• Re: Riemann Hypothesis in TEACHING TRUE MATH PROOFS by Archimedes Pluto

    From Archimedes Plutonium@21:1/5 to All on Mon Sep 18 23:42:37 2023
    I am going to use Wikipedia's Statement of the Riemann Hypothesis ---

    --- quoting Wikipedia on RH ---
    In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
    1
    /
    2
    . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is
    named.

    The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics
    Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.

    --- end quoting Wikipedia on the statement to be proved of RH --
  • From Archimedes Plutonium@21:1/5 to All on Tue Sep 19 00:02:15 2023
    #12-1, My 3rd published book

    AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into
    the Cylinder is in fact a ellipse, but never in a cone.

    Product details
    • ASIN ‏ : ‎ B07PLSDQWC
    • Publication date ‏ : ‎ March 11, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1621 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 20 pages
    • Lending ‏ : ‎ Enabled



    Proofs Ellipse is never a Conic section, always a Cylinder section and a Well Defined Oval definition//Student teaches professor series, book 5 Kindle Edition
    by Archimedes Plutonium (Author)

    Last revision was 14May2022. This is AP's 68th published book of science.

    Preface: A similar book on single cone cut is a oval, never a ellipse was published in 11Mar2019 as AP's 3rd published book, but Amazon Kindle converted it to pdf file, and since then, I was never able to edit this pdf file, and decided rather than
    struggle and waste time, decided to leave it frozen as is in pdf format. Any new news or edition of ellipse is never a conic in single cone is now done in this book. The last thing a scientist wants to do is wade and waddle through format, when all a
    scientist ever wants to do is science itself. So all my new news and thoughts of Conic Sections is carried out in this 68th book of AP. And believe you me, I have plenty of new news.

    In the course of 2019 through 2022, I have had to explain this proof often on Usenet, sci.math and sci.physics. And one thing that constant explaining does for a mind of science, is reduce the proof to its stripped down minimum format, to bare bones
    skeleton proof. I can prove the slant cut in single cone is a Oval, never the ellipse in just a one sentence proof. Proof-- A single cone and oval have just one axis of symmetry, while a ellipse requires 2 axes of symmetry, hence slant cut is always a
    oval, never the ellipse.

    Product details
    • ASIN ‏ : ‎ B081TWQ1G6
    • Publication date ‏ : ‎ November 21, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 827 KB
    • Simultaneous device usage ‏ : ‎ Unlimited
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 51 pages
    • Lending ‏ : ‎ Enabled

    #12-2, My 11th published book

    World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
    by Archimedes Plutonium (Author)

    Last revision was 15Dec2021. This is AP's 11th published book of science. Preface:
    Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not
    being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

    Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". And very surprising that most
    math professors cannot tell the difference between a "proving something" and that of "analyzing something". As if an analysis is the same as a proof. We often analyze various things each and every day, but few if none of us consider a analysis as a proof.
    Yet that is what happened in the science of mathematics where they took an analysis and elevated it to the stature of being a proof, when it was never a proof.

    To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC
    geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry
    proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow
    us to give a Geometry proof of the FTC?

    Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.


    Product details
    ASIN ‏ : ‎ B07PQTNHMY
    Publication date ‏ : ‎ March 14, 2019
    Language ‏ : ‎ English
    File size ‏ : ‎ 1309 KB
    Text-to-Speech ‏ : ‎ Enabled
    Screen Reader ‏ : ‎ Supported
    Enhanced typesetting ‏ : ‎ Enabled
    X-Ray ‏ : ‎ Not Enabled
    Word Wise ‏ : ‎ Not Enabled
    Print length ‏ : ‎ 154 pages
    Lending ‏ : ‎ Enabled
    Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
    #2 in 45-Minute Science & Math Short Reads
    #134 in Calculus (Books)
    #20 in Calculus (Kindle Store)


    #12-3, My 24th published book


    World's First Proof of Kepler Packing Problem KPP // Math proof series, book 3 by Archimedes Plutonium (Author) (Amazon's Kindle)

    There has been a alleged proof of KPP by Thomas Hales, but his is a fakery because he does not define what infinity actually means, for it means a borderline between finite and infinite numbers. Thus, KPP was never going to be proven until a well-defined
    infinity borderline was addressed within the proof. And because infinity has a borderline means that in free space with no borderlines to tackle and contend with, the 12 kissing point density that is the hexagonal close packed is the maximum density. But
    the truth and reality of Kepler Packing is asking for maximum packing out to infinity. That means you have to contend and fight with the packing of identical spheres up against a wall or border. And so, in tackling that wall, we can shift the hexagonal
    closed pack to another type of packing, a hybrid type of packing in order to get "maximum packing". So no proof ever of KPP is going to happen unless the proof tackles a infinity border wall. In free-space, a far distance away from a wall barrier of
    infinity border, then, hexagonal closed pack reigns and is the packing in all of free space-- but, the moment the packing gets nearby the walls of infinity border, then, we re-arrange the hexagonal closed pack to fit in more spheres. Not unlike us
    packing a suitcase and then rearranging to fit in more.

