/sci/ - Science & Math

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

>>8249606
>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, anon? It's the secret to mathematics

>>8249606
In section 3.2 of
https://www.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),

>>8249606

>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 /sci/.

>>8249625

>>8249625
>>8249619
>>8249609


thanks

>>8249591
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.

>>8249628
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.

>>8249676
wrong

>>8249591
Mochizuki lookin hella /fa/

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

>>8249628
>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: https://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.

>>8249693
Why can't books explain math like this?

Thanks friend

>>8249734
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: https://drive.google.com/drive/folders/0BxJBjbxm46r4c3hhMlFrVmZYNk0

>>8249846

>>8249846
looks like an asian melonusk

>>8249846
It would have fitted already creatly if you didn't switch the twi names, ununderstandable decission

>>8249847
women in math are total whores

>>8249847
>>8249983
>exposed shoulder
t-this is a blue board guys

>>8249983
>>8250004
https://www.youtube.com/watch?v=MUt7_6MuF_g
Do you think she fugged mochi

>>8249676
>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

>>8250015
>Not trying to get the seed of one of the smartest men alive

>>8249847
>tfw when no polish qt3 to call your own
H-hold me, /r9k/...

>>8250110
>rounding pi down to 3
She would be disgusted by your mere presence

>>8250118

This.

>>8250118
She doesn't seem to be a male homosexual, and therefore definitely not an engineer, so she wouldn't mind.

>>8249591
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.

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

>>8250149
Fesenko btfo

>>8249619

>>8249734
because books assume you actually want to learn
not just eat up simple explanations to feel good about yourself

>>8250341
Thanks, I was looking for that webm but had to settle for the jpeg

>>8249591
>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.

>>8250149
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

>>8250371
more like books are so afraid of not being rigorous enough that they become trash

>>8250341
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?

>>8249846
He looks like his mother picked his clothes out for him

>>8250985

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

You are contradicting yourself.

>>8250999
You mean he looks great?

>>8250985
That's not what's happening.

>>8250991
>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.

>>8251007
Obiously

>>8251008
>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

>>8250991
>>8251012
>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

>>8251012
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 4chan to give you a concise explanation that involves 0 knowledge of mathematics?

>>8250341
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?

>>8251021
>How is this useful in what way?
It helps us solve a lot of problems we couldn't solve before?

>>8251020
>You expect 4chan to give you a concise explanation that involves 0 knowledge of mathematics?
That's exactly what I'm expecting

>>8251026
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?

>>8251040
(You)

>>8251040
https://en.wikipedia.org/wiki/Abc_conjecture

>>8251040
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

>>8251073
Were you in that workshop?

>>8249591
stop shilling this fucking jap hack you weeaboo

>>8251078
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.

>>8251084
Did you meet the Wingding Samurai?

>>8251084
But Fesenko isn't japanese nor was the language of conduct of the conference

>>8251093
Yes, and? Mochizuki does.

>>8249846
What is that thing around his neck? A Phylactery?

>>8251101
A Soul Gem. It contains the souls of dead mathematicians he assassinated ninja style to gain their power.

>>8251112
>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

>>8251140
>How would you explain it to someone who has only taken Calc 1 2 3
You wouldn't.

>>8251140
Take Calc 5

>>8251140
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

>>8249591
>>8249619
>>8249625
>>8249630
>>8249693
so does it mean somebody has found a way to write good Object-oriented code?

>>8251101
It's a device that links him to Nyarlathotep.

>>8249846
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

>>8249846
Does Mochi only gives midnight lectures?

>>8251084
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.

>>8249591
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.

>>8252028
>http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf

>>8252028
see
>>8249619

>>8249693

>>8252047
no, just a low-grade master's student, and that description of the canonical deformation/theta-link is probably frighteningly inaccurate

>>8249591
Haha, that guy is funny. Begin your reading right at
>http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf
>Page 5

>>8252114
>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

>>8249591
>sidenote: which one of you runs this bizarre twitter account?
>https://twitter.com/math_jin
sup

>>8249591
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.

