If nobody understands a mathematical proof, does it count?

[Anonymous No.7334891]

If nobody understands a mathematical proof, does it count? Shinichi Mochizuki of Kyoto University, Japan, has tried to prove the ABC conjecture, a long-standing pure maths problem, but now says fellow mathematicians are failing to get to grips with his work.

http://www.newscientist.com/article/dn26753-mathematicians-anger-over-his-unread-500page-proof.html#.VYD1-FnBzGc

[Anonymous No.7334897]

>>7334891
>Most common mochi
>not even busting out moderate rares
>expects post to be taken seriously

[Anonymous No.7334899]

>>7334891

“For better or worse, no such researcher exists (other than myself) at the present time,” Mochizuki writes (his emphasis). The paradox is that usually the mathematicians that do proof verifications only engage with the topic at hand in “nibbles.” And, for more reasonable topics, nibbling is enough to determine if something is or isn’t correct. This is not the case here, however, and whoever verifies this proof will need to be already deep in it. Alas.

“With the exception of the handful of researchers already involved in the verification activities concerning IUTeich discussed in the present report,” Mochizuki continues, “every researcher in arithmetic geometry throughout the world is a complete novice with respect to the mathematics surrounding IUTeich, and hence, in particular, is simply not qualified to issue a definitive (i.e., mathematically meaningful) judgment concerning the validity of IUTeich on the basis of a ‘deep understanding’ arising from his/her previous research achievements.”

[Anonymous No.7334902]

>>7334899
The mathematician and blogger Cathy “Mathbabe” O’Neil, as quoted in a great essay by Caroline Chen called “The Paradox of the Proof,” is not interested in Mochizuki’s supergenius fucking around. “You don’t get to say you’ve proved something if you haven’t explained it. A proof is a social construct. If the community doesn’t understand it, you haven’t done your job.”

[Anonymous No.7334907]

The same goes for the classification of the finite simple groups. It cannot be understood in a satisfactory way so it doesn't count.

[Anonymous No.7334912]

>>7334907
I does count, it's a valid proof and the classification is a theorem.

[Anonymous No.7334915]

>>7334891
Despite what anyone on /sci/ says no his proof doesn't count (even if valid) until others can verify it.

[Anonymous No.7334931]

>>7334912
If the proof cannot be understood by a single person in a reasonable timeframe then it simply cannot be trusted. If the people revising the proof manage to make it both readable and shorter than a thousand pages then I might believe it.

[Anonymous No.7334937]

>>7334931
It's currently 500 pages.

[Anonymous No.7334942]

>>7334937
Have you read and verified it yet? 500 pages should be easy for you to read. Report back and tell us what you find. Don't be lazy.

[Anonymous No.7334948]

>>7334931
>>7334937
Proofs can be that long?I thought I hated analysis courses

[Anonymous No.7334954]

>>7334937
Every volume of the new proof is 500 pages long and there are six of them so far. They said there would be about ten volumes too.

[Anonymous No.7334958]

>>7334954
wtf

[Anonymous No.7334962]

>>7334931
The proof can be understood (and has been) by people. The timeframe has nothing to do with it. Each piece is not that hard to understand (and they are published in peer reviewed journals). There are just lots of pieces, and you can run through them linearly. It's not analogous to IUTeich at all.

[Anonymous No.7334970]

>>7334962
>Each piece is not that hard to understand (and they are published in peer reviewed journals).

Since you read it have you verified the proof? Do you understand it?

>The proof can be understood (and has been) by people.

Yeah like three people and so far they can't articulate it to the wider community so the proof remains invalid until it can be vetted against by other experts. Just because 4 people say it's true doesn't make it true. That's not how math works.

[Anonymous No.7334973]

>>7334899
>100+ years
>some guy making some machine
>assumes that ABC conjecture is a-ok
>runs quantumn compute or w.e on it
>it fails
>japanese chink becomes laughing stock in history textbooks
>alternatively, he goes down in history as one of the most prevalent mathematician in the early 21st century

[Anonymous No.7334975]

>>7334970
>Since you read it have you verified the proof? Do you understand it?
I've read parts of it and I understand the structure of it. The main reason it's long is because there are many simple groups, not because the structure is difficult. There is no point in verifying simple proofs for each group that have been published in peer reviewed journals.

