>The other thread will describe how to take the work done to solve Fermat Last theorem relates to our approach and why two objects that are identical types in number theory had to be proved so in a difficult to under proof, when in reality, with the right number system or model, this should have been obvious or a tautology.

Fermat's Last Theorem: there are no three positive integers a, b and c that satisfy the equation a^n + b^n = c^n for any n>=3.

You can read about the work done to solve Fermat's Last Theorem here:https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem

It involves the modularity theorem and elliptic curves, both of which VQC has already mentioned.

>The next piece that uses the same approach is not going to go into the details of elliptic curves and modular forms, it will be more about why these two identical things looked different, because realising they were the same thing solved a 350 year old math problem called Fermat's Last Theorem.

>What does it tell us about a language like maths when you need a virtually incomprehensible proof JUST to show two things are identical?

Thanks for creating this.

To start with, we do not need to know what modular forms or elliptic curves are in too much detail.

Just imagine them as areas of study in number theory.

Completely different areas.

Completely unrelated.

To solve Fermat's Last Theorem, it was necessary to prove they were identical objects.

Let that sink in.

The language of mathematics was so utterly unfit for purpose, that two identical or equivalent objects did not appear to be so.

Fundamental problem?

Hmm, I see someone is busy in the General Research today…

>>>/qresearch/1339160

>>5838

Ugh.

You caught me.

;)

>>5838

>>5842

Looking at this description, it's hard to make head nor tail.

The square of x plus the square of y being equal to r doesn't look like a circle either.

If you can pinpoint the discovery that lead to the idea that modular forms being equal to elliptic curves, you don't need to know the mathematics too much, that single step gave away the problem.

I'll bring it tomorrow if no one finds it before then…

Huuuddy….

What's goin' on here?

VQC!!Om5byg3jAU double trip

VQC!Nm8wdW6d92 single trip

Both: Id 91d952

Just curious :)

Y'didn't mention anything and then you had a new trip on RSA12

I'm fuckin' tardy lol

"Hey Buuuuuddy…"

>>5882

Something like this?

https://math.stackexchange.com/questions/1917984/the-corresponding-modular-form-of-an-elliptic-curve#1917997

>>5820

This is all new to me. Will try and keep up.

>>5905

Here is a quote from Andrew Wiles to inspire you anon. (see pic).

I'll wait WHILES you think on that and be back in a bit with some more Crummey (as in Chis Crummey, aka Chris Curtis).

>>5906

Thanks, MM. Much appreciated.

>>5906

Like the quote, MM! Thanks for blessing my first bread. Apparently we're only on the first small part of a larger voyage into the universe.

Blessings of love to (You) and (Yours) my brothers. Any sisters here? Just Checking.

To celebrate the latin in VA's handle, Fermat's words (copypasta) around 1630, when Pierre de Fermat wrote in the margin of his Latin version of Diophantus’ ARITHMETICA the following enigmatic lines, unaware of the passions they were about to unleash:

Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum, potestatem in duos ejusdem nominis fas est dividere. Cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.

In plain English, for those unfamiliar with Latin:

One cannot write a cube as a sum of two cubes, a fourth power as a sum of two fourth powers, and more generally a perfect power as a sum of two like powers. I have found a quite remarkable proof of this fact, but the margin is too narrow to contain it.

The sequel is well-known: Fermat never revealed his alleged proof. Thousands of mathematicians (from amateurs to most famous scholars) working desperately hard at refinding this proof were baffled for more than three centuries.

>>5909

Hmmm - was just writing the above, and then you popped in. Coincidence?? Your ears were burning…

>>5910

Wow. The Universe and Space Jesus are on duty tonight.

>>5911

Lupus in fabula - The wolf in the tale (i.e. Speak of the wolf, and he will come) (Terence)

(copy pasta from epic Fishing for Chris bread)

+++

++

+

In vein of blackboard images from RSA#10 of John Conway

>>4934 but more importantly, see:

>>4915

(Notice the n x (n+1) square, with triangle, with a section of it erased, leaving a cap?)

Attached is a blackboard image of Andrew Wiles. Couple more coming.

Notice the Q near his ear? Q?? haha.

So I had dug on this in mid Jan. Led to several tangents, geometric algebra, etc., so never finished. Jsut looked at notes and saved file and "cyclotomic fields", Earst Kummer, "Roots of Unity" were some of the terms that first popped up.

Back in a bit, but some symmetry for here, with some Q variables for fun.

More blackboard Wiles.