>>8250371
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.

>>8250991
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

>>8251093
were there a lot of anime fans there? How many of the people there just applied because they think they know japanese?

>>8253741
>Mochizuki refuses to rewrite material, on the grounds that this should not be necessary
The absolute madman.

>>8253741
This is basically good culture in the making. If I was an Author I would do it the same way.

>>8253812
What about angel hair?
Cooked or uncooked?

I just came here to see some funky ass heiroglyphics honestly

>>8251021
>physical representation
>taking place in our universe


HAH! oh my dear boy.

>>8250015
>"You can deduce everything from nowhere... basically"

DROPPED

>>8254117
if you love funky ass heiroglyphs and math, learn the APL programing language

>>8254276
>heiroglyphs
>programing language

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

>>8255174
https://www.physicsforums.com/threads/practical-applications-of-number-theory.253687/

>>8255174
at this point there is no more number. It litteraly deals with logic formulae and their interpretation in different model (thus the IUT name) and try to retrieve properties to transfer and other which change in order to say new things about some usual objects.

Concerning application, there are powerful theorem from number theory which can be solved this way (it's actually why he did all this machinery). In turn those theorem are readily appliable in other branch of mathematics : some are even useful for crypto or fundamental complexity questions. There are some use in theoretical physic which relies on algebraic geometry. Nowadays, you can't do anything without manifolds/varieties let's be real.

For end user, there is nothing, but please don't say it's useless, it's like saying 19th century's math and distribution theory was useless until jpeg appeared...

>>8255289
>you can't do anything without manifolds/varieties
Well, you can do well without varieties.

>>8255308
but they're linked to one another. And you've been studying baby tier varieties since middle school.

>>8255366
>they're linked to one another
More like varieties to manifolds, not vice versa. You don't even have to know varieties studying Einstein manifolds in relativity for instance or topological manifolds.
>baby tier varieties since middle school
You don't need any notion of variety here. Galois theory + complex analysis is overkill for this purpose but it still has no word "variety" in it. Except for when you purposely put it. But it would be wishful thinking.

>>8249591
what practical applications does IUT have?

>>8251329
>good
>Object-oriented code

>>8249625
>>8249630
This is so well written

>>8255472
>Related issues.
>It is clear how crucial long-term work is for real breakthroughs in mathematics. Questions arise such as how to increase the number of researchers able to work for a long time on fundamental problems so sedulously and successfully and what should be the amount of support to this strategically important type of
research work.
>Some roots of the decline of support to long-term fundamental work, such as the shortsighted race to higher number of publications and higher citation index, which often results in pressure to produce short-term work that consists essentially of minor improvements to known results, originate from causes external to the mathematical community. To do well in their academic career, young researchers are very often pushed to go along this path which typically implies a very narrow specialisation. The latter leads to the emphasis on technical perfection as opposite to innovation and on presentation rather than substance of work. Following this path
eventually makes it more difficult to think in broader terms, to learn new concepts, to develop in new directions. Lack of inventiveness, more widely spread imitation, very pragmatic attitudes to what and when to study in mathematics, lack of genuine enthusiasm to study new theories, fear to stand alone in scientific endeavour,
fear to look too far away are associated issues.
>**Some roots, such as the unnecessarily strong emphasis on
concrete applications**, originate from within the mathematical community.
>There is an issue about attitudes of number theorists towards the study of IUT and their unusually sluggish response. Reasons for this are related to the topics discussed in the third paragraph of 3.3 and in the previous paragraph. It seems that the number theory community is suffering from the problems listed there even more
than other mathematical communities.

And >>8255275
But really it's too early for this question

>>8255486
Well, It did take him 10 years to write it. He took his sweet time to perfect the paper. Still Mochizuki, still giving it to the bitches.

>>8255438
>More like varieties to manifolds, not vice versa.