>Yeah like three people and so far they can't articulate it to the wider community so the proof remains invalid until it can be vetted against by other experts.
You don't know what you're talking about. Time to leave.

[Anonymous No.7334976]

>>7334962
False proofs have been published and believed by the wider community many times. At over 10000 pages in its current form I just have no confidence that it is error free.

[Anonymous No.7334977]

>>7334902
>nope

the whole point of proofs are for more intelligent individuals to solve complex problems and provide foundations for dumber individuals to build upon.

I dont need to understand circuits to know how to program a simple 'hello world', etc...

ABC is pretty useless right now, and will probably only be used in the future. so that leaves plenty of time for current and future/upcoming mathematicians to learn and confirm his shit

[Anonymous No.7334983]

>>7334975
>You don't know what you're talking about. Time to leave.
math community doesn't agree with you. time for you to go.

[Anonymous No.7334986]

>>7334983
The math community uses the classification as a theorem, not a conjecture. You lose. Did you have fun pretending to be a mathematician?

[Anonymous No.7334989]

>>7334975


hey i proved p vs np. proof is 1,000 pages and i created my own mathematics. it's true because 3 other people said it's true. people on /sci/ argue in my favor even though they haven't read the entire proof because i claim it's true and 3 other people understand it. It's easy to understand. it's true and the math community doesn't need to verify it. 4 people including myself already have.

[Anonymous No.7334991]

>>7334986
The math community hasn't verified his proof of the ABC conjecture. It isn't considered a valid proof since it hasn't been peer reviewed and vetted against. Until it is, it will remain an unverified proof. You should stop pretending to know how peer review and math verification works. Go home, you don't do higher level math.

[Anonymous No.7334992]

>>7334976
OK, so show where the proof is wrong. You don't just get to assume peer reviewed proofs you don't like are wrong.

>>7334989
No new mathematics is needed to understand classification of finite groups. Every single piece uses standard techniques and the overlying structure is obvious. All this proves is that you don't understand the difference between high level math and novel math.

[Anonymous No.7334994]

>>7334991
Retard, read the fucking posts I'm replying to if you want to enter the conversation. I'm not talking about Mochizuki's proof.

[Anonymous No.7334996]

>>7334986
>trying this hard
>believing a proof cause his hero says its true
>gets butthurt when people question the proof
>hasn't read the entire proof himself
>thinks he knows mathematics
>cries when people disagrees
>kek

[Anonymous No.7334998]

>>7334996
See >>7334994

Learn how to read or go back to /b/ you greentexting faggot.

[Anonymous No.7334999]

>>7334994
>>7334992
I'm talking about Mochizuki's proof.

The guy that initially responded to you about finite groups hasn't replied since >>7334907 this initial response.

[Anonymous No.7335001]

>>7334992
The burden of proof isn't on the reviewer. The burden of proof is on the mathematician claiming he proven the ABC conjecture. So far, it isn't accepted the ABC conjecture has been formally proven.

[Anonymous No.7335002]

>>7334999
>I'm talking about Mochizuki's proof.
Yes, and YOU replied to my post not talking about Mochizuki's proof as if I was, because you didn't read the fucking thread. Now fuck off you illiterate piece of shit.

[Anonymous No.7335004]

>>7334998
>has assburgers
>cries on /sci/
>kek

[Anonymous No.7335005]

>>7335002

[Anonymous No.7335007]

>>7335001
I'm not talking about the ABC conjecture, you illiterate fuck. I'm talking about classification of finite groups. Read the fucking thread before you make a fool of yourself.

[Anonymous No.7335008]

>>7335005
>>7335002
same fags

le edge

[Anonymous No.7335009]

>>7335002

[Anonymous No.7335010]

>>7334986
The proof is controversial within the field too. I've heard that some of the authorities on the topic will tell you this same opinion that the proof is unacceptable. On the other hand it might be that I've spent my time as a grad student inside a nest of haters or something.
Hot damn are there some emotions being provoked in this thread. I could probably troll a whole representation theory conference with this.

[Anonymous No.7335011]

>>7335008

[Anonymous No.7335014]

>>7335010
>Hot damn are there some emotions being provoked in this thread.

