Are you ready for “Inter-universal Mellin...

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Are you ready for “Inter-universal Mellin transform”?

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

Remark 2.2.1

Mochizuki hopes to solve the Riemann Hypothesis

>>

do you know what he means with those comparisons to

int exp(-x^2) dx = pi^{1/2}

??

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>>6931583

what do you even hope to accomplish by asking this here? it's all there. if you don't understand it then you won't. It's advanced math.

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>>6931583

That's the Gaussian integral. You should know that.

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>>6931583

Use polar coordinates and you should be able to solve that

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>>6931583

Read part II of his IUTeich papers.

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And people are already reviewing his work.

Even "double checks" were carried out.

http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202013-12.pdf

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>>6932510

That will silence those pseudo-scientists saying his proof wasn't acceptable because it was too hard and nobody would understand it.

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>>6932510

Basically he hand picks people to read through his papers / verify his results and then conclude they are correct in a non-biased fashion? Thus this means he proved the Twin Prime Conjecture and he should be promptly be awarded the Fields Medal?

I don't buy it sir. Not until it gets the proper review it deserves from the wider mathematical community. If he is unwilling to explain his results and his proofs are considered incomprehensible then the proof isn't considered valid at this current time.

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>observed that the “1/2" that appears here is strongly reminiscent of the "1/2" that appears in the Riemann hypothesis

why did this make me laugh

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>>6933604

>If he is unwilling to explain his results

He isn't, you idiot. He has done many seminars at Kyoto University and plans to do a lengthy workshop in March.

>and his proofs are considered incomprehensible

They aren't. Go Yamashita and Mohamed Saıdi learned it directly from him and Akio Tamagawa, Yuichiro Hoshi and Makoto Matsumoto learned it from Go Yamashita. Also, many more researchers are studying this on their own and many seminars, conferences and workshops are being delivered.

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>>6933604

> if one proceeds to study carefully step by step, starting from the “preparatory papers”, there is no reason that one should encounter any insurmountable difficulties.

That's what the people studying it said.

Just because it's "incomprehensible" to pseudo-scientists and freshmen kids it doesn't mean it's incomprehensible to everybody. Of course it isn't something easy to follow, but top mathematicians on the number theory field shouldn't have any trouble if they really want to dig into IUTeich.

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>>6933689

Because I'll fucking rapefuck your mouth-pussy, you sissy bitch-slut.

>>

Short talks by the million dollar babies have been uploaded a few days ago, together with an interview discussion where they comment on the "proves that need to be checked" situation

25:40 here

https://www.youtube.com/watch?v=eNgUQlpc1m0#t=25m40s

also

>dat brainpower line-up

>>6931588

I hoped OP might know - looks like he read into it

>>

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>>6933715

Yeah because MO is full of "pseudo-scientist" that work in the field who also don't fully understand it. Sounds like you are a fanboy. The burden of proof is one them to show it is watertight and not gibberish mathematics.

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>>6934112

I'm not saying his proof is correct, I'm saying claiming it to be "incomprehensible" is retarded. As stated by the two independent people that worked through it, the amount of time necessary to arrive at a reasonable understanding of the theory should be a matter of months — i.e., roughly half a year or so — not a matter of years, as claimed by many pseudo-scientists.

Go Yamashita is already writing an independent survey of 200~300 pages in length and teaching 3 other people about IUTeich and its initial results.

Mohamed Saıdi also supports these ideas.

It might take some more time for this proof to be verified, but stop bullshiting and claiming it to be too far-fetched and incomprehensible: it isn't.

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>>6933604

>Fields Medal

He's 45.

Sorry anon.

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>>6934120

How can you be this fucking retarded? The proof is in the papers. If you are too idiotic to comprehend it then you have no say in calling it in question. People are reviewing it and that's all your useless shithead needs to know.

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>>6934221

You tried to one up the guy, but came off as a fucking retard yourself. You apparently don't know this but mathematics is fairly specialized. His "proof" will not be "comprehensible" to a large majority of mathematicians outside the field. This means you have PhDs in mathematics that will not be able to decipher his work. Those experts in his field should be able to verify his claims. Does this mean that those other mathematicians (outside the field) are "useless shitheads"(as you suggested)? No, sounds like you are the useless shithead that doesn't even study math. Fuck off pleb.

