Heisenberg magnets: the most retarded electron configuration in the history of humanity?

Magnetism

Lately I viewed a video from physics professor Stephen Blundell and I more or less thought like ‘may be something for a new post on magnetics’? And yes why not? Not that people like Stephen will react on this post: lately I arrived at the conclusion that physics professors are more or less the same as math professors and as such they are a bunch of overpaid incompetent shitholes. After having said that, the video is relatively good and can give a lot of thoughts to ponder.
It is important to stress that I do not want to insult Stephen Blundell, there is no reason for that at all. If Stephen thinks electrons are bipolar little magnets, he is for sure an idiot but again this is not an insult. It is just an objective observation: If a person takes for true things that are not logical on all levels of thinking, you can observe that and simply say ‘Likely just another idiot doing electron spin’.
The main reason for me picking this video is because Stephen is more or less a high IQ person, he does not use it but he is relatively smart. I also viewed a video where some other idiot explained the magnetic properties of iron by the fact that iron atoms were bound by unpaired electrons…
And compared to Stephen Blundell that is another level of how dumb can you be? It made me wonder: why do people make video’s about magnetism if they do not understand anything from magnetism? But those persons often think ‘I understand’ it is ‘unpaired electrons’…

Heisenberg magnets. I never heard from this concept of Heisenberg magnets. They are just a bunch of horizontal spins and all spins are pointing up and of course Stephen does not explain it but this should be the so called ‘ground state’. That was more or less the reason I decided to write the post of 10 pictures long. Heisenberg lived in the beginning of the 20th century so why do people still repeat weird stuff from that guy? Very simple: this is the Heisenberg from the Heisenberg uncertainty principle in quantum mechanics. Now should you worry that this important principle is also totally idiot? No, the uncertainty principle is more or less a consequence of Fourier transformations and as such you can trust that part of the science of physics.

But what you cannot trust is people like professor Stephen Blundell explaining that electrons are magnetic dipoles without giving any experimental proof at all. Gauss died long before the first electrons were discovered so can you apply the Gauss law for magnetism to electrons? Only if you have plenty of experimental evidence & proof that indeed the Gauss law for magnetism is valid for electrons.
Hey try to explain that to idiots like Stephen, what will he say after recieving such a quest for an explanation? He will simply remark that this is not needed because ‘everybody knows’ that electrons have magnetic spin and that is bipolar by definition.

By saying Stephen is an equivalence class on his own I mean that he represents the collective of physics professors that believe electrons are little magnets with a north and a south pole. Basically that is 100% of all physics professors out there because you will never ever get a physics professorship if you think that it is ´just not logical´ that electrons are magnetic dipoles. Only when you are willing to think as an idiot you can become a member of this club of physics idiots.

This post is 10 pictures long but all in all I more or less concentrated upon how Stephen explains permanent magnets. Again it is not an insult but the idiot explanation is that it is alignment of unpaired electrons. About four years back I did some experiments with that myself, after all if it is just a matter of unpaired electrons to align themselves in that case always with a strong magnet you can change a weak magnet. All this nonsense that unpaired electrons will align or anti/align themselves with an applied magnetic field faded into nonsense with my small experiment.

May be you have heard from the g-2 experiment from Fermilab that came out a few weeks ago. If you see video’s from that experiment (it is with muons and not with electrons) it all looks so highly convincing. It looks like a lot of high class physics people doing their thing and they are smart! But are they? Every time an electron or a muon enters a magnetic field they claim the spin axis starts to wobble until the spin is aligned (or anti aligned). So what to think of that? Below you see my own 100% amateur experiment where the weak magnets are hold in place with some wood. And after 24 hours waiting, non of the electrons in the weak magnet has ‘flipped’. So I wonder one more time: Why do the people from Fermilab talk about a ‘wobble’ of an electron or a muon? I don’t know and only look in bewilderment at their explanations…
Ok, like said before, this post is 10 pictures long so lets get started:

Please remark that if electrons carry magnetic charge, likely such super positions do not exist.
The strong field is perpendicular to the weak magnets; yet zero spin flip observed…
Likely the physics professors do not understand why the Curie temp leads to a loss of magnetism.