It literally is one person shitposting over and over again, don't mistake it for multiple people. He has assburgers.

[Anonymous No.7335015]

>>7335010
They are in the minority. Most of the field has moved on already.

[Anonymous No.7335016]

>>7335015
>>7335011
>7335011
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>>7334897

Shitpost

[Anonymous No.7335017]

>>7335014
Yes, one person posted these in less than a minute.

>>7334991
>>7334992

>>7334994
>>7334996

[Anonymous No.7335018]

>>7335016
Forgot to add your own post to the list

[Anonymous No.7335020]

>>7335007
>>7335002
>>7334999
>>7334998
>>7334994
>>7334992
>>7334986
samefag

[Anonymous No.7335022]

>>7335020
So close, yet so retarded.

[Anonymous No.7335024]

No, I accidentally clicked someone else. I obviously know when you post.

[Anonymous No.7335025]

>>7335022
>>7335020
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>>7335018
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>>7334891
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>>7334942

samefags

[Anonymous No.7335031]

>>7335015
What is your expertise in the field besides shitposting assburgers rants on 4chins?

[Anonymous No.7335033]

>>7334977
>ABC is pretty useless right now, and will probably only be used in the future.

True.

[Anonymous No.7335059]

Have you noticed how in his pictures Mochizuki's always looking upwards? That's because he's seen the light, the absolute mathematical truth, and he will bring this to attention using anime as a medium.

[Anonymous No.7335093]

>>7334891
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[Anonymous No.7335095]

>>7334899
>>7334902
>>7334907
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[Anonymous No.7335113]

>>7334891
>If nobody understands a mathematical proof, does it count?
Yea why not?

[Anonymous No.7335173]

I've read it whole
Baby tier math
Article is just sensationalism
Everyone with a little bit of mathematical insight can understand is easily

[Anonymous No.7335295]

>>7335173
K explain his 500 page long proof to us. Bet you that you can't do this. All talk no game.

[Anonymous No.7335415]

>>7335295
>Bet you
>All talk no game
... being self-referential?

[Anonymous No.7335441]

>>7335113
Because here, a proof is a social construct meant to convince other mathematicians that a formal proof could be constructed if necessary. If nobody is convinced, then it fails.

[Anonymous No.7335631]

>>7335113
I have a proof of P vs NP. But no one else understands it. I claim it's valid & you're too stupid to understand it. Does that make my proof count?

[Anonymous No.7335634]

>>7335415
You aren't answering the question. Explain his proof since it's really easy to understand and since you understand its validity yourself. Until you do, you are full of shit like most people on this board.

[Anonymous No.7335662]

>>7334891
>If nobody understands a mathematical proof, does it count?

Yes, a proof is valid regardless of who understands it.

Not many people know if this truth is valid though.
Whether it is valid or invalid though will not change based on who understands it. Right now it is either valid or invalid and nothing will change that.

[Anonymous No.7335665]

>>7335662
>Yes, a proof is valid regardless of who understands it.

I have a proof of P vs NP. It is valid and you're too stupid to understand it.

[Anonymous No.7335670]

>>7335665
You might think it is valid but that might not be the case.

Whether it is valid or invalid though is not based on our understanding of it.
Right now it is either valid or invalid and no amount of understanding will ever change that.

[Anonymous No.7335680]

>>7335670
There is a subtle distinction to be made here.

Person A claims proof B is valid. The validity of B is independent of our understanding of B (as you said-- this is correct).

But socially, B may not be considered "valid" due to not being widely understood and/or vetted against by a rigorous and anonymous peer reviewed process. Until B can be vetted against in such a process and widely understood by the larger mathematical community it is not going to be considered widely accepted or valid.

Shinichi isn't playing by the rules and unless Go can dumb it down and express it to the larger community it may not be going anywhere anytime soon.

[Anonymous No.7335681]

>>7335680
Yes, the proof should not be considered valid until we know it is valid.

[Anonymous No.7335685]

The correct answer is: "I don't know." We don't know if it's valid proof and we don't know if it's an invalid proof.

Until people start figuring it out, there's no way of knowing whether it's valid or not.