    Cover picture: is a container and so the closed packing must be modified once the border is nearly reached to maximize the number of spheres.

    Product details
    • ASIN ‏ : ‎ B07NMV8NQQ
    • Publication date ‏ : ‎ March 20, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1241 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 60 pages
    • Lending ‏ : ‎ Enabled

    #12-4, My 28th published book

    World's First Valid Proof of 4 Color Mapping Problem// Math proof series, book 4
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Now in the math literature it is alleged that Appel & Haken proved this conjecture that 4 colors are sufficient to color all planar maps such that no two adjacent countries have the same color. Appel & Haken's fake proof was a computer proof and it is
    fake because their method is Indirect Nonexistence method. Unfortunately in the time of Appel & Haken few in mathematics had a firm grip on true Logic, where they did not even know that Boole's logic is fakery with his 3 OR 2 = 5 with 3 AND 2 = 1, when
    even the local village idiot knows that 3 AND 2 = 5 with 3 OR 2 = either 3 or 2 depending on which is subtracted. But the grave error in logic of Appel & Haken is their use of a utterly fake method of proof-- indirect nonexistence (see my textbook on
    Reductio Ad Absurdum). Wiles with his alleged proof of Fermat's Last Theorem is another indirect nonexistence as well as Hales's fake proof of Kepler Packing is indirect nonexistence.
    Appel & Haken were in a time period when computers used in mathematics was a novelty, and instead of focusing on whether their proof was sound, everyone was dazzled not with the logic argument but the fact of using computers to generate a proof. And of
    course big big money was attached to this event and so, math is stuck with a fake proof of 4-Color-Mapping. And so, AP starting in around 1993, eventually gives the World's first valid proof of 4-Color-Mapping. Sorry, no computer fanfare, but just strict
    logical and sound argument.

    Cover picture: Shows four countries colored yellow, red, green, purple and all four are mutually adjacent. And where the Purple colored country is landlocked, so that if it were considered that a 5th color is needed, that 5th color should be purple,
    hence, 4 colors are sufficient.

    Product details
    ASIN ‏ : ‎ B07PZ2Y5RV
    Publication date ‏ : ‎ March 23, 2019
    Language ‏ : ‎ English
    File size ‏ : ‎ 1183 KB
    Text-to-Speech ‏ : ‎ Enabled
    Screen Reader ‏ : ‎ Supported
    Enhanced typesetting ‏ : ‎ Enabled
    X-Ray ‏ : ‎ Not Enabled
    Word Wise ‏ : ‎ Not Enabled
    Print length ‏ : ‎ 34 pages
    Lending ‏ : ‎ Enabled




    #12-5, My 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) (Amazon's Kindle)

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

    Preface: Truthful 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).

    Product details
    • ASIN ‏ : ‎ B07PQKGW4M
    • Publication date ‏ : ‎ March 12, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1503 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 156 pages
    • Best Sellers Rank: #4,327,817 in Kindle Store (See Top 100 in Kindle Store)
    ◦ #589 in Number Theory (Kindle Store)
    ◦ #3,085 in Number Theory (Books)


    #12-6, 19th published book

    World's First Proof of Collatz Conjecture// Math proof series, book 6
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was 14May2022. This is AP's 19th published book.

    Preface: Old Math's Collatz conjecture, 1937, was this: If you land on an even number, you divide by 2 until you come to an odd number. If you come to or land on an odd number, you do a 3N+1 then proceed further. The conjecture then says that no matter
    what number you start with, it ends up being 1.

    What the Collatz proof of math tells us, is that so very often mathematicians pose a conjecture in which their initial formulation of the conjecture is murky, obfuscation and poorly designed statement. Such poorly designed statements can never be proven
    true or false. An example that comes to mind of another poorly designed conjecture is the No Odd Perfect Conjecture, in which the statement is obfuscation of factors. So for the odd number 9, is it 1+3, or is it 1+ 3 + 3. So when a mathematics conjecture
    is full of obfuscation and error in the statement, then these type of conjectures never have a proof. And takes a person with a logical mind to fix and straighten out the conjecture statement and then provide a proof, thereof.

    A return to my Collatz proof in 2022, allowed me a second proof of Collatz with only 3N+1, in a mathematical induction proof, using the Decimal Grid System of Numbers. The true numbers of mathematics are the Decimal Grid System Numbers and this allows a
    Collatz proof of stand alone 3N+1.

    Cover picture: when I think of Collatz, I think of a slide, a slide down and so my French curve is the best slide I can think of, other than a slide-ruler, but a slide ruler is slide across.