In the process of making permanent magnets in the industry, the metal is heated above the Curie temperature. A strong magnetic field is applied all the time while the metal slowly cools. After cooling down the permanents magnets are ready for use. That is one way of making permanent magnets. Another ways is the application of a very strong magnetic field for a short time, it is more like a magnetic pulse, and after that the permanent magnet is ready. This is nicely in line with electrons being magnetic monopoles.
Why do you make so much noise?
What you say, I can’t hear you!
Oh magnetic monopoles should be treated the Paul Dirac way?
Well I wish you luck with that one…

In picture number 10 you will find an important secret as why permanent magnets are permanent: The unpaired electrons are locked inside the inner shells of for example iron atoms. I hope you understand as why this is logical while the explanation given by that idiot Stephen Blundell with all electron spins aligned is something only other idiots will find ‘logical’.

I skipped an awful lot while writing this post. For example silver has only one unpaired electron and in the old Stern-Gerlach experiment from 1922 the beam of silver atoms was split in two. Silver has about 107 protons and neutrons and as such the mass of the nucleus is about 200 thousand more. Yet that lonely unpaired electron is capable of splitting the beam of silver atoms in two…

The retarded overpaid physics professors still try to explain this via inhomeogenous magnetic fields. It only makes we wonder: How can you be a full century ultra stupid?
Well my dear Stephen, why ten years in the future you will still think electrons are bipolar little magnets? In my view it is because the physics professors are mostly make up of sino’s. And a sino is a Scientist In Name Only.
After having said this all you can now enjoy the wisdom of physics professor Stephen Blundell in the next Youtube video:

Ok, that was it for this post. See you around and try to prevent this utter stupidity as people like Stephen Blundell have with all this bipolar nonsense.

A second proof of the new little theorem of Monsieur Pierre de Fermat.

Last Fermat theorem

This is not a totally new proof, basically it is already part of the proof in the previous post. But I was able to write it down a bit more compact. It seems that you can skip large parts of the previous proof and still the result is standing. The stuff you can skip is not unimportant or so; it is where I compared those additive and multiplicative orbits and you really need that in order to understand a bit more of what is happening in rings like the integers modulo 35 (or any other composite number of course).
Often I name the ordinary intergers ‘real integers’. I hope that is not confusing, with a real integer I mean whole numbers as they are found on the real line. I do that do make clear the difference with the Gaussian integers as they are found in the diverse complex spaces.

Right now I am already about four months busy with this stuff that all started in January with counter examples to the last theorem of Fermat. All in all I never expected to be able to make an improvement on the little theorem of Fermat. But sometimes the old little theorem gives answers that are indeed correct but still is not that satisfactory. In the old little theorem you take some real integer a, you pick a prime number p that has no common factors with a and you know that in that case:
a^p mod p = a. But if the prime number p is relatively small, I mean a is larger, you don’t get back a but a mod p.

This post is short, only three pictures in the usual format of 550×775 pixels but I added two appendices so all in all there are five pictures in this post. In the second appendix I show you that if we square 125, the old little theorem gives back a 1 while my new version of the little theorem nicely gives back 125. Of course there is always much discussion possible of something is ‘better’ or not. It is only in the sense that also with small prime numbers you get back your a I mean it is ‘better’. One thing is clear: it is definitely more beautiful. My favorite formulation stays the formulation with two prime numbers like in:

p^q = p mod pq &
q^p = q mod pq.

The symmetry in the pair of equations above is, in my opinion, more beautiful compared to the old version of the little theorem of Fermat. At last I want to remark that I have a thing in common with Monsieur Fermat: math is a hobby for me. Now the old little theorem was improved upon by the professional professor Euler and with a little smile on my face I can say: Hey Euler did you miss the above pair of cute equations?

