The Yokozuna Blossoms

newscientist.com/article/2099534-mathematicians-finally-starting-to-understand-epic-abc-proof/

>The breakthrough seems to have come from Mochizuki explaining his theory in person. He refuses to travel abroad, only speaking via Skype at the Oxford meeting, which had made it harder for mathematicians outside Japan to get to grips with his work. “It was the key part of the meeting,” says Fesenko. “He was climbing the summit of his theory, and pulling other participants with him, holding their hands.”

>At least 10 people now understand the theory in detail, says Fesenko, and the IUT papers have almost passed peer review so should be officially published in a journal in the next year or so.

>The glimmer of understanding that has started to emerge is well worth the effort, says Fesenko. “I expect that at least 100 of the most important open problems in number theory will be solved using Mochizuki’s theory and further development.”

Time to start reading those papers if you want to be relevant in 21st century mathematics:
>the originals
kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf
kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory II.pdf
kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory III.pdf
kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory IV.pdf

>describing the philosophical analogy between IUTT and Gaussian
kurims.kyoto-u.ac.jp/~motizuki/Alien Copies, Gaussians, and Inter-universal Teichmuller Theory.pdf

>Fesenko's 'ARITHMETIC DEFORMATION THEORY VIAARITHMETIC FUNDAMENTAL GROUPS AND NONARCHIMEDEAN THETA-FUNCTIONS,NOTES ON THE WORK OF SHINICHI MOCHIZUKI'
maths.nottingham.ac.uk/personal/ibf/notesoniut.pdf

sidenote: which one of you runs this bizarre twitter account?
twitter.com/math_jin

Other urls found in this thread:

maths.nottingham.ac.uk/personal/ibf/notesoniut.pdf
en.wikipedia.org/wiki/Algebraic_number_field
drive.google.com/drive/folders/0BxJBjbxm46r4c3hhMlFrVmZYNk0
youtube.com/watch?v=MUt7_6MuF_g
math.columbia.edu/~woit/wordpress/?p=8663
en.wikipedia.org/wiki/Abc_conjecture
kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf
kurims.kyoto-u.ac.jp/~motizuki/Alien Copies, Gaussians, and Inter-universal Teichmuller Theory.pdf
twitter.com/math_jin
twitter.com/AnonBabble

Mochizuki is the new Gauss

can you tl:dr me?

I wonder what fields of mathematics one needs to be proficient in, in order to actually understand the proof.

t. undergrad physicist

this is big gentlemen

shame the guy is super autistic, he's the kind of brain that could pull humanity into a new century

>I wonder what fields of mathematics one needs to be proficient in, in order to actually understand the proof.

Arithmetic Geometry + Mochizuki's previous work

Why aren't you doing aikido, user? It's the secret to mathematics

In section 3.2 of
maths.nottingham.ac.uk/personal/ibf/notesoniut.pdf
Fesenko gives a roadmap depending on your background. Keywords include arithmetic geometry (especially elliptic curves), special complex functions like theta functions and modular forms (they're bound to show up when elliptic curves do), anabelian geometry (I know next to nothing),

...

>Inter-universal Teichmuller theory concerns the construction of "canonical deformations of the ring structure of a number field"

can someone give me a response to exactly what the quoted part of that sentence means?

What is a number field?

How can someone interpret a number field as a ring structure?

What is canonical deformation?

I'll most likely end up googling all the terms in the end, but if anyone is up for a simple explanation of that, I'd greatly appreciate from my colleagues here at Veeky Forums.

...

thanks

That article was really one-sided.

The other guy who attended said it would take at least 3 more years to finish verifying it, and it seems longer and longer the more he understands it.

simple explanations add unneeded confusion because they force the novel new concept down to the level of your current thinking. The purpose of development is the opposite; to push your thinking higher.

wrong

Mochizuki lookin hella Veeky Forums

>inb4 someone asks whether the proof goes through in Peano arithmetic

>What is a number field?
a field of numbers containing the rational numbers Q which have a finite-dimensional vector space structure over Q (makes them nice to work with).
basic examples include:
Q(sqrt(2)) (numbers that look like a+b*sqrt(2) with a and b rational)
Q(i) (numbers that look like a+b*i with a,b rational)
see: en.wikipedia.org/wiki/Algebraic_number_field

>How can someone interpret a number field as a ring structure?
A field is just a ring where every non-zero element is invertible (this is the definition of field). The ring structure just refers to the field's multiplicative behaviour and additive behaviour.

