

s = e^2 + 3f^2
so that

u = e ( e^2 − 9f^2)
v = 3f ( e^2 − f^2)
Since u is even and v odd, then e is even and f is odd. Since

r3 = 2u = 2e (e − 3f)(e + 3f)
The factors 2e, (e–3f ), and (e+3f ) are coprime since 3 cannot divide e: If e were divisible by 3, then 3 would divide u, violating the designation of u and v as coprime. Since the three factors on the right-hand side are coprime, they must individually equal cubes of smaller integers

−2e = k^3
e − 3f = l^3
e + 3f = m^3
which yields a smaller solution k^3 + l^3 + m^3= 0. Therefore, by the argument of infinite descent, the original solution (x, y, z) was impossible.