Yes he did, just like a guy named Einstein never had a fucking clue about electron spin. But likely that is a story for another day, in the meantime we have five pictures with the second proof of the new little theorem. Have fun reading it and never forget: If it is math, sometimes you need a few more days to figure it all out!

In a wiki upon proofs of the little Fermat theorem you can find that one of the authors did indeed find a counter example to the last theorem of Fermat. You can find it under ´Multinomial proofs´in the next link:
Proofs of Fermat´s little theorem. Link used:
https://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem

Ok, that was it for this post. Thanks for your attention.

Proof of the conjecture on Fermat’s little theorem.

Last Fermat theorem

The proof is finished and in the end it went rather different from what I expected before the writing down of this new proof. I hope the main ideas are easy to understand. I formulated the proof with a concrete example; so not two general prime number p and q. But I took p = 5 and q = 7 and as such we are calculating in the ring of integers modulo 35.
One of the key ideas is that we have so called additive orbits, for example the additive orbit of 5 is the set {0, 5, 10, 15, 20, 25, 30}. The additive orbit are just the multiples of 5, it is handy to view the above set as multiples of five and as such: {0, 5, 2*5, 3*5, 4*5, 6*5}.
On the other hand we have exponential orbits, the exponential orbit of 5 are the powers of 5 like in the next sequence: 5, 5^2, 5^3, 5^4…
An important observation is that any power of five is also a multiple of five; that means the exponential orbit is inside the additive orbit. For example 5^3 is on the exponential orbit, 5^3 = 125 = 20 modulo 35 = 4* 5.
So the number 5^3 from the exponential oribt corresponds to 4*5 on the additive orbit. The goal of the proof is to show that the period of 5 in her exponential oribt is 6 and the period of the exponential orbit of 7 is 4.
That will ensure our new little theorems of Fermat:
p^q = 5^7 = 5 modulo 35 &
q^p = 7^5 = 7 modulo 35.
Remark that powers of 5 can never be a multiple of 35 simply because any power of 5 does not contain a prime factor 7, so not all of the numbers on the additive orbit are allowed.
Another key idea is that if we reduce stuff modulo 35, this is the same as reducing stuff modulo 7 on the multiples of 5. Let me explain: Take the number 50, inside the mod 35 ring this is 15. But 50 = 10* 5 = (10 – 7)*5. I was able to pull that modulo 35 stuff on a ring back to modulo 7 stuff on a field…

Another thing I want to remark is that I formulated these new little theorems of Fermat mostly in prime numbers. That makes them more symmetric like the beautiful pair of equations above, but it can be a bit more general like I showed you in the last post using the number 210 that is made up of four different prime factors. And even that is not needed; prime factors can be double or triple it does not matter. As long as the exponent is a prime number my freshly crafted proof will sail you through all the troubles there are.

In a parallel development I found a perfect math professor. It’s a female and she has an amazing career record: At age three already a Fields medal while before she was nine years of age already the third Abel prize for lifetime achievement math… It is surely amazing…;)

Unlike other math professors, she is thinking it all through… Amazing!

But serious, this post is not that long. Only five pictures and like I said above it is not a ‘most general’ kind of proof but it uses a fixed pair of prime numbers. I think it is better this way because if I would formulate all the stuff in a general setting the only people who could understand such a writing are the ones who already figured the stuff out for themselves… Ok, all pictures are in the usual 550×775 pixelf format so here we go:

We are almost at the end: Let me give you one more example as why only in the exponent you need a prime number. We take the number 8 and raise it to the power 5 and do the reducing modulo thing by 40.
Doing so gives that: 8^5 mod 40 = 32768 mod 40 = 32768 – 819*40 = 8.

Ok, that is what I had to say for this post.

More versions of Fermat’s little theorem using the number 210.