>What is canonical deformation?
foreword: i do not understand this well, but:
one of mochizuki's main tools is something called a theta-link, using this link requires 'initial theta data'.

This data includes a number field, an elliptic curve defined over that number field, and a prime number.

the deformation of the number field acts on this data in a way to bound the height (basically a measure of size/complexity) of the points on the elliptic curve.

Why can't books explain math like this?

Thanks friend

the ideas of rings/fields are in any algebra book, and number fields in any algebraic number theory book. a classic book on these would be hilbert's.

you wont find these theta links in any textbooks though, maybe in a few years.

>Dr. ABC, I'm Mochizuki

here are the pictures of the conference: drive.google.com/drive/folders/0BxJBjbxm46r4c3hhMlFrVmZYNk0

...

looks like an asian melonusk

It would have fitted already creatly if you didn't switch the twi names, ununderstandable decission

women in math are total whores

>exposed shoulder
t-this is a blue board guys

youtube.com/watch?v=MUt7_6MuF_g
Do you think she fugged mochi

>I climb on top of things, then kick the ladder away from the building and when people ask me how I got here, I tell them I flew. I just hope they don't find the ladder on the other side of the building.

>tfw Brian Conrad didn't go and write an awesome writeup like he did before

hope he goes to the next one senpai

>Not trying to get the seed of one of the smartest men alive

>tfw when no polish qt3 to call your own
H-hold me, /r9k/...

>rounding pi down to 3
She would be disgusted by your mere presence

This.

She doesn't seem to be a male homosexual, and therefore definitely not an engineer, so she wouldn't mind.

That Fesenko guy organized the workshop, I don't think you can trust him.

I think this gives a better idea of what's going on.

math.columbia.edu/~woit/wordpress/?p=8663

Fesenko btfo

...

because books assume you actually want to learn
not just eat up simple explanations to feel good about yourself

Thanks, I was looking for that webm but had to settle for the jpeg

>IUT actually isn't a meme.

Oh god...soon we'll have that stupid fucking >le little girl staring through universes analogy taught in textbooks.

He's the hero math deserves, but not the one it needs right now. So we'll hunt him. Because he can take it. Because he's not our hero.

LMAO

This is mindblowing. This Japanese guy solves the biggest math problem ever, and these dumbass Western mathematicians can't understand him and keep complaining that he didn't use standard notation even though they can't find a single flaw

more like books are so afraid of not being rigorous enough that they become trash

Can someone explain this to me? Wasn't the IUT supposed to solve the abc conjecture? How exactly does it do that? What does algebraic theory have to do with number theory, and these visual representations?

He looks like his mother picked his clothes out for him

>he didn't use standard notation
>they can't find a single flaw

You are contradicting yourself.

You mean he looks great?

That's not what's happening.

>What does algebraic theory have to do with number theory
Do you know any math at all? I don't see how you expect to understand his work.

Obiously

>Do you know any math at all? I don't see how you expect to understand his work.
Think of it as a challenge to test your understanding of his theory, to try to explain it as simply as possible

>can someone explain to me in simple terms this theory that is so complex that only a hand full of people understand it
Nice bait

The world's leading experts in number theory have been dedicating entire conferences to trying to pin down the ideas behind Mochizuki's recent papers, and haven't been particularly successful. You expect Veeky Forums to give you a concise explanation that involves 0 knowledge of mathematics?

Someone explain to me, as someone who doesn't know much about uni level math, what the fuck am I looking at?
Is there any physical representation of this?
How is this useful in what way?

>How is this useful in what way?
It helps us solve a lot of problems we couldn't solve before?

>You expect Veeky Forums to give you a concise explanation that involves 0 knowledge of mathematics?
That's exactly what I'm expecting

How? What problems?
>The 500-page proof was published online by Shinichi Mochizuki of Kyoto University, Japan in 2012 and offers a solution to a longstanding problem known as the ABC conjecture, which explores the fundamental relationships between numbers, addition and multiplication beginning with the simple equation a + b = c.
How is this even a problem in mathematicians eyes?
1+2=3 because if you put together a set of 1 point and a set of 2 points, you'll end up with a set of 3 points.
2*3=6 because 2 sets of 3 points, or 3 sets of 2 points, equals 6 points in total.
How can numbers possibly go any deeper?