    Product details
    • ASIN ‏ : ‎ B07PS98K5H
    • Publication date ‏ : ‎ March 16, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1990 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 113 pages
    • Lending ‏ : ‎ Enabled
    • Best Sellers Rank: #212,131 in Kindle Store (See Top 100 in Kindle Store)
    ◦ #4 in 45-Minute Science & Math Short Reads
    ◦ #9 in Number Theory (Kindle Store)
    ◦ #32 in Number Theory (Books)




    #12-7, My 20th published book
    World's First Proofs that No Perfect Cuboid Exists// Math proof series, book 7 by Archimedes Plutonium (Author) (Amazon's Kindle)

    Someone on the Internet posed the unproven No Perfect Cuboid, and so I took up the challenge. I am usually a sucker for geometry riddles, more so than number theory. So I obliged. Then by 2014 I proved the matter and looking back at it now in 2019, I
    really really do not see what all the fuss was about-- that it was not that hard not hard at all. You just have to look carefully at sets of 4 right triangles and find an Impossibility Construction, why you cannot have those 4 right triangles all with
    positive integer numbers for their 3 sides. But the proof method is so hugely important in math-- impossibility of construction. And, please, do not confuse that method with Reductio Ad Absurdum, for RAA is not a valid proof method in mathematics (see my
    logic book on RAA). But, the method of Impossible Construction, although it might look like RAA, is totally different and fully valid in all aspects.

    But now, in hindsight in March 2019, writing this up, I see a very close connection of No Perfect Cuboid to that of Generalized Fermat's Last Theorem with its equation of A^x + B^y = C^z and the way I proved Generalized FLT was with "condensed rectangles"
    and the No Perfect Cuboid is a 3rd Dimension object but it is 4 rectangles of 4 right triangles we inspect. And we can pursue that connection between Generalized FLT and No Perfect Cuboid further, but not now.

    Cover Picture: Is that of 4 rectangular boxes, 2 of which are cubes sitting atop a book page of the Cubic Set for the Transuranium Atoms, from the textbook "The Elements Beyond Uranium" , Seaborg, Loveland, 1990. I am always looking for connections.


    Product details
    • ASIN ‏ : ‎ B07PMZQNNT
    • Publication date ‏ : ‎ March 16, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1382 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 61 pages
    • Lending ‏ : ‎ Enabled







    #12-8, My 21st published book

    World's First Proofs of Mathematics Oldest Unsolved Problems: No Odd Perfect and Finiteness of Perfect Numbers // Math proof series, book 8
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was 26Apr2021. And this is AP's 21st published book.

    Preface: Now my history with these proofs goes back to 1991 to 1993, and have been finessing the proofs ever since. Some math proofs just nag nag and nag you. They just cannot be settled still. Their proof is a tiny tiny sliver of impossibility that is
    easily overlooked. Like an optical illusion that you are mislead into, or like those pictures where you look at it one way and you see a young lady and another way you see a very old lady.

    Now the No Odd Perfect Number is not a important proof in mathematics but mostly a spectacle for it does not teach much beyond making proper correct definitions. And murky definitions is what held a proof of No Odd Perfect, other than 1, held it back.
    The murky definition of factors, do we include 1 or not include, for example the odd number 9, do we include 3 twice or once for that we have 1* 9 and we have 3*3 and Old Math looked at that as 1 + 3, whereas I would look at that as 1 + 3 + 3. So when
    you have messy definitions, murky and messy, of course no proof will be found in over 2,000 years.

    Cover Picture: Shows our modern day new reality of the situation where the definition of "perfect" was a Ancient Greek idea, steeped in murky messy idea of factors and when to add factors, that no longer is suitable for mathematics.

    Product details
    • ASIN ‏ : ‎ B07PN1CPRP
    • Publication date ‏ : ‎ March 16, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1534 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 28 pages
    • Lending ‏ : ‎ Enabled


    #12-9, My 15th published book

    World's First Proofs of Infinitude of Twin-Primes, and Polignac Proved // Math proof series, book 9
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was September 2023. And this is AP's 15th published book of science.

    Preface: Much has changed in the general ideas of Logical Math Proofs, since 1991, when I first wrote a proof of Infinitude of Twin Primes. And by 2023, as I revise this book, I need to incorporate those changes. Even my outlook on what Primes are in
    mathematics, as a vague and incoherent set.
    Many in math would be surprised to hear me say that Primes of mathematics is a vague incoherent set. But from 1991 when I first penned a Old Math proof of Infinitude of Twin Primes, so much has changed about what is a valid math proof and what are these
    curious numbers we call Primes. This book is my history of my encounter and battling of a very old conjecture-- the infinitude of twin primes.

    Cover Picture: Is a picture of the first five twin-primes.

    Product details
    ASIN ‏ : ‎ B07PMY1YWB
    Publication date ‏ : ‎ March 15, 2019
    Language ‏ : ‎ English
    File size ‏ : ‎ 1664 KB
    Text-to-Speech ‏ : ‎ Enabled
    Screen Reader ‏ : ‎ Supported
    Enhanced typesetting ‏ : ‎ Enabled
    X-Ray ‏ : ‎ Not Enabled
    Word Wise ‏ : ‎ Not Enabled
    Sticky notes ‏ : ‎ On Kindle Scribe
    Print length ‏ : ‎ 38 pages



    #12-10, 16th published book

    World's First Proofs of Goldbach, Legendre, Staircase Conjectures// Math proof series, book 10
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was September 2023. And this is AP's 16th published book of science.