Excellent read/flip, in powerpoint format:

https:// folk.uio.no/rognes/papers/wileskoll.pdf

Fermat, Taniyama–Shimura–Weil and Andrew Wiles

by John Rognes, University of Oslo, Norway, May 13th and 20th 2016

Short, accessible article

https:// sites.math.washington.edu/~morrow/336_14/papers/vladimir.pdf

Fermat’s Last Theorem

Vladimir Korukov, May 15, 2014

More technical getting beyond me

http:// www.numdam.org/article/AFST_2009_6_18_S2_5_0.pdf

Interesting readable abstract, but rest of this paper by Tom Lovering of Harvard is jibberish to me. Muh math skillz lacking.

https:// tlovering.files.wordpress.com/2015/02/cyclotomic-fields-and-flt5.pdf

gnite/gday anons.

>>5882

Hey dog

Yo nigga like we take these straightforward algebra I motherfuckers and then apply “clock” arithmetic to dey asses and to hide the fact this is literally straightforward as fuk we make up fancy and unapproachable names for every minor detail just cause we hood niggas like dat

Protect yo turf lil nigga

Check check also niggas dun plan, niggas can’t decision tree or defer steps based on dem otha niggas. Niggas gotta live in the moment n’ have dey shit balanced all the time continuously else some nigga check yo shit. So nigga, foget yo ass precalcuatin’ decision tree motherfucka haven’ bytch ass nigga

>>5917

Being slightly less of a faggot no…

Modular forms or adaptations of the larger principle of modular forms which I’d guess is literally “shit repeating in a similar fashion” but was inevitably “simolified” by faggots into lol must repeat exactly.

The former definition would help fill triangles while the latter NEET definition jerks off with his realdoll

>>5915

So I decided to see if my original senpai was published anywhere involving modular elliptic curves. And I found a video!

Well, thaaaat video has to do with hyperbolic geometry, seen here:

https://youtu.be/ZNNZFSxe7oA

But what got me to post is that I was looking for oooother videos with the same guy in it and I could only find him on one channel.

That channel just so happened to have this lil' tidbit published 2 videos earlier:

Chalkboard Wiley.

https://youtu.be/0Soa_tdZIPU

And fuck it! Here's Don Zagier in the same channel. Take a look at the related video titles:

https://youtu.be/ndTESFYSkTU

>>5882

>The square of x plus the square of y being equal to r doesn't look like a circle either.

Important bit, back to Pythagorean triples? Core to Fermat's definition of problem.

>>5920

Then there's the Cardioid, linking unit circles to Mandelbrot set (right lobe), and a perfect circle (left lobe). (see pics).

Some Cardioid love for you anons.

>>5921

I'm gonna fucking facepalm to the nth power if:

"Vortex" math = Ellipticals Curves.

LEMME SHOW YOU WHAT I MEAN!

First image:

1. Triangular Spiral (fuck the pedos, I'm talking Positive Gold instead of inverse blue) and regular curvilinear spiral. You'd know that every point of the T-Spiral aligns with the C-Spiral.

2. Even if it's expanding. Whatever the one does, so does the other. It's the same spiral.

3. I'm guessing that if you were to do this to a spiral, you'd get my Polite Pyramid diagram with one side a constant unit larger on one side than the other. Remember the shells?

4. Look familiar?

5. You seein' what I'm seein'? Expand the shell like the Even|Odd Polite Pyramid set up. Mirror horizontally along the midpoint of the larger side so you have something that looks like:

.+

-+-

-+-

-+-

And then expand it out.

Due to the overlay, the mid section should…

If I'm imagining this correctly, complete itself (think slinky) but in a double helix pattern.

soooooo

…x

.+x+

-+x+-

x=core

+=original smaller side

-=scaling outward/down accordingly

I tried searching for a topology of a spiral like that concentric split and off the bat…

What we're dealing with…

1. Could it be said that one is a shadow of the other?

2. Look at how this drill bit is being formed.

Think of the seashell. (if it plays)

1. Speaking of which… Spiral Topology III by Lyle London

2. M0ar

3. If this plays… looks like the Even|Odd Polite Pyramid setup to me…

>>5923

I wonder if I derped or there was just too much data for one post…

>>5882

>I'll bring it tomorrow if no one finds it before then…

…tick tock

Homomorphism: Homomorphism, (from Greek homoios morphe, "similar form"), a special correspondence between the members (elements) of two algebraic systems, such as two groups, two rings, or two fields.

Britannica.com

>>5939

I've been trying to find the specific book.

It has a superb intro that talks about the Taylor series in a way that we layman can understand.

If I don't find it, I'll paraphrase.

Thanks for your patience.

It's from the nineties.

>>5943 That's cool, thanks.

So, seems you've dropped another crumb.