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>>6931488

This seems very reminiscent of the "field with one element" plans to prove the Riemann hypothesis.

I am unsure of these techniques. I hope it works, nonetheless - the analogy between function fields and number fields is interesting, but can be deceptive.

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>>6934112

well you just won the biggest retard in the thread medal by not giving up here.

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>>6934221

Do you have a 300 page paper explaining why you are so mad that I can study for 6 months to understand?

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>>6934221

Says the guy that hasn't even completed reading the shit that he protects and holds dear to his heart. You can squarely fuck off.

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>all these heated opinions about this paper

>not a single one of these people has knowledge to legitimately critique this paper to any degree

>:(

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>>6933604

He doesn't seem to actually care and seems to go out of his way to downplay the proof of the ABC theorem and other such things because they're more of just neat side results of his theory that aren't really related to the core of it.

>>6939864

Very few people on the planet are familiar with it. The dude didn't just write a paper proving the ABC conjecture, he wrote a series of papers developing an entire new field of research where a proof of the ABC conjecture just happened to show up along the way.

Refer to >>6932510

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>>6939874

>Very few people on the planet are familiar with it

I heard that he worked in isolation for so long that the structure he built kept piling up, the papers released in 2012 ended up being in Alien language to the most specialized guys in the field

>insert image from that manga Kokou no Hito about the guy climbing mountains alone

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>>6940315

He is either an intelligent crackpot with a PhD (likely)

or

He is a genius that revolutionized the field of mathematics and as a byproduct of his theories solved several open problems in math.

I wonder how long it'll be until there is a general consensus on whether his proofs are valid?

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>>6940916

He's not "an intelligent crackpot with a PhD", he was famous for his work long before the claim to have proven the abc-conjecture.

On MathOverflow here

http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture

you have people in that field comment on what the work is about

e.g. this guy in pic related (and incidentally Terrence Tao in the comments)

http://en.wikipedia.org/wiki/Minhyong_Kim

and making clear that it's hard for him even to understand the papers because Mochizuki started to care for and is using concepts of more remote fields as well in his work.

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>>6940930

Regardless of whether his proof is correct, this is an appeal to authority. His previous work signifies that his proposed proof should be taken seriously and vetted against. It doesn't mean that based on past mathematicalachievements that this proposed proof is correct.

The proof may be "correct" (i.e. every step in the proof is truth-preserving), but it isn't yet "verified". I'm skeptical until there is a wider consensus among experts. Just because there are good discussions going on in MO about it doesn't mean the ABC conjecture has been solved in his papers. It is possible there are flaws in his proof, but there are other nuggets from his theories that are useful. It is remained to be seen. To comment otherwise on it's correctness (at this point) would be foolish until it can be widely understood among the experts.

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>>6940947

not sure exactly why you make that a response to me - I don't say anything about it's correctness. In fact I don't even know much about field extensions etc.

I read the posts (3 times over the year actually) in hope I could translate some of the ideas for elaboration here, but it's not worth it.

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>>6940957

Okay no problem. His area is outside my own, so trying to decipher through it is an utter waste of my time. Hopefully one day soon we'll hear more about it.

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>>6940930

>can someone comment briefly on the philosophy behind his work

Hahaha, philosophy? Who does he think this is, Norman Wildberger? Math isn't philosophy, /sci/ says, so we should disregard.

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Is Mochizuki still okay? His safety confirmation has not been updated since mid november.

http://www.kurims.kyoto-u.ac.jp/~motizuki/anpi-kakunin-jouhou.html

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>>6941297

lol, what is this?

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>>6941332

Typical procedure for aspie hermit mathematicians.

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>>6941297

It hasn't even been a month, anon.

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what's up with the formatting? Why is every fourth word italicized?

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>>6941591

You gotta put stress on those important words bro.