    Preface: AP proved the Goldbach Conjecture starting 1993 where the Algebra Columns is the bedrock-key of the proof involved. The Algebra Column Array is the tool and no-one was going to prove Goldbach unless they had that tool, which the 2014 post of
    mine makes the array tool crystal clear. So starting 1993, I posted to sci.math about Array or Algebra Column which as a tool would render all proofs of this nature. The Goldbach conjecture historically dates back to 1742, and the Legendre conjecture
    dates 1752-1833. The Staircase conjecture is a wholly new conjecture proposed by AP circa 2016.

    Cover: Is an Algebra Column Array sequence starting with 6 Array and then 8 Array.


    Product details
    • ASIN ‏ : ‎ B07PS6MR48
    • Publication date ‏ : ‎ March 15, 2019
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1743 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 44 pages
    • Lending ‏ : ‎ Enabled
    Amazon Best Sellers Rank: #148,852 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
    #4 in Number Theory (Kindle Store)
    #38 in Number Theory (Books)
    #7 in One-Hour Science & Math Short Reads


    #12-11, My 25th published book.

    Disproof of Riemann Hypothesis // Math proof series, book 11
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was 31Oct2021. This is AP's 25th book of science.

    Preface: The Riemann Hypothesis was a conjecture never able to be proven and for good reason, for it was the last symptom of a rampant disease inside of mathematics. Old Math did not have the true numbers that compose mathematics. Old Math had a rag-tag
    ugly collection of fake numbers with their Reals, their Negative numbers compounded with Rationals compounded with Irrationals and then adding on the Imaginary. These are fake numbers, when the true numbers of mathematics are the Decimal Grid Numbers.
    Because Old Math uses fake numbers, is the reason that Riemann Hypothesis just languished, languished and languished. You cannot prove something riddled in fakery. Below I demonstrate why having fake numbers in math, creates fake proofs, fake theorems,
    and creates a conjecture that can never be proven.

    Cover picture: Riemann Hypothesis deals with fake numbers of mathematics. When what is needed is the true numbers-- Decimal Grid Numbers. We learn Decimal Grid Numbers when very young, when just toddlers, wood counting blocks. All the true numbers of
    mathematics come from Mathematical Induction-- counting. Mathematical Induction is utterly absent in the Riemann Hypothesis, when it should be central to the hypothesis.


    Product details
    ASIN ‏ : ‎ B07PVDS1RC
    Publication date ‏ : ‎ March 20, 2019
    Language ‏ : ‎ English
    File size ‏ : ‎ 1475 KB
    Text-to-Speech ‏ : ‎ Enabled
    Screen Reader ‏ : ‎ Supported
    Enhanced typesetting ‏ : ‎ Enabled
    X-Ray ‏ : ‎ Not Enabled
    Word Wise ‏ : ‎ Not Enabled
    Print length ‏ : ‎ 58 pages
    Lending ‏ : ‎ Enabled
    Best Sellers Rank: #5,118,638 in Kindle Store (See Top 100 in Kindle Store)
    ◦ #643 in Number Theory (Kindle Store)
    ◦ #1,398 in One-Hour Science & Math Short Reads
    ◦ #3,559 in Number Theory (Books)

    #12-12, My 152nd published book.
    The 6th Regular Polyhedron-- hexagonal faces at infinity is nonexistent // Math proof series, book 12
    by Archimedes Plutonium (Author) (Amazon's Kindle)

    Last revision was 2Aug2022. And this is AP's 152nd published book of science.

    Preface: I started this book in September 2021, and not until July 2022, did I uncover my gross error-- the nonexistence of the 6th Regular Polyhedron. I so much wanted there to be a 6th regular polyhedron and looking in the Internet, the world wide web,
    are many images of a cell of 7 regular hexagons, a central hexagon surrounded by 6 more regular hexagons tiling a sphere surface. Plenty of these images, but the tipping point for me is the Goldberg polyhedron, here again the cell of 7 regular hexagons
    tiling a sphere surface. And so, using that 7 cell as supporting evidence of the existence of a 6th Regular Polyhedron, AP proceeds to publish such. Even though I knew of the University of Utah beware caution web page stating that a vertex of 3 regular
    polygons is an angle of 120 +120+120= 360 degrees and thus laying flat as a plane, no bending, hence no tiling a sphere.

    So I published this book in Sept2021, and not until July2022, needing a coordinate system of points on a sphere for my Ecology book "_Complete Ecology_ with Generalized Faraday Law and revised food chain // Ecology science". That I finally realize my
    mistake-- Uof U completely correct, and why on Earth did I want to believe Goldberg polyhedron and all those fake geometry images of regular hexagons tiling a sphere surface. This is a massive computer problem of our times, in that it is super easy to
    make optical illusions in geometry and filling web sites with fake geometry images.