The dual use comes into play more in like String Theory w/ calabi-yau manifolds and other complex manifolds. B/c of the whole GAGA thing.

>>8255504
Yes but it's not like "you can't do anything without varieties". I mean seriously.

>>8255174
>physical application
>>8255472
>practical applications


Yes, see the paper 'Yang-Mills Theory and the ABC Conjecture' http://arxiv.org/pdf/1602.01780v1.pdf

Why is everyone just talking out of their ass?

>>8255609
Becuz string theory is not physics nor mathematics :3

>>8255659
N = 4 SYM does not rely on string theory, you could say you could rely on N = 4 SYM when studying string theory but not the other way around.

>>8255609
>"stop talking out of your ass guise"
>posts supersymmetry

This is awesome! I was already on the brink of desperation and starting to think Mochizuki was just crazy and shit, but no, he certainly wasn't! Or actually, he is crazy in the way one is an absolute madman, not like those guys ezplaining the universe through conscious aether flows etc.

>>8252037
MAKI DOESN'T SMOKE

>>8251213
>mfw
>and you

Unforgivable

>>8250985
DAMN HWHITE WASCISTS!!!!

>Kedlaya’s opinion is the one likely to carry most weight in the math community, since he’s a prominent and well-respected expert in this field.

. . . WAIT A SECOND!

>Kiran Sridhara Kedlaya is an Indian American mathematician.

>>8256560
>Kiran Sridhara Kedlaya
This guy has some serious street cred, not nearly to the level of Ravi Vakil though

Do you ever consider pretending to be autistic if you ever proved something like this or poincare conjecture (i know theres a tiny chance any of us would) just to fit in with these guys?

>>8256767
whoever solves the next millennium problem really should reject the million just for the sake of it

>>8256823
Honestly if they did it would put a ton of pressure on everyone else who solved one to do it too. Not sure how I feel about that. Most mathematicians who are devoted enough to do it probably won't care about the money, though.

>>8256842
If anyone solved any of those equations, wouldnt they get shit loads of well paying job offerers?

>300k starting

>>8256846
>If anyone solved any of those equations, wouldnt they get shit loads of well paying job offerers?

Well they would from any math department that pays that good. Which there aren't that many of.

>>8252037
>>8255860
Take your pedophile cartoons back to >>>/a/.

Fucking degenerates.

>>8256851

> implying anybody solving a problem on the scale of the millenium problems is on an actual jobhunt.

I dont understand anything of this

>>8256823
>millenium problem
So you think this development will allow to solve them?

>>8249676
So you're saying you don't have the first clue what it means. Gotcha.

>>8249591
>“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.”

Holy fuck, what a time to be alive. Pure nerdchills.

>>8256851
There is a mathematical physicist at my school making >400k a year. I want to be that.

>>8254288
This looks like Haskell.

>>8257761
probably not, i was just following the reference to the poincare conjecture in the post i quoted

mochizuki wrote some remark about the riemann hypothesis in one of these IUTT papers but i dont think it was any sort of strategy to solve it

>>8249591
>The Yokozuna Blossoms

what do you mean?

>>8258072

>>8258054
>filename

And yeah, it's the definition of the List functor action on functions

>>8258084
thank you based 'zuki

thank you based 'zuki

>>8249846
how do I get swole like Mochizuki?

>>8258084
Merci, 'Zuki le basé.

>>8258086
>Big words mean big ideas!!
It's a fucking map function just shut the hell up already.

Christ you retards are annoying.

>>8258470
>>>/out/

How is this even useful? All I see is complicated math puzzles for mental masturbation

>>8249591
>mochizuki actually was not full of shit and was legitimate
Whelp time to go piss 10 years on learning an entirely new math field.

>>8258481
That shit might not seem useful now, but who knows.

>>8258481
it proved the abc conjecture

>>8258533
>>8258551
>number theory
meh, not really my thing but I can see why you guys are excited about it.