[Anonymous No.7335802]

>>7335662
A truth and a proof are two different things

A truth is a truth proven or not

A proof is a tool to explain a truth, so if it doesn't explain it, it doesn't work

[Anonymous No.7335853]

So much sperging over so little. Yeah, Mochizuki's proof might be wrong, get over it. People have been checking his stuff for years without spotting any fatal error, and they will keep checking in the coming years. Just let the relevant professional do their works and expertise about UIT will eventually trickle down until the arithmetic geommetry community achieves a consensus about wether Mochizuki is right. This is how it's always done, here the checking process will simply be longer and harder, as it's often the case when groundbreaking math is involved.

No need to write article about how proofs are social constructs and people need to make themselves understood. This is obvious and besides the point. Verification takes time. There have been worse in the history of mathematics, for instance lost work that wasn't recovered until half a century later (or that wasn't recovered at all).

[Anonymous No.7335882]

>>7335853
>for instance lost work that wasn't recovered until half a century later (or that wasn't recovered at all).
Like which?

[Anonymous No.7335930]

So he invented a new kind of math so solve this? Is he like Newton and calculus?

[Anonymous No.7336001]

[Anonymous No.7336006]

What's he looking at? I bet it's one of those demon things from Death Note telling him about the advanced mathematics.

[Anonymous No.7336565]

>>7336006
Shinichigami Notechizuki?

[Anonymous No.7336587]

https://www.maths.nottingham.ac.uk/personal/ibf/symcor.conf.html

[Anonymous No.7336939]

>>7336587
The starting point of “IUTeich” (i.e., Inter-universal Teichm¨uller Theory) lies in
the image of a
sequence of nested universes.
This sort of image apparently goes back to ancient times and appears not only
in the “Sokkuri Hausu” (i.e., “Identical House”) animation discussed here, but in
various stories and myths all over the world. In the case of IUTeich, the various
universes correspond to
“classical arithmetic geometry theaters
in which conventional ring theory/scheme theory is valid”.
In the “Sokkuri animation”, these universes are represented by “houses”. Within
each classical arithmetic geometry theater, one has a theta function; it is this
theta function that plays the role of “Frobenioid-theoretic” (i.e., non-scheme-theoretic!
— cf. Frobenioids I, II; Etale Theta ´ ) “bridge” to the “next universe”. In the
“Sokkuri animation”, this link furnished by the
theta function corresponds to
the gaze of the little girl into the “small house”

[Anonymous No.7337049]

>>7336939
Doesn't sound remarkable; just sounds like some cosimplicial doctrine, right?

[Anonymous No.7337249]

>>7335882
Riemann personal's notes, that were burned after his death iirc.
Fourier's later work that wasn't give a proper reading until the twentieth century.
Galois' original work, as submitted to the academy, was lost and found back years later.

Wolfgang Doeblin proved a result very similar to Ito's Lemma, using a sligtly different definition of the stochastic integral, independantly and roughly at the same time (1940). His work was left sealed in a letter and ignored until it was opened in 2000.

That's not talking about the countless persnal notes we might not even be aware of.

[Anonymous No.7337537]

>>7334891
>If nobody understands a mathematical proof, does it count?
this is indeed the most important question in maths and you have the same difficulty with unread proofs or proofs from computers.

[Anonymous No.7337552]

>>7335665
But P != NP.
Might be impossible to prove, but logic tells its true.
Also, the world around you, your bank, https and all computer encryptions relies on the fact that NPs cant be solved in P time.

[Anonymous No.7337558]

>>7337552
> logic tells its true.
If that was the case, then you'd have a proof.
> your bank, https and all computer encryptions relies on the fact that NPs cant be solved in P time.
Not quite, but even if it was true, that wouldn't be proof. In the the Stone Age no one had light bulbs, but that didn't mean electricity didn't exist.

[Anonymous No.7337628]

>>7334891
What if his proof isn't explained well? From the article it says other Mathematicians don't understand it well, but is that because they don't know the subject matter, or because he does a poor job explaining it?

If Newton's Principia was too technical and not explained well it would not have been as well utilized.

This is pure conjecture, but maybe this guy is just too uncompromising and refuses to elaborate further.

[Anonymous No.7337642]

>>7337628
They don't know the subject matter. The guy basically invented this entire branch of mathematics by himself and the ABC theorem is just one of the results in it.