    Well, AP was fooled and fell victim to computer graphics showing where a sphere surface tiling of a central regular hexagon and surrounded by 6 more regular hexagons. There are many pictures and images of a sphere tiling on the Internet of 7 regular
    hexagons, a central one and surrounded and encircled by 6 more regular hexagons. There is even geometry of what is called Goldberg polyhedron with more pictures and images, all deceptive, all wrong. So this book ends up about the theme of how deceptive
    computer imaging can be, and not what AP hoped for-- the existence of a regular polyhedra with regular hexagon faces.

    If it were true that a cell of 7 regular polygons has a bend to it, so that it can eventually circle around a sphere surface, then my first publication of this book would have been true. But instead, the truth is the nonexistence of the 6th Regular
    Polyhedron.


    Cover Picture: is my iphone photograph of a soccer ball of 20 hexagons, 12 pentagons; and a glass ball covered by netting of tiny hexagons. Both objects I use in experiments of trying to prove the 6th Regular Polyhedron only it is nonexistent as I
    eventually found in July 2022.



    Product details
    • ASIN ‏ : ‎ B09K4PWKVK
    • Publication date ‏ : ‎ October 21, 2021
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 853 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Enabled
    • Print length ‏ : ‎ 91 pages




    #12-13, My 207th published book.

    Building the Axioms of Mathematics, thereby the Rational Numbers are proven fake// Math proofs

    by Archimedes Plutonium (Author) (Kindle edition)

    Preface: In this, my 207th published book of science, I detail what the first three axioms (postulates) of mathematics Algebra-Numbers must be. And by doing so, I discover that Time is an essential ingredient in mathematics for the first axiom of Algebra-
    Numbers is the creation of Counting Numbers which is not a concept of quantity but a concept of Ordered Sequence, which is Time. And Time-- an Ordered-Sequence comes way before Quantity. Of course, in this book I prove the Rationals of Old Math are fake
    numbers,--- what I mean by fake, is that they are not primal numbers but derivations, derivates of primal numbers -- the Decimal Grid Numbers. Old Math Rationals are simply a division exercise unfinished by a lazy person. And since Rationals are fake
    numbers, secondary numbers means the Reals of Old Math are fake numbers since the Reals are built from Rationals. 

    I have written a remarkable book here. I started out with the intent of proving that Rational Numbers were not the true numbers of mathematics, but a unfinished division exercise, by lazy persons doing math. A proof came in my work. But what I discovered
    that is so remarkable, is that the Axioms of Numbers require a Order Sequence first, and only secondly does Quantity pop-out and enter the picture. This Order-Sequence is of course Time in physics.

    Cover Picture: My iphone photograph of a Google search hits on "Euclid postulates axioms".



    Product details
    • ASIN ‏ : ‎ B0BGH88WFT
    • Publication date ‏ : ‎ September 25, 2022
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 563 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
    • Word Wise ‏ : ‎ Not Enabled
    • Print length ‏ : ‎ 34 pages
    • Lending ‏ : ‎ Enabled



    #12-14, My 160th published book.

    MATHOPEDIA-- List of 82 fakes and mistakes of Old Math// mathematics & logic by Archimedes Plutonium (Author) (Amazon's Kindle)

    Preface:
    A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.

    The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.

    The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery.
    I know because I have been there.

    Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.

    I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream".
    Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future
    generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see
    AP's book of logic on Pragmatism).

    Product details
    • ASIN ‏ : ‎ B09MZTLRL5 and ASIN ‏ : ‎ B09ZWFLKHC
    • Publication date ‏ : ‎ December 2, 2021
    • Language ‏ : ‎ English
    • File size ‏ : ‎ 1155 KB
    • Text-to-Speech ‏ : ‎ Enabled
    • Screen Reader ‏ : ‎ Supported
    • Enhanced typesetting ‏ : ‎ Enabled
    • X-Ray ‏ : ‎ Not Enabled
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    • Print length ‏ : ‎ 70 pages
    • Lending ‏ : ‎ Enabled






    y  z
    |  /
    | /
    |/______ x

    Read my recent posts in peace and quiet. https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe   Archimedes Plutonium

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  • From Archimedes Plutonium@21:1/5 to Archimedes Plutonium on Tue Sep 19 00:31:16 2023
    On Tuesday, September 19, 2023 at 1:42:43 AM UTC-5, Archimedes Plutonium wrote:
    I am going to use Wikipedia's Statement of the Riemann Hypothesis ---

    --- quoting Wikipedia on RH ---
    In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
    1
    /
    2
    . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is
    named.


    So in my history of the Riemann Hypothesis disproof, by 2013 I realize the true numbers of mathematics are not the Reals+Complex but that these are fake numbers with their continuum aspect. No calculus can exist in a world of continuums. Calculus needs
    empty space from one number to the next in order to even have a calculus.