Last Fermat theorem

A few posts back I used the number 210 to craft seven so called ‘primitive’ counter examples to the famous last theorem of Fermat. Each of those seven primitives can be changed in an infinite number of ways so we have seven streams of counter examples to the last Fermat theorem. It has to be remarked that all counter examples I found since Jan are all based on the so called divisors of zero idea. So if you hear people talking about that in a timespan of 3.5 centuries nobody was able to find counter examples, they are not lying if they mean a counter example on the space of real integers. Yet in Jan this year we observed I had two counter examples using the 3D Gaussian integers, it was one or two days later I found all those counter examples on the spaces of modulo arithmetic.
Beside his so called last theorem Fermat has done a lot more and one of those things is Fermat’s little theorem. To my surprise there are many more variants possible of this little theorem. The little theorem says that for a number a coprime to some prime number p the following holds:
a^p = a mod p. Two numbers are coprime if they share no common factor, if a is a number between 1 and p this is always the case.

The most simple example: a = 2 and p = 3. The little theorem now says that 2^3 mod 3 = 2. This is correct because the remainder of 8 divided by 3 equals 2.

The variants I found can be summarized as next:
2^3 mod 6 = 2 and
3^2 mod 6 = 3.
As you see I take it modulo a composite number. I still do not have a satisfactory proof so for the time being this is a conjecture. I am planning a seperate post for outlining where in my view the problems are that must be proved for the status of conjecture being dropped. So for the time being this is Reinko’s little conjecture.

But can you use a composite number with more than two factors? Yes but you can only use prime numbers in the exponent. Not that it will always fail if you do not use a prime exponent but that is a mathematical story for another day. Anyway this post uses the number 210 because it is the smallest number with four prime factors.
Before we go to the content of this post, to my surprise yesterday I observed a proof that is strikinly similar to the easy way I constructed those counter examples to the last theorem of Fermat. I found it on brilliant.org, here is a link:
https://brilliant.org/wiki/fermats-little-theorem/
Over there they prove the little theorem for a + 1 if it is true for a. Now why do they not use it for finding counter examples to the last theorem of Fermat? Well my dear reader, the human mind is bad at math. We are only monkeys or smart apes if you want, math is something that fascinates our minds but humans are horribly bad at math. Believe me: I am a human myself…;)
Here is a picture from that proof from brilliant dot org:

It is a bit hard to read but all those middle terms contain factors of p.
Therefore they vanish when you take the modulo p thing.

The whole post is only two pictures long, each of the ususal size of 550×775 pixels. Here we go:

Ok, that was it for this post. Thanks for your attention & see you in the next post.

A conjecture on Fermat’s little theorem.

Last Fermat theorem

To my amazement there are many more forms of the so called Fermat little theorem. Fermat’s little theorem uses numbers that are relatively prime to each other (also known as coprime numbers or better: coprime real integers). I hope it is not confusing for you that I write ‘real integers’ but that is meant to make clear these are not Gaussian integers but integers from the real line.
The little theorem of Fermat has some generalizations like the Euler theorem and a person named Carmichael also worked on stuff like that. Yet the coprime stuff is always assumed while the results I found last week do not need that at all. But I do need prime numbers in the exponent, that’s all.
When I found those counter examples to Fermat’s last theorem about 3 months back I was amazed I could find nothing of that on the entire internet. Ok my first stuff was done with 3D complex & circular Gaussian integers so that is logical nobody else writes about that. But that expressions like 5^n + 7^n = 12^n modulo 35 is something that baffled my mind. This is so simple to prove that it is hard to understand why this is not a standard counter example to the last theorem of Fermat. To refresh your mind: the last theorem of Fermat says there exists no integers such that x^n + y^n = z^n for n > 2. This has been an open problem for about 3.5 centuries of time, it was solved by Andrew Wiles in the beginning of the nineties of the last century but even Andrew never mentions those easy to craft counter examples to the last theorem of Fermat.