It's like if you went back to 300 BC and published a 500 page paper developing modern topology along with a proof of the fixed point theorem. It would take people a while to read, understand, and believe the material. Possibly even years.

[Anonymous No.7337734]

>>7334891
Stop reading pop-sci bullshit articles.
There are lots of respected mathematicians around the world studying IUTeich.
Even a conference is being held at Oxford in December with big names such as Andrew Wiles and Gerd Faltings attending.

https://www.maths.nottingham.ac.uk/personal/ibf/symcor.conf.html

[Anonymous No.7337762]

But is the (irrational) reason that you appreciate Mochininja so much? I mean, certainly, you don't get a fuck in his poorly written materials. So you must have an irrational and intuitive feeling that he's cool or something. What is that reason? And why don't you feel the opposite to say, Wildburger?

[Anonymous No.7337855]

truth exists whether or not someone believes in it

[Anonymous No.7338188]

>>7334891
The most important part of mathematics is being able to explain your work. My calc II teacher forced us to write down what we are doing, and my classmates still bitch about how awful he was for that, but it isn't the goal that matters, it is how you get there.

This goes all the way up to even the most complicated mathematics. You need to be able to explain whatever you do to others. And if that involves breaking it down to the most basic level to show, then god dammit you had better do it.

[Anonymous No.7338221]

>>7338188
That is what we did. The problem isn't his explanation. It's the shear size of the body of work.

[Anonymous No.7338289]

>>7338221
Okay, I see what the thread is about. My mistake.

I mean, the proof is there, and if the conjecture still doesn't have a solid proof, it is up to someone to grab their coffee and take a read of it. I mean, surely if it is bullshit, it isn't gonna take somebody 500 pages to figure it out.

[Anonymous No.7338892]

>>7338188
this

[Anonymous No.7338898]

>>7338289
Yes. It is going to take them reading through ALL of it carefully. People are struggling with it, it's hard mathematics, and only people within that very specific field and with very specific training on it will be able to decipher it, much less spot mistakes.

[Anonymous No.7340645]

>>7335882
All the stuff surrounding Grothendeick at the time he withdrew from mathematics comes to mind.

[Anonymous No.7340967]

http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

/thread

[Anonymous No.7341151]

i'm a retard who doesn't understand basic analysis
thus calculus is fake
qed mathfaggets
your department funds will be reallocated to classes where kids learn how to write hello world in java

[Anonymous No.7341791]

>>7341151
MATHCUCKS BTFO

[Anonymous No.7342240]

>>7334937
>500 pages to prove a+b=c
Autism everyone.

[Anonymous No.7342268]

>>7334902
>a proof is a social construct
That's code for "I'm a stupid fuck and don't want to think".

[Anonymous No.7342545]

>>7334902
>A proof is a social construct
Literally what the fuck
I can't believe a mathematician said that.

[Anonymous No.7342816]

This is the most cancerous thread I have ever seen on /sci/

[Anonymous No.7342839]

>>7342268
>>7342545

It makes sense though. Why the hell do we even give proofs to theorems? We do it so another entity can verify our claim and thus we obtain objectivity, altough our personal viewpoint is strictly subjective, since we are humans after all.

Now comes the kicker though, it only works if the other entity can actually do this with whatever we wrote down as a "proof". If I give you a proof in a language that I totally pulled out of my ass and shot my self in the head afterwards, would you count it as a proof? Nope.

Just because mathematics is above any kind of human limitations doesn't mean that for us humans there are no limitations for doing math.

[Anonymous No.7342842]

>>7342816
>actual mathematics discussion
>cancer
go make another university recommendations thread

[Anonymous No.7342844]

>>7342842
I would say a good 4/5 of this thread is people having a shitty memespewing war

[Anonymous No.7342864]

>>7334902
>Cathy
Why do only women have social construct vision?

[Anonymous No.7342870]

>>7342844
comes with the territory

[Anonymous No.7343358]

Who cares about the abc conjecture when he thinks he's on a proof for the Riemann hypothesis? Also,

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

I quote:

Here, we recall that "multiradial algorithms" are algorithms that make sense from the point of view of an "alien arithmetic holomorphic structure", i.e., the ring/scheme structure of a <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]NF-Hodge theater related to a given <span class="math">\Theta^{\pm\mathrm{ell}}[\math]NF-Hodge theater by means of a non-ring/scheme-theoretic horizontal arrow of the log-theta-lattice.