(You)

en.wikipedia.org/wiki/Abc_conjecture

Ignoring your ignorance on the topic, he did more than just prove the ABC conjecture. He has formalized a whole new set of ideas regarding deforming number fields that could be revolutionary.

I was in that workshop

Ask me anything

Were you in that workshop?

stop shilling this fucking jap hack you weeaboo

Yeah, I am not a notable mathematician, but I speak Japanese, so I sent an email to Fesenko and he invited me

I am working towards a standardization of the work of Mochizuki, but this is so huge. The guy basically invented a whole new field on his own.

Did you meet the Wingding Samurai?

But Fesenko isn't japanese nor was the language of conduct of the conference

Yes, and? Mochizuki does.

What is that thing around his neck? A Phylactery?

A Soul Gem. It contains the souls of dead mathematicians he assassinated ninja style to gain their power.

>A Soul Gem
Mochizuki confirmed to be a magical girl.

I have no clue what any of this means. How would you explain it to someone who has only taken Calc 1 2 3

>How would you explain it to someone who has only taken Calc 1 2 3
You wouldn't.

Take Calc 5

You need to be able to solve tripe integrals. But none has managed to do that yet.

>mfw IUTT 'clicks' and you realize that the ABC conjecture is now Mochizuki's theorem

so does it mean somebody has found a way to write good Object-oriented code?

It's a device that links him to Nyarlathotep.

All those front row seats empty

Man id be suckin dick up there asking a miilion questions this shit would go hours longer because of me

Does Mochi only gives midnight lectures?

Is Mochizuki as eccentric as people say? Can you tell some stories?

I also noticed lot of the great mathematicians that went to Oxford's workshop didn't attend Kyoto's, with few exceptions. Do you think people are giving up? What did the participants think?

By participants read *real* participants. Not Fesenko's friends on unrelated fields.

Hi guys just wanted to ask where can I begin study his theory and what do I expect? I don't want his proof of this shitty theorem I'm just curious about the theory around it.

>kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf

see

...

no, just a low-grade master's student, and that description of the canonical deformation/theta-link is probably frighteningly inaccurate

Haha, that guy is funny. Begin your reading right at
>kurims.kyoto-u.ac.jp/~motizuki/Alien Copies, Gaussians, and Inter-universal Teichmuller Theory.pdf
>Page 5

>Here, let us recall that our hypothetical high-school student was already in a mental state of extreme frustration as a result of the student’s intensive and heroic attempts in Step 2 which led only to an endless labyrinth of meaningless and increasingly complicated mathematical expressions. This experience left our hypothetical high-school student with the impression that the Gaussian integral was without question by far the most difficult integral that the student had ever encountered. In light
of this experience, the suggestion of Step 3 evoked a reaction of intense indignation and distrust on the part of the student. That is to say, the idea that meaningful progress could be made in the computation of such an exceedingly difficult integral simply by considering two identical copies of the integral — i.e., as opposed to a single copy — struck the student as being utterly ludicrous

>sidenote: which one of you runs this bizarre twitter account?
>twitter.com/math_jin
sup

The problem I think is basically that
1. Mochizuki refuses to rewrite material, on the grounds that this should not be necessary, people should just spend the time it takes to understand what he has written.

2. The small number of people who were supposed to have digested this material, and rewrite it in this manner (e.g. Go Yamashita), have not been able to complete this task.

3. Others have been unable to digest the material. If you can’t understand yourself why a proof works, you’re not going to be able to rewrite it for others to understand.

That, four years later, no one else has been able to write up their own version of the proof is the central mystery here.

I can teach any child what evolution is in 3 sentences. It will then be able to identify evolutionary processes.

You can give the origin of species to 50 people before you get bored by the obvious uselessness of that action.

If you you take 2 spagetti horizontally and lay 3 spagetti vertically over them and then you count the intersections you will have calculaterd what 2*3 is. This works for any number of spagetti

were there a lot of anime fans there? How many of the people there just applied because they think they know japanese?

>Mochizuki refuses to rewrite material, on the grounds that this should not be necessary
The absolute madman.

This is basically good culture in the making. If I was an Author I would do it the same way.

What about angel hair?
Cooked or uncooked?

I just came here to see some funky ass heiroglyphics honestly

>physical representation
>taking place in our universe


HAH! oh my dear boy.

>"You can deduce everything from nowhere... basically"

DROPPED

if you love funky ass heiroglyphs and math, learn the APL programing language

>heiroglyphs
>programing language

So could this stuff ever have a physical application, or is it pure masturbation with numbers?