>>8258481
I don't know anything about IUT, but I do know it is based on Arithmetic Geometry.

Arithmetic Geometry allows for geometric approaches to problems in algebraic number theory.

I know solutions to problems in number theory can have applications to computer science. So maybe many years from now when it is better understood, IUT could have applications to computer science.

who wants to start writing an introductory IUTT textbook?

we can cook up some nice exercises so the more intimidated students can get some experience using the theory

Has Little Terry been BTFO?

>>8258734
daily reminder
https://terrytao.wordpress.com/2016/06/04/it-ought-to-be-common-knowledge-that-donald-trump-is-not-fit-for-the-presidency-of-the-united-states-of-america/

who's another top researcher at RIMS? i know of Mukai, and have heard of Hoshi through the IUTT conferences but not many others

http://www.kurims.kyoto-u.ac.jp/en/list-01.html

>>8258077
holy shit this is beautiful

>>8258084
thank you based zuki

>>8249600
numbers are freakin NUTS

>>8258743

This article is trash though

Terence is good at math, and that's all

>>8258802
True. He's not even that good at giving lectures.

>>8258811
yeah he seems pretty shy

>>8258734
did terry do anything on this level?

>>8258908
>did terry do anything on this level?

lolno

He proved some open stuff but he hasn't invented any crazy new techniques and theories like this. Plus abc was thought to be extremely hard, far harder than anything he's proved.

>>8258929
that is what i though

>>8258933
k

>>8258933
t

>>8253741
>this was allowed to happen because it's 2016 and being politically correct is more important than forcing a mentally disabled jap number magician to divulge his knowlege properly

should've sent the inquisition

>>8255487

that is some plain fucking english
was not expecting
will probably tattoo it on my back and frame it in my office

>>8258942
You are clearly having butthurt because this "jap" is the one to solve the hardest problem and others are unable to even understand his work.

>>8258961
>"jap"

i'm being facetious, friend

>>8258942
>it explains the IUT or it gets the nuke again

>>8258992
He does pretty much to explain his work. But c'mon it took him 20 years to write, it could take another 20 to explain others.

>>8259019
https://www.youtube.com/watch?v=UN-nRM_ZCGs

On the Verification of Inter-universal Teichmuller Theory: A Progress Report (as of December 2014):
http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

>On the other hand, my experiences over the years in educating various students such as Hoshi (cf. the final portion of (4) above, as well as the discussion at the beginning of (6)), as well as of listening to the comments of various researchers who encountered substantial difficulties in their study of IUTeich and related topics, have left the following impression on me: From the point of view of achieving an effective solution to this sort of problem, the most essential stumbling block lies not so much in the need for the acquisition of new knowledge , but rather in the need for researchers (i.e., who encounter substantial difficulties in their study of IUTeich and related topics) to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.

sounds like number theorists are scared to admit they're back at square one when reading these papers

>>8259672
They're not "scared" they just don't want to devote a year to understand some shit that may or may not pay off. They got their own research to think about.

>>8259672
> the need for researchers (i.e., who encounter substantial difficulties in their study of IUTeich and related topics) to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.
That is a kind of strange thing to say considering how advanced prerequisites to his theory are.

>>8259728
Perhaps he's referencing the concept of "beginner's mind": https://en.wikipedia.org/wiki/Shoshin

Mathematicians(not plebs) join ##sci in webchat.freenode.net and let's discuss IUT

Type /join ##sci upon connecting

>>8249847
>that creep staring at the smug qtπ

>>8259909
kek

>>8258084
thank you based 'zuki

>>8251101
A specialized sonichu medallion.

>>8249591
I portend that his paper will be the greatest. Idiots will retract their stupid, ignorant statements.

>>8258481
Mental masturbation today means the mushrooms of science growing on mental cumrags tommorow.

>>8258743
>like

>>8260426
nice

>>8260426
That's a disturbingly accurate metaphor. N-not that I've experienced anything like that, o-obviously.