How am I supposed to not think this guy is a crackpot when it just sounds like he made a paper generator with markov chains?[/spoiler]

[Anonymous No.7343362]

Who cares about the abc conjecture when he thinks he's on a proof for the Riemann hypothesis? Also,

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

I quote:

Here, we recall that "multiradial algorithms" are algorithms that make sense from the point of view of an "alien arithmetic holomorphic structure", i.e., the ring/scheme structure of a <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]ellNF-Hodge theater related to a given <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]NF-Hodge theater by means of a non-ring/scheme-theoretic horizontal arrow of the log-theta-lattice. How am I supposed to not think this guy is a crackpot when it just sounds like he made a paper generator with markov chains?

[Anonymous No.7343370]

Who cares about the abc conjecture when he thinks he's on a proof for the Riemann hypothesis? Also,

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

I quote:

Here, we recall that "multiradial algorithms" are algorithms that make sense from the point of view of an "alien arithmetic holomorphic structure", i.e., the ring/scheme structure of a <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]NF-Hodge theater related to a given <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]NF-Hodge theater by means of a non-ring/scheme-theoretic horizontal arrow of the log-theta-lattice.


How am I supposed to not think this guy is a crackpot when it just sounds like he made a paper generator with markov chains? Sorry for the typos.

[Anonymous No.7343471]

Something interesting that hasn't been mentioned ITT yet:
Mochizuki is fully convinced not only that his proof is correct, but that there are NO OTHER proofs that use significantly different methods.
To quote:
>IUTeich is “the correct theory” in the sense that it leads one to doubt the existence of any sort of “alternative proof”, i.e., via essentially different techniques, of the ABC Conjecture.
http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

[Anonymous No.7343779]

>>7334891
If his proof is right what does that mean? I heard about the implications of p = np but what exactly are the implications of proving ABC conjecture?

If it gets proven right does that mean that it will be taught in college? Does that mean that graduate students of pure math will spend their entire time in school learning this Mochi sans math and proof?

[Anonymous No.7343785]

>>7334902
>The Paradox of the Proof
>A proof is a social construct
>If the female nigger doesn’t understand it, you haven’t done your job.

[Anonymous No.7343788]

>>7334902
Proof is about as much of a social construct as gender. Which is pretty much 0 next to nil.

[Anonymous No.7343791]

>>7342839
there is an inductive part for every proof with some bayesian probability increasing about its validity when more and more mathematicians accept it (well those who are interested in the field, accept the -the logic, -the axioms)

[Anonymous No.7343901]

>>7337537
who wrote this?

[Anonymous No.7343903]

>>7343785
>>7343788
>>7342864


Formal proof is not a social construct.
Informal proof is however, since you try to convince the reader a formal proof exists.

Since the proof Mochizuki gives is obviously informal, it is a social construct. As of yet, it is not a very good proof since it convinced almost noone that a formal proof of the abc conjecture can be constructed.

>>7343791
Some /lit/fag is posting this all over the board. It is utter bullshit. No mathematician worries about which quantifiers he uses, and almost noone worries about which axioms he is using, after all, who cares about ZFC?
A lot of big words, but it is obviously written by someone unable to pass even an undergrad algebra course.

[Anonymous No.7343948]

>>7343370
>alien arithmetic holomorphic structure
arithmetic holomorphic structures that lie on the opposite side of a Θ-link from a given arithmetic holomorphic structure
If you don't know what a holomorphic structure is, then that's your issue. Start here: https://en.wikipedia.org/wiki/Holomorphic_vector_bundle

>the ring/scheme structure of a <span class="math">\Theta^{\pm\mathrm{ell}}[/spoiler]NF-Hodge theater
Hodge theaters are discussed on the first paper of the series.
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf
How the hell you want to understand something from the 4th paper without reading and understanding the 3 preceding papers? That's your mistake again.