There's Shimura-Taniyama-Weil bit for the Modularity Conjecture that Wiles used.

Now it seems you're hinting at the Birch and Swinnerton-Dyer conjecture?

"The Birch-Swinnerton-Dyer (BSD) conjecture is one of the seven Clay Millennium problems" - hmmm, another Millennium prize…

>>5943

I was just learning about the Taylor series recently. It's not too difficult to figure out how to use it on polynomials and what you use it to look for (e.g. tangent lines to functions or calculating natural logs) but I have no idea why it works or how factorials relate to polynomials. I take it that's what you mean when you talk about a layman's explanation? Actually explaining what the thing is instead of just how to use it?

>>5948

>>5958

Love you guys.

I read the first 70 pages of the Art of the Deal on the plane to Poland.

When Trump talks about those who have the genes to succeed… you anons.

Think of the Taylor series as a fingerprint.

You don't have to know how the swirls work so much as to know what uniqueness is.

Fermat's Last Theorem.

Just prove that two apples are both apples.

"Bonkers"

Every company i go into.

Speghetti code.

Put together over a few years.

Can't support it.

Can't understand the business processes.

MATHS.

Put together over thousands of years in different languages, differnt cultures, different vernaculars.

Different symbols.

Logic.

Fit for purpose.

Paradoxes are not paradoxes.

Incompleteness theorem or not?

>>5979

When is a spade not a spade?

When is it? Prove it?

https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

>>5979

Love this thread already! I love that we're looking for the Layman's Explanation, not the Academic explanation.

>>5978 Looking into the fingerprints, don't have a match, but some interesting patterns… ha

>>6037

Dafuq? Let's get Senpai up in here.

Indeed, nice of you to pop in VA!! (need to go through your last walkthrough of PMA's output in No.12, love what is habbenin.)

Am just super busy atm and figured V was as well given trips to Poland and all.

(pic not exactly related, just grabbed from open tab).

Looked at a number of journal papers. Here's an example of one that uses elliptic-curves for modeling:

"Estimating Ridge Topologies with High Curvature for Fingerprint Authentication Systems"

https:// researchbank.rmit.edu.au/eserv/rmit:1572/n2006006557.pdf

>>6046 Also, looked for a few references from the 90's. See pic, the list has Wiles, Taylor, and Conrad in it. Hmm, maybe V will chime in…

>>6049

Hello MM! Nice to see ya! Did VQC ever tell us the title of the book that has the good into about the Taylor series? I don't know much about Fermat or Taylor (yet), and when I try to follow the equations, I just get confused (for now). So I hope he passes along the title

>>5979

>Paradoxes are not paradoxes

Whoa! That's deep.

Found this Croc of Shit interesting

>>>/qresearch/1489598

>>5979

Questioning the incompletnewss theorem is ballsy. I took a few logic courses at my university (and I'll admit I couldn't wrap my head around his theorem), but it has been generally accepted by a lot (most? "everyone") for a long time.

Something something squaring circles and Flower of Life into Mandelbrot transforms…

Something something.

Other anon went to bed but I think is is what they were getting at… or something.

>>6879

Cardioid is that you?

Linked Duo

1-0.20-0.10

I was told to come to this board.

My bread is.

https://8ch.net/qresearch/res/2126184.html#2452017

>>7095

>>5820

From the beginning.

Lorentz transformation.

Or basic spin on the axis that is your problem in seeing two sets that should be the same and are not.

It will not always work but you should run every set through all lorentz to see if same or not before assuming it is not the same set.

Picture the same set.

>>7053

Please define this - it is valid - this may be the link of fractal to 4D. Please define the process and math.

If I can spin in 3D I can spin in 4D

MF do it!!!!!!!!!!!!!!!!!!!!!!

Tensors cross dimensions get it?

deep projection of the 30 degree cube rotation.

>>5921

I found this very interesting and wanted to see if it worked. It does.

>>5917

>clock” arithmetic to dey asses

Thanks for the laugh m80

>>7103

The numbers and angles.

>>2651134

K>>2651107

>>>2651107 (You)

>

>So then just put it in the Sonoluminescence or Fermat's Last Theorem breads. Those are way more applicable to what you're doing IF YOU CANNOT SHOW HOW IT'S RELATED TO RSA.

>

>Get it through your head.

Sorry just following orders.

>>5979

https://www.philosophybasics.com/branch_logic.html

>>5774

https://arxiv.org/PS_cache/chao-dyn/pdf/9406/9406003v1.pdf

>>10016

Don't ask.

"Why was this visual proof missed for 400 years? (Fermat's two square theorem)"