>He refuses to travel abroad, only speaking via Skype at the Oxford meeting
He's an obvious fraud.

>>8261652
just because you refuse to read his papers doesn't mean he has to fly to your house to teach you it

I was in the Kyoto conference and I'm starting to slowly understand the material. I've been working with Hoshi, Yamashita and a few others on a more accessible introduction. Stay tuned.

>>8261688
Does this theory change the way you look at baby tier arithmetic problems? Does it make it easier to understand some trivial concepts / solve some interesting class of problems we couldn't before?

>>8261730
Blimey, I just wrote a lengthy reply, but lost all of it because of Firefox's stupid Ctrl+Q binding, so here's just the tl;dr:
>Does this theory change the way you look at baby tier arithmetic problems?
No (at least not yet), in the same sense that topos theory doesn't change the way you look at sets.
>Does it make it easier to understand some trivial concepts / solve some interesting class of problems we couldn't before?
I don't think it makes anything easier (at least at this point). If anything, it makes certain things possible. We're currently working on transporting some of the techniques to existing mathematical settings so that a larger portion of the community can join, learn, use and research the theory.

By the way, the paper linked in OP, 'From Gaussian Integral to IUT' is really good. The first chapter should be accessible to anyone with a freshman-level Calc knowledge, the last chapter is also useful. It gets a wee bit hairy in between, but experts in the field should be able to grasp that.

I don't practice math much, but I just want to say how proud I am of you guys who do, who are interested and fascinated by it. You have my eternal gratitude for carrying the torch of human ingenuity toward new horizons.

I just wanted to get this off my chest. Godspeed, blessed anons.

I still don't get why Mochi refuses to travel abroad and answer questions. Isn't it a little arrogant? Or does he have a phobia for planes?

>>8258942
>forcing an autist to do something
you know so little and yet you have such a loud mouth

>>8261852
your brainlet mind couldn't understand.

he sees things we don't

I don't know much math past the Calculus (Calculi?) and I would even need to brush up on those, but this looks interesting to me. Would it make sense for me to start working my way through these prerequisites >>8249619
and whatever other prerequisites they might have, while ignoring unrelated areas of advanced mathematics? I mean as a personal interest thing, not professionally.

>>8261910
You can try, but be prepared to work fuckton of hours every day for a few years until you will be able to comprehend even the prerequisites. It might be better to just sit tight and wait for more experienced lads to do the hard work and read up on what they chewed for us mortals later.

>>8261852
He's very available via email, and answers questions carefully and thoroughly. It's 2016, he doesn't need to travel to answer questions.

>>8260426
Truly disgusting. The Faraday quote does not really apply here.

>>8261629
fuck off to leddit

>>8262812
Don't tell me what's inside the bottles.

>>8258084
thank you based 'zuki

>>8249591
>this is what mathematicians do all day
And then you wonder why your profession hasn't been relevant in decades.

>>8262884
Mathematics is more relevant today than ever before.

>>8261802
k

>>8262812
>fuck off to leddit
>posts le reddit pic
wew

>>8261802
Thanks anon.

>>8261802
top autism

>>8261802
This is the sort of thing drunk people say about three minutes before the inconsolable sobbing phase begins.

>>8263419
Speaking from experience?

>>8263461
Are you accusing me of having interacted with drunk people?

How dare you, sir.

>>8263465
My sincere apologies, m'lord. I most certainly did not intend to insinuate any kind of indecent behaviour on your part.

>>8263411
Checked

>>8250985
Can you be anymore of a weeb faggot?

Is arithmetic geometry the new category theory?

>>8261852
too busy proving the Riemann Hypothesis senpai

>>8264122
>praise European
>nothing wrong

>praise American
Europeans: EW STOP PRAISING TERRORISTS PLSSSS

>praise non-Japanese Asian
Europeans: EW STOP PRAISING PAJEET PLSSS

>praise Japanese
Europeans: EW YOU WEEB

But do start posting IQ graphs saying "Asians are smarter, b-but we're more creative!!".