    And so, when someone builds a system of science on that of fake elements, it is only a matter of time that someone comes up with a conjecture or hypothesis on that system for which there can never be a proof. Never a proof because the numbers are fakery
    in the first place.

    There is no Riemann Hypothesis when the true numbers of mathematics are Decimal Grid Numbers.

    But after 2013, I discovered something else, not as potent as Reals are fake numbers but potent enough. And it goes to show how much the concept of Primes in Old Math had lead many many astray.

    For the concept of Primes is a division operation upon Counting Numbers. Numbers in mathematics are well defined, yes Well-Defined, if when doing a operation on two numbers, the result returns you a number that is in the starting given set. Addition and
    Multiplication are Well defined over Counting Numbers. Hand me any two counting numbers and I add them. They return me another Counting Number. Same goes for Multiplication.

    However, hand me any two counting numbers and I divide one into the other. Sometimes they return me a Counting Number but often they do not. 10/5 is a counting number 2, but 5/10 is not a counting number.

    Counting Numbers are ill-defined, yes ill defined over division and subtraction. This is why Primes never have a pattern, because they are ill-defined on division. But kooks of math love primes, never figuring out why they have no pattern no formula.
    They see primes as a mystery to solve, not understanding they are delusional. It is like talking about witches flying on broomsticks in physics class where they laugh you out of the class as a waste of time.

    Mathematics wasted its time on Primes, as fake numbers that do not exist. For math is about Pattern, and primes have no pattern, and how could they for they are ill-defined over division. What if I asked you what is the set of bad numbers? Or the set of
    green numbers? Or the set of sexy numbers? These are more ill-defined sets.

    So the motivation of a Riemann Hypothesis and its link to Primes of Old Math caused the RH to be far far over hyped, when in truth, RH was a stupid false conjecture.

    Ask yourself in chemistry, is there a concept of primes emerging in the chemical elements? Is lithium element 3 have a quality characteristic of primeness that fluorine element 9 does not have? Or nitrogen 7 compared to phosphorus 15, can we see a
    primeness in nitrogen but not phosphorus? Ask the same question in physics is there a concept of prime as compared to composite in physics? No, never was.

    So prime concept in math became a kook corner for delusional kooks to play around in.

    The Riemann Hypothesis was a kook conjecture as a result of the building of mathematics from fake numbers, not the true numbers of mathematics.

    AP, King of Science

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  • From Archimedes Plutonium@21:1/5 to All on Tue Sep 19 10:31:53 2023
    On Tuesday, September 19, 2023 at 2:31:22 AM UTC-5, sci.math wrote:
    On Tuesday, September 19, 2023 at 1:42:43 AM UTC-5, Archimedes Plutonium wrote:
    I am going to use Wikipedia's Statement of the Riemann Hypothesis ---

    --- quoting Wikipedia on RH ---
    In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
    1
    /
    2
    . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it
    is named.


    In my 1991 proofs of Riemann Hypothesis, I used a different statement, the Moebius function equivalent to the RH statement. Funny how Wikipedia entry of the RH talks long, but fails to include the equivalent statement of RH, the Moebius function. In 1991,
    when I set myself to the task of proving 10 of the worst conjectures in math, one of the very first things I would do, is list any equivalent statement of the conjecture I was trying to prove. To find the one statement that was the best statement for me
    to start on. Usually I was looking for a geometrical equivalent statement, for my strongest suit in mathematics is geometry, not algebra.

    A geometrical proof follows: It was proved 
    that the Riemann hypothesis is equivalent to the 
    following: the Moebius function mu of x, m(x), and 
    adding-up the values of m(x) for all n less than or 
    equal to N giving M(N). That M(N) grows no faster than 
    a constant multiple k of N^1/2N^e as N goes to infinity 
    (e is arbitrary but greater than 0). Figure1, by 
    setting-up a logarithmic spiral in a rectangle of 
    whirling squares where the squares are the sequences:  1,1,2,3,5,8,13,21,34,55,89, . . . 2,2,4,6,10,16,26, . . . 
    3,3,6,9,15,24,39, . . . then every number appears in at 
    least one of these sequences because every number will 
    start a sequence. Since all numbers are represented 
    uniquely by prime factors (the unique prime factorization 
    theorem or called the fundamental theorem of arithmetic) 
    and The Prime Numbers Theorem: the distribution of 
    prime numbers is governed by a logarithmic function, 
    where (N/Logarithm of N). 
    It is one of the most beautiful things in all of the 
    known world, that the distribution of prime numbers is 
    governed by a logarithmic function where these two 
    mathematical concepts-- one of prime numbers, and the 
    other, logarithms seem unconnected at first appearance, 
    but in reality they are totally connected. 
    Geometrically, the logarithmic spiral exhausts every 
    positive integer, see figure 1. The area of the 
    rectangles containing the logarithmic spiral is always 
    greater, since the spiral is always inside the rectangles. 
    Thus the Moebius function k N^1/2N^e is satisfied since 
    the area of the logarithmic spiral is less than the 
    rectangle whose area represents the number N, and whose 
    sides represent its factors. The area of a logarithmic 
    spiral is represented by r=r0e^Ej , and so depending on 
    where the point of origin for the spiral is taken r0 
    determines k, and depending on the value of E, E 
    determines the e value for N, when E=0 then the 
    curve is a circle. The logarithmic spiral inside 
    rectangles of whirling squares implies that for any 
    number N then N^1/2 is the limit of the factors for N, 
    for example, given the number 28, then 28^1/2=5.2915. . 
    and so looking for the factors of 28, it is useless 
    to try beyond 5 because the factors repeat, 4X7 then 
    repeats as 7X4. But if the Moebius function was false 
    then there must exist a number M such that M^1/2 is 
    not the limit of the factors for M and the spiral is 
    outside of the square, which is impossible, hence the 
    Moebius function is true. Therefore the Riemann 
    hypothesis is proved. Q.E.D. 