>log-theta-lattice
https://en.wikipedia.org/wiki/Theta_function_of_a_lattice

-----------------------------------------------------------------------------------

Mochizuki isn't a crackpot, it's just that you aren't familiar with the concepts he deals with and, as such, it's confusing to you.
But he's a respectable mathematician. Just look up who solved the profinite Grothendieck conjecture for hyperbolic curves over number fields back in 1999? That's right, Mochizuki.

[Anonymous No.7343950]

http://trustyservant.com/archives/7748

[Anonymous No.7343951]

>>7343471
Interesting, indeed. Quite a bold claim.

[Anonymous No.7343956]

>>7343779
>If his proof is right what does that mean?
Nobody knows. Yet.

"In the 1800s mathematicians expended a lot of energy on the wave equation; a partial differential equation arising from the physical properties of waves in a string or in fluid. Despite the physical origin, the problem was one of pure mathematics: no-body could think of a practical use for waves. In 1864 Maxwell laid down a number of equations to describe electrical phenomena. A simple manipulation of those equations produces the wave equation. This led Maxwell to predict the existence of electrical waves. In 1888 Hertz confirmed Maxwell's predictions experimentally, detecting radio waves in the laboratory. In 1896 Marconi made the first radio transmission.

This sequence of events is typical of the way in which pure mathematics becomes useful. First, the pure mathematician playing about with the problem for the fun of it. Second, the theoretician, applying the mathematics but making no attempt to test his theory. Third, the experimental scientist, confirming the theory but not developing any use for it. Finally the practical man, who delivers the goods to the waiting world.

The same sequence of events occurs in the development of atomic power; or in matrix theory (used in engineering and economics); or in integral equations.

Observe the time-scale. From the wave equation to Marconi: 150 years. From differential geometry to the atomic bomb: 100 years. From Cayley's first use of matrices to their use by economists: 100 years. Integral equations took thirty years to get from the point where Courant and Hilbert developed them into a useful mathematical tool to the point where they became useful in quantum theory, and it was many years after that before any practical applications came out of quantum theory. Nobody could have realized at the time that their mathematics would turn out to be needed a century or more later!"

[Anonymous No.7344016]

>>7343903
>No mathematician worries about which quantifiers he uses, and almost noone worries about which axioms he is using, after all, who cares about ZFC?
this is what is said in the first lines

[Anonymous No.7344166]

>>7343956

Hmmm, that's interesting

[Anonymous No.7344320]

>>7343791
tl;dr

[Anonymous No.7344324]

>>7343948
If all that is so well understood then how come mathematicians haven't come to a consensus on his paper?

[Anonymous No.7344402]

>>7344324
It isn't so well understood.
Not that many mathematicians have a grasp of all the concepts IUTeich engulfs: people may know Hodge theory, but Hodge–Arakelov theory? That's something most will have to study before even reading the 4 IUTeich papers.

And even if they have all prerequisites already, they still have to read all ~500 pages that is IUTeich in its entirety, which most mathematicians in the field are too busy/lazy/uninterested to do.

Just read Mochizuki's latest progress report.

http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

[Anonymous No.7344438]

People confirmed to be currently studying IUTeich:

> A. Beilinson (Chicago)
> G. Faltings (Bonn)
> I. Fesenko (Nottingham)
> D. Goldfeld (Columbia Univ.)
> Ch. Haesemeyer (Los Angeles)
> N. Hitchin (Oxford)
> Yu. Hoshi (Kyoto)
> E. Hrushovski (Jerusalem)
> K. Kedlaya (San Diego)
> M. Kim (Oxford)
> K. Kremnitzer (Oxford)
> U. Kühn (Hamburg)
> F. Loeser (Paris)
> Ch.P. Mok (Purdue Univ.)
> A. Schmidt (Heidelberg)
> J. Stix (Frankfurt)
> T. Szamuely (Budapest)
> F. Tan (Shanghai)
> D. Thakur (Rochester)
> Yu. Tschinkel (New York)
> F. Voloch (Austin)
> Sir A. Wiles (Oxford)
> G. Yamashita (Kyoto)
> S.-W. Zhang (Princeton)
> B. Zilber (Oxford)

https://www.maths.nottingham.ac.uk/personal/ibf/symcor.conf.html

[Anonymous No.7346120]

>>7344438
Thanks.