>>8262174
>tfw you'll never get a love email from Shinchan

>>8264285
I don't think so. Arithmetic geometry is much more narrow than category theory.
Categories are memes (on /sci/) because they are so general and can be applied to anything, even when it make little sense to do so, such as in physics. Sure string theorists might use category theory for algebraic geometry and D-branes and stuff, but there are people trying to phrase everything relating to mathematical physics in categorical terms and it makes no sense. You see the same thing in other areas of mathematics, and that is why I think this board mislikes categories.
Arithmetic geometry doesn't have the same generality - it just lets you do some stuff in number theory.

>>8265795
I meant it in the memery sense, so yeah, it is.

>>8265795
>there are people trying to phrase everything relating to mathematical physics in categorical terms and it makes no sense.

It makes perfect sense. I could explain but you should just read this:

http://math.ucr.edu/home/baez/quantum/node1.html

Long story short, category theory is probably going to be a major element in any theory of quantum gravity.

>>8265849
No it's not a "meme" you moron. It's a legitimate field of math research that has been going on for decades.

>>8265956
It's been going nowhere until Mochi came and now it's lively again, that's fits the definition of a meme.

>>8249847
>nip with a mask
Is this considered normal there? Is IUTT that dangerous?

>>8251058
>that could be revolutionary
>could be
yawn

>>8265996
>Is this considered normal there?
Actually yeah, you'd be surprised

>>8260426
underrated post
nice

>>8265795
This reminds me of my ironic project to construct a categorical approach to economics. I personally have no idea about economics and this guy I did it with had no idea about the mathematical aspects of our work. I succeeded in topologizising his examples, but to construct an economical category was too much. My reasoning itself was sound but the premises I had to construct were really farfetched. "That's economics" is what this guy always said.

>>8265978
That's patently false. I didn't expect the kind of person who calls things they don't understand memes to have any grasp on current research, though.

>>8266024
>meme, n.
>Any unit of cultural information, such as a practice or idea, that is transmitted verbally or by repeated action from one mind to another in a comparable way to the transmission of genes.
kys faggot

>>8266026
>kys
Wow, you really are fucking 17 aren't you? That's not how you used meme. For instance, you specifically said "memery."

>>8266028
>not addressing the point
keep crying bae

thank you based 'zuki

why are japanese so selfish?
are they afraid the white man will beat them?

>>8266362
The opposite, they know whiteys have no match to their diligence and intelligence.

>>8258084
thank you based 'zuki

>tfw physics graduate and I will never understand this

>The photograph image shown on this Nature article during 3 days was illegally taken from the webpage of the workshop without getting any authorization from the workshop organizers. In his three Nature articles, its author very substantially misleads readers of Nature about the substance of IUT theory of Shinichi Mochizuki and its role, as well as as the outcomes of the two conferences on it and gigantic efforts of many mathematicians involved to present, discuss and study aspects of the theory. If anyone is to be "tormented" for "years to come", it is no doubt the author of these unsatisfactory Nature articles.
salty

>>8265795
> Arithmetic Spacetime Geometry from String Theory
https://arxiv.org/abs/hep-th/0510091

>>8265978
this is clearly false. just to name one example, higher topos theory is barely 7 years old and people are still working on developments in algebraic geometry, logic, and algebraic topology/homotopy theory based on discoveries in that book alone.

>>8265978
heck, the work of Andrei Okounkov which won him the fields medal (only three awards ago) is largely in the language of and uses techniques from the category-theoretic approach to algebra

>>8266647
>tfw aeronautical engineering

It's ok physics-friend

>>8265996
>Is this considered normal there?
Literally any sort of behavior is considered normal for mathematicians of their level
>Is IUTT that dangerous?
Esoteric samurai math is not to be trifled with

>>8266362
>confusing selfishness with autism

>>8261802
Faggot

>>8251390
>>8263224
Take your pedophile cartoons back to >>>/a/.