    Comments in 2023, as I read the above some 2023 subtract 1991, some 32 years later, knowing the Primes are a ill-defined notion and realizing that the above was not a proof at all, but a argument in Old Math, using Old Math to its fullest extent. What is
    missing in the above is the acknowledgement that when you have the false and fake numbers of mathematics-- the Reals and Complex, a jumbled mess of wrong numbers for mathematics. That you end up with a monster of a conjecture that is unprovable, only
    because the Numbers of Mathematics are never the Reals and Complex.

    There is no Riemann Hypothesis idiocy when the true numbers of mathematics are Discrete numbers with empty space in between one number and the successor number.

    There is a very astute saying in Ancient Indian and Chinese culture-- do not paint legs on a snake. The RH of Old Math was a snake with legs painted on that snake.

    The RH of Old Math was the end extreme of where Old Math could go. They could go to the point where Primes, that horrible ill-defined set of numbers had a pattern as enunciated by the Riemann Hypothesis.

    Yet in true reality, Primes are still that obnoxious ill-defined notion with no pattern because division is not a operator on Counting Numbers. Only addition and multiplication are well defined on Counting Numbers.

    Can I blame the century of the 20th century of its burning of coal and other fossil fuel for filling the air with lead in leaded gasoline and mercury, to weaken the minds and brains of scientists and especially mathematicians to come up with a Riemann
    Hypothesis as a patterned primes??? How much can I blame mathematicians for wanted more and more and higher and higher continuity when Planck and quantum mechanics was going in the opposite direction with discrete physics. Yet math with Cohen going 180
    degrees opposite with continuum hypothesis.

    Can and should we compare the idiocy of the Continuum Hypothesis and the Riemann Hypothesis?

    Aha, AP should look into Cohen's silly adventure of continuum. Did Cohen use a Reductio Ad Absurdum for Continuum Hypothesis?? Without looking I would bet 95% that Cohen has a RAA fake proof. Without looking I bet Cohen struck up a RAA argument. And of
    course RAA is __not a valid___ proof argument.

    But back to RH, and it is a miracle, that anyone and everyone neglects the Moebius equivalent of RH. Moebius is a geometrical argument. And why is AP the only one doing a RH proof from the basis of Moebius?

    And what is the flaw in AP's above 1991 proof of Riemann Hypothesis?? The only flaw I can see is that it is a Reductio Ad Absurdum RAA argument, and those type of arguments only have a probability of being true, not a valid proof. And that is why I
    turned to a Disproof argument of RH after the year 2013 when I realized the true numbers of mathematics were Decimal Grid Numbers. There is no RH statement in a world of numbers that is Decimal Grid Numbers, and there are no prime numbers in Decimal Grid
    Numbers.

    The most important proof in the entire 20th century was not RH, but rather was the valid proof of Fundamental Theorem of Calculus. It is a geometry proof for calculus is geometry, and in order to prove FTC, you cannot have Reals and Complex as the
    numbers of mathematics.

    AP, King of Science

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  • From Archimedes Plutonium@21:1/5 to All on Tue Sep 19 22:42:30 2023
    Slowly but surely I am revising many of my math books, and about time for much has changed from the 1990s when I discovered the main engine of how they work as a proof, and the succeeding decades. In those succeeding decades I would discover the concept
    of Infinity needed a borderline to be a precise concept, no longer this loose ended dangling stupid string of "endlessness". The Huygens Tractrix is essential geometry of a figure of endless reach, but finite area, and that is the pivotal concept for a
    precision definition of infinity-- a borderline. It is a shame that Huygens is not recognized more than what current academics gives him. For Huygens is a towering genius of science, not only math but physics.

