>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.”
>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
I wonder what fields of mathematics one needs to be proficient in, in order to actually understand the proof.
t. undergrad physicist
Matthew Martin
this is big gentlemen
shame the guy is super autistic, he's the kind of brain that could pull humanity into a new century
Sebastian Phillips
>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
Carter Clark
Why aren't you doing aikido, user? It's the secret to mathematics
Nicholas Perry
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),
Dominic Allen
...
Sebastian Cooper
>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.
Julian Nguyen
...
Cameron Ross
thanks
Elijah Diaz
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.
Jacob Gutierrez
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.
Jaxson Wilson
wrong
Evan Nguyen
Mochizuki lookin hella Veeky Forums
Adam Powell
>inb4 someone asks whether the proof goes through in Peano arithmetic
Samuel Young
>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.
Jackson Reyes
Why can't books explain math like this?
Thanks friend
Jason Cook
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.
>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.
William Cox
>tfw Brian Conrad didn't go and write an awesome writeup like he did before
hope he goes to the next one senpai
Justin Russell
>Not trying to get the seed of one of the smartest men alive
Justin Miller
>tfw when no polish qt3 to call your own H-hold me, /r9k/...
John Powell
>rounding pi down to 3 She would be disgusted by your mere presence
Nathan Nguyen
This.
Cooper Collins
She doesn't seem to be a male homosexual, and therefore definitely not an engineer, so she wouldn't mind.
Carson Robinson
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.
because books assume you actually want to learn not just eat up simple explanations to feel good about yourself
Justin Sanchez
Thanks, I was looking for that webm but had to settle for the jpeg
Chase Campbell
>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.
Aaron Harris
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.
Jaxon Nguyen
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
Hudson Morales
more like books are so afraid of not being rigorous enough that they become trash
Zachary Butler
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?
Justin Davis
He looks like his mother picked his clothes out for him
Samuel Bailey
>he didn't use standard notation >they can't find a single flaw
You are contradicting yourself.
Blake Green
You mean he looks great?
Landon Robinson
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.
Thomas Cox
Obiously
Christopher Green
>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
Zachary Bennett
>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
Elijah Parker
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?
Parker Sullivan
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?
Connor Jackson
>How is this useful in what way? It helps us solve a lot of problems we couldn't solve before?
Eli Nguyen
>You expect Veeky Forums to give you a concise explanation that involves 0 knowledge of mathematics? That's exactly what I'm expecting
Levi Gonzalez
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?
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.
Christopher Edwards
I was in that workshop
Ask me anything
Brayden Campbell
Were you in that workshop?
Landon Foster
stop shilling this fucking jap hack you weeaboo
Kayden Barnes
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.
Andrew Peterson
Did you meet the Wingding Samurai?
Gabriel Anderson
But Fesenko isn't japanese nor was the language of conduct of the conference
Asher Clark
Yes, and? Mochizuki does.
Ayden Foster
What is that thing around his neck? A Phylactery?
Ryder White
A Soul Gem. It contains the souls of dead mathematicians he assassinated ninja style to gain their power.
Ethan Turner
>A Soul Gem Mochizuki confirmed to be a magical girl.
Connor Turner
I have no clue what any of this means. How would you explain it to someone who has only taken Calc 1 2 3
Hudson Perez
>How would you explain it to someone who has only taken Calc 1 2 3 You wouldn't.
Cooper Fisher
Take Calc 5
Dylan Adams
You need to be able to solve tripe integrals. But none has managed to do that yet.
Chase Powell
>mfw IUTT 'clicks' and you realize that the ABC conjecture is now Mochizuki's theorem
Alexander Thompson
so does it mean somebody has found a way to write good Object-oriented code?
Angel Jackson
It's a device that links him to Nyarlathotep.
Wyatt Wilson
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
Henry Taylor
Does Mochi only gives midnight lectures?
Jason Kelly
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.
Jason Hall
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.
>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
Nicholas Bailey
>sidenote: which one of you runs this bizarre twitter account? >twitter.com/math_jin sup
Bentley Baker
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.
Adrian Young
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.
Wyatt Gonzalez
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
Nolan Campbell
were there a lot of anime fans there? How many of the people there just applied because they think they know japanese?
Blake Nelson
>Mochizuki refuses to rewrite material, on the grounds that this should not be necessary The absolute madman.
Wyatt Brown
This is basically good culture in the making. If I was an Author I would do it the same way.
Samuel Hernandez
What about angel hair? Cooked or uncooked?
Alexander Brooks
I just came here to see some funky ass heiroglyphics honestly
Josiah Gutierrez
>physical representation >taking place in our universe
HAH! oh my dear boy.
Nolan Clark
>"You can deduce everything from nowhere... basically"
DROPPED
Charles Nelson
if you love funky ass heiroglyphs and math, learn the APL programing language
Lincoln Roberts
>heiroglyphs >programing language
Lucas Anderson
So could this stuff ever have a physical application, or is it pure masturbation with numbers?