>>8249693
Theoretical math fucks my shit up, senpai.

>>8250495
>.gif

lel stop playing with file extensions

Bump for the math ninja.

>>8267274
>tfw organic chemist
(I love mathematical mumbo-jumbo though)

>>8265947
>implying Beaz didn't drop quantum gravity after decades of research and is now in something I can only phrase as "statistic methods motivated by wanting to deal with with climate change but not use boring math"

If Mochizuki is correct, does that mean he's the greatest living mathematician?

>>8270551
witten btfo

>>8265795
>there are people trying to phrase everything relating to mathematical physics in categorical terms and it makes no sense

Idk about that. This is actually a really good way to look at a QFT.

https://arxiv.org/pdf/math/0512103v1.pdf

>>8270336

Actually I didn't imply that at all...anyways, plenty of other people are working on it, and they're making tons of progress. Abramsky and Coecke's categorical setting for quantum protocols is only 12 years old, and Vicary recently just characterized QM using dagger limits.

>>8260426
does anyone have the picture of the mushrooms growing on the wanking sock or whatever it was?

>>8265996

>>8266015
>econ
>>8266015

I am extremely interested in what you have to say about that. Can you show some of what you did?

0192837465n@gmail.com

>>8270692
Define progress.

It's a "prettyfication" at best.

>>8272591

Progress can mean understanding the basic concepts underlying QM better, and seeing how they compare to other theories like GR. Quantum gravity is going to involve keeping the most essential aspects of QM and GR and removing whatever is extra or conjectural. You can only do this by carefully examining their structure. Category theory isn't the only way to do this but it definitely helps.

>>8266015
>implying you can't just throw literally any math at economics and it won't make less sense than the "serious" models

>>8271572
sent ;^)

>>8271230
Tell me about that guy. Why does he wear the mask?

>>8273095
>Quantum social science is not about reformulating social science on a quantum size scale. The macroscopic world does not operate at the Planck scale. On prima facie, this obvious statement does not need any further explanation. However, if the human experience is centered around consciousness and the functioning of the brain, then we are much less sure to claim there is a total absence of quantum processes. Roger Penrose has proposed the idea that the brain can operate according to quantum mechanics.

>>8273402
A lotta loyalty for a hired PhD.

>>8273378
Oops, that was the wrong email.

pls resend.

1092837465n@gmail.com

>>8258802
why has 4chan become several times as political and reactionary and only a fraction as creative (not counting unflattering caricatures of libs)?
did all the conservatards just get together and decide to take a giant dump on moot's website one day?

>math so advanced nobody else is able to follow it

Is he the greatest of all time or just crazy?

>>8274113

Conservatives are being pushed out of the public discourse because their beliefs have been widely disproved. For the first time they have felt what it is like to be marginalized like they have done to actually valid political perspectives for decades. In their desperate bid to reclaim the narrative and spurred on by the likes of Trump they have become toxic and very vocal. We just have to wait as the youngest of them grow up and see the real world and the oldest of them finally die of old age.

>>8258743
like

>>8274150
>widely disproved

>>8274150
This more or less. I've been on 4chan since 2004. It's mostly perpetuated by the people who now populate /pol/ and /r9k/.
>my life isn't everything I dreamed it would be and I need something to blame

>>8274150
I kind of hope Teump wins though so he can destroy the standing of the Republican party for good. Conservatives are right about Islam and SJW feminists being toxic undesirables though.

>>8274290
From the ashes of the republican party will rise a new, even further right wing party.

Careful ese.

>tfw genius and none of this crap will ever be relevant to your life and work

Number theory is the meme discipline to end all meme disciplines.

>>8274113
But he's right. I'm not even conservative.

>>8273095
>>8273441

If our thoughts are to be subject to quantum law, then individual neurones must be able to be in a superposition of firing and not firing.

This would mean that around a million sodium atoms would have to be in two places at once: both inside and outside the neurone.