    So by 2009, I had to go back and look at my proofs done, for the concept of infinity had radically changed, especially my Kepler Packing Problem proof. Then by 2013, another huge change came in that the true numbers of mathematics were not the Reals and
    Complex with their idiotic continuity, but was the Discrete numbers of Decimal Grid Number Systems, for in Reals, you cannot get a valid proof of Fundamental Theorem of Calculus, but you easily get a valid proof of FTC using Decimal Grid Numbers. Then
    finally a third major change occurred in 2015 when I finally completed the overhaul of the Logic Connectors, the AND, the OR, the Equal/Not, and the If-->Then. Why is that overhaul so hugely important for math proofs?? It is because Reductio Ad Absurdum,
    proof by contradiction is not a valid proof method in mathematics. That is worth repeating--- Reductio Ad Absurdum is not a valid proof method in mathematics. It has to do with the truth table of If-->Then connector that a premiss starting out as False
    cannot conclude a true end result, only a probability conclusion. If the Moon is made of cheese, we cannot get a true conclusion. And this Reductio Ad Absurdum method is the most trafficked, most used method in all of mathematics proof, simply because it
    is the easiest. And the reason it is the easiest is because it is invalid. Invariably the fake proofs of mathematics in Old Math, invariably over 90% are Reductio Ad Absurdum.

    So shortly after 2015, as I overhauled Logic of its truth tables, I realized my Riemann Hypothesis proofs of 1991 and thereafter were invalid proofs because they were Reductio Ad Absurdum. And when I could find some time, I needed to revise RH and other
    proofs.

    AP

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  • From Archimedes Plutonium@21:1/5 to All on Wed Sep 20 00:54:34 2023
    The Summary of Riemann Hypothesis and its Disproof

    Those in Old Math looked upon RH as the big thing, the idol of math proofs. Their big high flying star of math. Turns out that RH was the last symptoms of a dying and dead mathematics. The RH was a conjecture which could never be proved because it used
    the fake numbers of Reals and Complex in mathematics. And that is very surprizing that everyone in math from year 1900 with Planck and his quantum mechanics and a world of physics of discreteness. Yet here in mathematics, lunatics chasing for more and
    more continuity with Reals and Complex.

    The greatest math problem and challenge from 1800s onwards was not the Riemann Hypothesis in 1859, but was calculus.

    Calculus is the highest and greatest achievement of mathematics. And surprizingly from 1800 onwards, no-one in math was inspecting the number one proof of calculus-- the Fundamental Theorem of Calculus, FTC. Oh, yes in the 1800s, Cauchy kept getting
    penetrating questions from his brightest young students-- who differed with Cauchy on how in the world the integral can go to zero width and still have interior area of the rectangles involved.

    Here was Cauchy's great opportunity to make calculus true, by looking for a geometry proof of FTC. No, instead, Cauchy went in opposite direction of cloaking and covering calculus in mud and mire and obfuscation with the dumb "limit analysis". The limit
    analysis would stop the smart students in his class for Cauchy would end up saying " Young one-- you just do not understand the limit". Limit analysis in math is a stupid silly excuse-- a cover up --- a sham. Each of us, everyday inspect and analyze 10
    or more things. I start the day with a quick analysis of what is in the refrigerator to eat on the spot. And Cauchy would think that AP proved something about my refrigerator.

    The world of mathematics was knocked off course with the silly RH in 1859 when what was to be done was a geometry proof of FTC. Calculus is the greatest math to date. And we must have Calculus tip top shape as #1 priority.

    Instead of the crazy Cohen continuum hypothesis while physics was going 180 degrees opposite in the discrete Quantum Mechanics. Remember-- "quantum" means discrete.

    So why were all the mathematicians from 1900 ignoring and sneering at physics in going discrete while they went ever more deeper in a cesspool of continuum?? I lived through math education in college 1968 onwards and I noticed from college and especially
    books written on math, that mathematicians were arrogant and looked down on physicists. That many in math thought the final thought of the Cosmos would be some math expression. And it is easy to see the hype in the 20th century of E = mc^2 predominated
    academic circles. So it is easy to see fat-heads amoung mathematicians, that they were superior elites over physicists. Turns out by 1990 onwards, that the mathematician is the inferior to the physicists. That math is a subset of physics. That physics
    dominates math. For numbers exist only because Atoms are numerous, and geometry exists only because Atoms have shape and size.

    Perhaps the answer to that vexing question of why mathematicians were arrogant and stupid in the 20th centurey may lie in the environment pollution of the 1900s, where colleges were in big cities and there was tetraethyl-lead in gasoline and there was
    fossil fuel burning releasing prodigious amounts of mercury into the air, that the brains and minds of mathematicians were laboring under a poisoned brain from lead and mercury.

    Finally by AP wanting to do a textbook series called True Calculus that omits the limit, that AP stumbles upon a geometry proof of FTC in 2013. In that geometry proof of FTC, it is clear the numbers of mathematics have to be discrete numbers not Reals +
    Complex. And this destroys Old Math Reals and Complex numbers and destroys their Riemann Hypothesis folly.

    RH was folly, not math at all.

    AP, King of Science

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