A paradox.
The last theorem of Fermat was unproven for centuries. But the far more easy little theorem of Fermat was proven rather quick and that proof is very easy compared to the Andrew Wiles thing. Now I am having the opposite problem: The counter examples to Fermat’s last theorem are so simple to construct that in the beginning I was hesitant to use it all. While for these new variants of the little theorem of Fermat, I do not know how to prove that. So my stuff is more or less opposite to the historical developments as they are known; that is why I consider this a little paradox.

In this post I formulate a few easy to understand variants of the little theorem of Fermat. In this post I choose to do it as symmetrical as possible like in the next pair:
7^11 = 7 modulo 77 &
11^7 = 11 modulo 77.
As you see on inspection; these are clearly variants of the little theorem but the exponents and the 77 of the modulo thing are not coprime. For myself speaking I consider the above pair as an example of ‘mathematical beauty’. Of course it is hard to give a definition of ‘math beauty’, you recognize it when you see it but it is hard to define because beauty itself is not a mathematical object or so.

Anyway beautiful or ugly as a math professor, this post is six pictures long all in the standard format of 550×775 pixels. Here we go with the picture stuff:

Typo at ‘w often looked’ should be ‘we often looked’.
Remark we are using the counter examples to the last theorem of Fermat…

A few posts back I crafted seven counter examples to the last theorem of Fermat and those were based on the number 210. Actually each of those seven ‘primitives’ gave rise to an infinite series of counter examples so that the overpaid math professors once more know their contribution to this all: ZERO!
But you can make four new little Fermat theorems using the number 210 so may be that is the next post. On the other hand the USA based Fermilab has all kinds of new results out upon the muon and they keep on thinking that elementary particles like electrons and muons are magnetic dipoles. Instead of offering some fundamental proof for the magnetic dipole nature of electrons we only get a complicated story that, as usual, neglects that electrons and muons get accelerated by magnetic fields.

So I don’t know about the next post. Well thanks for your attention, have a healthy life and ruthlessly kill all math professors. Or may be not…;)

Side remarks on the Frey elliptic curve.

Last Fermat theorem

Since this is the post number six on the Fermat stuff already, I decided to create a new category for this kind of math. It is no secret my knowledge of algebra is rather rudimentary, a lot of things in algebra are things I do not like to study or think about. I always had trouble learning algebra, often those people come up with say 15 definitions of algebra objects but all those definitions have the weight of a fly and rather soon I am lost in the forest. I much more prefer more heavy definitions of math objects (like the Cauchy-Riemann equations) and not stuff that is a semi-simple defined on a semi-simple kind of curve…
So I do not know much about number theory, a few days ago I downloaded the entire proof of Andrew Wiles where he proves that the last theorem of Fermat is actually true. Well already in the very first line I get lost; and in that proof you have all that Galois stuff so I think that I skip that entire proof for the time being.
A lot of things are weird in number theory. For example that Frey elliptic curve is based on a hypothetical solution to the Fermat equation a^n + b^n = c^n. If you interchange a and b in the Fermat thing, every thing stays the same. But you get a different elliptic curve if you interchange a and b in that Frey ellipic curve. So I just had no clue; wtf is going on here? Luckily I found a video of Gerhard Frey explaining a bit about what and why and the elliptic curve he defined is done in that way so that the discriminant can be simplified using that theoretical solution to the last Fermat theorem. So it is not crazy but it has it’s own logic, yet search for yourself: how many texts are there that speak about this Frey elliptic curve and actually tell you this? Most math writers simply repeat the (old) knowledge and are bad at explaining why stuff is such and so.

I always work alone, actually it is not work but an important hobby, and because I have to figure out every thing alone I have no access to people with a lot of knowledge on the details & the broader lines of some kind of math theory. Because I work alone this often takes more time. Yet on the universities where the people are supposed to work together they have never found 3D complex numbers or counter examples to the last Fermat theorem. In other sciences like physics it also goes like crazy if you read what they made of electron spin in 100 years of time. So working together is not a guarantee of speeding things up. On the contrary if after a full century you still think that, for example, the electrons is a magnetic dipole you are crazy to the bone.