Quantum superpositions can only exist providing that they are not 'observed' or interacted with.

So how long could a neurone exist in a superposition, without being interacted with?

Approximately 10^-20 or ten billionths of a trillionth of a second.

That's how long it would typically take before a random water molecule bumped into one of the sodium atoms and collapsed the wave function.

In light of this, you would have to be able to think 10,000,000,000,000 thoughts per second in order for your thoughts to correspond to a quantum computation.

>>8274113
>>8274150

Spoken like a true delusional libtard.

It would make a bit of sense if only we lived in a parallel dimension where leftard supported BLMs didn't shoot cops and attack innocent citizens, and maybe islamic terrorists didn't gain power to infiltrate everywhere with your support, and taxpayers money didn't go to lazy leeching rapefugees.

Then maybe you'd have some moral grounds to call people and ideas "toxic" and maybe someone would take you seriously. Now please kill yourself so we can all live in a civilized world.

>>8274120
about 10people could follow until date. thats what they claim at least. maybe they are crazy too.

>>8273095
This is precisely where he got the idea from. My constructions were like this:

If there is a city with n car owners and n parking spots, and the city decides to make the owners pay sums depending on some property, one can topologize the set of car owners with a Zariski-like way. Choosing any sum of money, define an open set to be the set of car owners ready to pay this sum. To keep it real, n is an integer, and so there exists an owner with the most money, say m. One can easily check that the set of owners ready to park for free is the whole set and the set of owners ready to pay m+1 is empty. Moreover, the intersections correspond to raising the costs and unions to lowering them. This gives a non-Hausdorff topology for the set of car owners in the city.

We then constructed another topology for the same set with respect to some property I can't remember, and used these two to construct the third with open sets the finite intersections of the sets from both these topologies. This gave us a finer topology than the one described above, so we could then define an open "preference function" as he called it to somehow simulate the accumulated effect of price and the other property.

This all went rather well until we decided to construct an "economical category". One approach was to have different companies represent the objects and investments in other companies represent the hom-sets. This lead to a category equivalent to one created from a preordered set, since the only reasonable way to do the investments was to either have Hom(A, B) empty or a singleton, but we were pursuing an Abelian category so that we could have embedded it into some module category, but that didn't quite work out and I said I had better and more important thongs to do.

>>8275392
>thongs
LOL, things*

>>8274919

Luckily I have already won the debate in the public arena and your ideas have been systematically demolished by both the experience of the average person and academia. I know you think that repeating your ignorance will change this, but we've already heard your ignorance for decades. It had its time and it crashed our economy and eroded the social fabric of our society. Victim blaming is being discredited. Racism is being discredited. Xenophobia is being discredited. Your ideas have lost the debate. Go back to your cave. We don't care that you're angry.

>>8274120
more like nobody cares ,lel

Anyone have that anime song about IUTeich?

>>8274113
Social self-segregation processes. See Schelling or Axelrods' models.

>>8275710
>we are winning
>even though the far right (not cuckservatives, the true far right) is bigger than ever since the 30s

>>8275765

Nah, just more vocal because they are more marginalized than ever. They are being pushed into a corner where they can shout it out, like when you put a child in time out.

>>8275773
>biggest party in Sweden
>50% in Austria
>54% in Britain
>every single other party had to team up to defeat them in France
>second biggest party in Germany (where being Nazi is like killing your mother)

And this aren't just Reagan-type conservatives or something. This is full blown xenophobia we are talking about here.

>>8275710
Xenophobia has a place though. We shouldn't allow Islam to take more and more control, as anyone who has read the Quran like me would know.

>>8249591

>>8274299
Doubt it. If the Republicans fell apart, the Libertarians would replace them long before nationalists

>>8274150
Actually, science proves everything that reactionaries say about race true.

so whats this "japanese tradition" of mathematics?

>>8249847
>white bitch looking pensive while not taking any notes

>>8277988
what's that on her lap?
>>>/r9k/