This post is a short one, only four pictures long. I nicely work out what that discriminant is supposed to be. Likely people like Andrew Wiles and Gerhard Frey have never seen counter examples to the last theorem of Fermat, so why not at the end of my post take a look at what happens in that case? Well it does not look very promising for the collective of overpaid math professors; such a determinant of the Frey elliptic curve is always zero… Anyway on all spaces I found where we have counter examples to the last Fermat theorem, such a discriminant is always zero.
And that is regardless of the last Fermat theorem counter example being true or false; sorry Gerhard Frey I don’t think this approach will bring any fruits at all…
Well here are the four pictures, all of the standard size of 550×775 pixels.

The only reason I wrote six posts on the Fermat stuff is that those counter examples like 5^n + 7^n = 12^n modulo 35 are too cute to ignore.
End of this post, thanks for your attention.

Counter examples to the last theorem of Fermat using the number 210.

Last Fermat theorem, Uncategorized

Ok ok one more post upon the easy to find counter examples to the last theorem of Fermat. In this post we will take a look at the real integers modulo 15 and modulo 210. It still amazes me how easy it is to find counter examples to the last Fermat theorem using the integers modulo n where n has at least two prime factors. From my own education I remember that the integers modulo n are studied in math mostly via additive groups and multiplicative groups. For some strange reason it is not commonly studied via rings where you have the benefit of addition and multiplication inside one simple to understand structure of numbers… Inside professional math there is always that tendency to study fields only, of course there a legitimate reasons for that like it makes math life often more simple. But rings are not fields, rings allow for non zero numbers that are non-invertible anyway. As such you can always find plenty of pairs of so called ‘divisors of zero’ and once you have stuff like that it is always a piece of cake to find counter examples to the last theorem of Fermat.

Yet I tried a few times to find some counter examples on the internet but all I got was boatload after boatload of total nonsense like the weird stuff paraded in the previous post. Could it be that math professors tried to find counter examples to the last theorem of Fermat while they never dipped into the power of the divisors of zero? That’s crazy because the Fermat theorem was open for about 350 years. I think many people have found the easy to understand results in this post before I did but if they tried to get the stuff out they were blocked by the scientists of those days and as such in the year 2021 it is hard to find something back.

Compare it to electron spin; it is hard to swallow that I am the very first person in history that claims electrons cannot be magnetic dipoles because it is just not logical for hundreds of reasons. Yet in the daily practice of how science is done at the universities, it is a no show that electrons are magnetic monopoles. What happened to all those other persons that understood that electrons cannot be magnetic dipoles? Well at least they got neglected and university life just went on with electrons being a magnetic dipole because ‘we are so smart’ and ‘the standard model explains almost everything’. And more of that nonsense…

This post is 8 pictures long, all of the usual size of 550X775 pixels.
Since it is about counter examples to the last Fermat theorem I expect it will not make much headlines in the news for another 3500 years.
After all the only thing university people are good at is being incompetent…;)
Here we go:

At last I found a more or less readable article about near misses of the last Fermat theorem. It was found inside old work from Ramanujan so that is always interesting. Most of the time when I looked for counter example to the last Fermat theorem I only find piles of garbage but this time I tried it with Duckduckgo and something readable comes floating up:
Ramanujan surprises again.
https://plus.maths.org/content/ramanujan

Ok that was it for this post. Thanks for your attention.

Why can’t I find counter examples to Fermat’s last theorem on the internet?

3D complex numbers, Last Fermat theorem, Uncategorized

After a few weeks it is finally dawning on me that it might very well be possible that the professional math people just do not have a clue about how easy it is to find counter examples to the FLT. (FLT = Fermat’s Last Theorem.) That is hard to digest because it is so utterly simple to do and understand on those rings of integers modulo n.
But I did not search long and deep and I skipped places like the preprint archive and only used a bit of the Google thing. And if you use the Google thing of course you get more results from extravert people. That skews the results of course because for extraverts talking is much more important compared to the content of what you are talking or communicating. That is the problem with extraverts; they might be highly social but they pay a severe price for that: their thinking will always be shallow and never some stuff deeply thought through…

As far as I know rings of the integers modulo n are not studied very much. Of course the additive groups modulo n are studied and the multiplicative groups modulo n are studied but when it comes to rings all of a sudden it is silent always everywhere. And now I am looking at it myself I am surprised how much similarity there is between those kind of rings and the 3D complex & circular numbers. Of course they are very different objects of study but you can all chop them in two parts: The numbers that are invertible versus the set of non-invertibles. For example in the ring of integers modulo 15 the prime factors of 15 are 3 and 5. And those prime factors are the non-invertibles inside this ring. This has all kinds of interesting math results, for example take the (exponential) orbit of 3. That is the sequence of powers of 3 like in: 3, 3^2 = 9, 3^3 = 27 = 12 (mod 15), 3^4 = 36 = 6 (mod 15) and 3^5 = 18 = 3. As you see this orbit avoids the number 1 because if it would pass through 1 you would have found an inverse of 3 inside our ring and that is not possible because 3 is a non invertible number…

Likely my next post will be about such stuff, I am still a bit hesitant about it because it is all so utterly simple but you must never underestimate how dumb the overpaid math professors can be: Just neglecting rings modulo n could very well be a common thing over there while in the meantime they try to act as a high IQ person by stating ‘We are doing the Langlands program’ & and more of that advanced blah blah blah.
Anyway it is getting late at night so from all that nonsense weird stuff you can find on Google by searching for counter examples to the last theorem of Fermat I crafted 3 pictures. Here is the first one:

I found this retarded question on quora. For me it is hard to process what the person asking this question was actually thinking. Why would the 2.999…. be important? What is this person thinking? Does he have integer solutions to say 2.9 and 2.99 and is this person wondering what would happen if you apply those integer solutions to 2.99999999…..???????

It is retarded, or shallow, on all levels possible. So to honor the math skills of the average human let’s make a new picture of this nonsense:

We will never be intimidated by the stupidity of such questions and simply observe these are our fellow human beings. And if ok, if you are a human being running into tons of problems, in the end you can always wonder ‘Am I a problem myself because I am so stupid?’

If you have figured out that question, you are getting more solid & you look more like a little cube:

I want to end this post on a positive note: Once you understand how stupid humans are you must not view that as a negative. On the contrary, that shows there is room for improvement.

The last Fermat theorem (positive version) versus the number 1.

Last Fermat theorem, Uncategorized

This is a short post; just over 3 pictures long. We make a few calculation on the ring of integers modulo 35. Of course that is a ring and not a field because 35 has two prime factors namely p = 5 and q = 7. These two prime factors form so called divisors of zero, that means that pq = 35 = 0 inside the ring of integers modulo 35.
Because the two prime factors have this property, that has all kinds of simplications when it comes to expanding (p + q)^n inside this ring. That is what I name the ‘positive version’ of the last theorem of Fermat: The ring of integers modulo 35 is a simple number space where the last theorem of Fermat is possible, here we again have 12^n = (5 + 7)^n = 5^n + 7^n.

In this post I use the fact that the prime numbers 5 and 7 are also relatively prime and as such you can make a linear combination of them to get the number 1. And once you have the number 1 you can use them as a basis for the entire ring of integers modulo 35. But if you have a healthy brain, likely you will remark that it is far more easy to just use the counting numbers 1, …, 35 or just 1 to craft such a basis… So I understand that you might think I am crazy to the bone. Of course I am crazy to the bone but there is a goal in this utter madness. Take for example 3*5 – 2*7 = 1, this is one possibility to form the number 1 as a linear combination of 5 and 7. Since both terms contain one of the pairs of divisors of zero as a factor, this linear combination allows for a positive last theorem of Fermat decomposition: For a natural numbers n we have that: (15 – 14)^n = 15^n + (-1)^n*14^n = 1.
Although such expressions are very cute looking, it has no significant math depth anyway. All in all this post it totally unimportant because it is all so simple. The post upon the 3D Gaussian integers is far more important because there it was possible to write the number 3 as a linear combination of two 3D Gaussian integers. As such for the first time in about 350 years it was the first serious counter example against the last theorem of Fermat because that number 3 was just on the line of integers. It was not something inside some modulo number space or so, that was the real deal for the first time in 350 years.

Will math professors react on such a finding? Of course not. For example they would reason before the finding that if you can’t use 3D complex numbers to find only one significant result in algebra or number theory, that proves 3D complex numbers are useless.
And after the counter example to the last fermat theorem? Well math professors are the most smart people on earth, they are higly agile and adeptable and now the reasoning will likely be something like: In the entire history of mathematics nobody has ever used 3D Gaussian integers. This all is so far fetched that this is not serious math…

Well that is how they are and there is no changing that kind of behavior I just guess. Anyway enough of the blah blah blah. The post is just over 3 pictures long, has no mathematical significance anyway and I hope you have some fun reading it.

For odd n you get a minus sign, for even n you get a plus sign.
It is not significant math, but it sure looks very cute!

It is now one hour after mdinight so it is time to hit that button named ‘Publish website’. Live well & think well my dear reader. See you in the next post or so.

Another counter example to Fermat’s last theorem using 4D complex numbers.

4D complex numbers, Last Fermat theorem

All in all I am not super satisfied with this post because the math result is not that deep. Ok ok the 4D complex numbers also contain non-invertible numbers, say P and Q, and these are divisors of zero. That means PQ = 0 while both P and Q are non-zero. And just like we did in the case of 3D circular and complex numbers because of the simple property PQ = 0 all mixed terms in (P + Q)^n become 0 and as such: (P + Q)^n = P^n + Q^n.

In the space of 4D complex numbers an important feature of the determinant det(Z) of a 4D complex number Z is that it is non-negative. As such there is not a clear defined layer between the part of the number space where the determinant is positive versus the negative part. During the writing of this post it dawned on me that Gaussian integers in the 4D complex space always have a non-zero determinant. As such the inverse of such a Gaussian exists although often this is not a Gaussian integer just like the inverse of say the number 5 is not an integer. A completely unexpected finding is that the 4D complex fractions form a field…

That made me laugh because the professional math professors always rejected higher dimensional complex numbers because they are not a field. For some strange reason math professors always accept or embrace stuff that forms a field while they go bonkers & beserk when some set or group or ring is not a field. This is a strange behavior because the counter examples that I found against Fermat his last theorem are only there because 3D and 4D numbers are not a field: there are always non zero numbers that you cannot invert.
As such a lot of math professors are often busy to make so called field extensions of the rational numbers. And oh oh oh that is just soo important and our perfumed princes ride high on that kind of stuff. And now those nasty 4D complex numbers from those unemployed plebs form a field too…
I had to smile softly because 150 years have gone since the last 4D field was discovered, that is known as the quaternions, and now there is that 4D field of rationals that are embedded into something the cheap plebs name ‘4D complex numbers’? How shall the professional math professors react on this because it is at the root of their own behavior over decades & centuries of time?

Do not worry my dear reader: They will stay the overpaid perfumed princes as they are. Field or no field, perfumed princes are not known to act as adult people.

After having said that, this post is only five pictures long all of the ususal size of 550×775 pixels. For myself speaking I like the situation on the 3D numbers more because there you can easily craft an infinite amount of counter examples against the last theorem of Fermat.
Ok, here we go:

Yes I have to smile softly: all this hysteria from overpaid math professors about stuff being a field or not. And now we are likely into a situation where the 4D complex numbers are not a field but the space of 4D complex rationals is a field…

Will the math professors act as adults? Of course not.
Ok, let’s end this post because you just like me will always have other things to do in the short time that we have on this pale blue dot known as planet earth. Till updates.