You can't just explain what they mean, you gotta use the non-abelian manifolds to conjecture the hodge-terrence-mandrake theorem on the basalt structure of K-groups and lambda calculus.

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Here's a gentle introduction to inter-universal teichmüller theory by way of a similar house animation that is unfortunately not online anymore.

http://www.kurims.kyoto-u.ac.jp/~motizuki/sokkuri-hausu-link-english.pdf

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Question.

Would solving the Riemann Hypothesis would have any important applications?

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>>6931488

Damn, taking a look at all these mathematicians who are involved in awesome stuff like this makes me reconsider whether going to Med school was the right choice despite math being my favorite subject.

Too late for a change now, I guess.

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>>6941637

When getting these thoughts just remember that the grass is greener on the other side.

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>>6941599

https://njwildberger.wordpress.com/2014/03/18/let-h-be-a-load-of-hogwash/

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>>6941634

There's a ton of number theory and other areas of mathematics dependent on the Riemann hypothesis being true. It's the linchpin of a large part of modern math.

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>>6941538

no seriously what is this?

is he afraid to die or something?

>>6941634

The pudding is in the proof.

>>6941599

there is no lambda calculus in this work.

Nevertheless, Anabelian cateogries alla Grothendieck are concerned with varieties of purely algebraic flavour afaik, so no smooth structure there.

Are there other notions of "non-abelian manifolds" other than Connes non-commutative geometry?

>>6941637

You can always do and learn math as a hobby. Just because you might not plan on publishing in this field doesn't matter you can't fall in love with Mellin transforms. The only question is how long you're going to be motivated without irl people around you to do the same.

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>>6941664

>no seriously what is this?

>is he afraid to die or something?

I was only joking when I posted it (obv) but I'm not sure. There's a link to that on his news page

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html

maybe it's just for people who want to know if he's still alive.

http://www.oia.hokudai.ac.jp/current-students/safety/safety-confirmation-system/

or in the case of disasters, specifically

Anyway wasn't this whole IUTeich abc thing a few years ago, and haven't there been lectures and people seriously reading into it, so far? Any results?

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>>6941715

>Anyway wasn't this whole IUTeich abc thing a few years ago, and haven't there been lectures and people seriously reading into it, so far? Any results?

Yes, that's what is described here.

http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202013-12.pdf

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>>6941754

thanks

>Moreover, I never envisaged that these papers

might elicit

reactions

consisting of

non-mathematical content

from

non-specialists

.

Ihave

no intention

of

responding

to such non-mathematical reactions.

I like this guy

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What did the math community use as criteria for determining the 7 Millenium problems? This guy pulled off a Newton and invented new stuff to explain a problem, why isn't the abc conjecture a Millenium problem?

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>>6941861

From the looks of it he has a good chance of proving the riemann hypothesis within ten years, so he may get one yet.

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I'm so glad I stuck with physics and not math

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>>6942684

Hopefully.

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>>6934221

i think the guy you quote meant that you should be able to express your thoughts clearly

if i hand in a bunch of hieroglyphs claiming this is a proof without explaining the hieroglyphs, everyone will call me a retard even if what i meant is true

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>>6939864

this

none of us here are qualified to comment on this

we are just plebs

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>>6943884

I'm pretty sure nobody's even try

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>>6941627

I tried looking for the animation but could not find it. This is the closest thing I could find.

Some posts on the net made it sound like it was an album. So perhaps it's a music video?

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>>6943937

Sorry, I meant:

>from an album

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>>6943875

But he explains everything through a series of papers. And others have already learnt it; even without his direct aid. Stop with this bullshit already, IUTeich isn't "incomprehensible" or "would take a decade for someone to learn". Read this again before going out there spreading shit: http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202013-12.pdf

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In october Tao and Green mentioned that the review of his papers should be the topic of a polymath project, which i think is an excellent idea.

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>>6939920

bravo, my sides were gone by the end of the first sentence

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>>6944010

imho anything is better than reducing some bound whos value has no impact on anything from 500.000 to 500

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>>6943983

Math doesn't work that way. Just because 1 or 2 people confirm that what his theories are correct DOES NOT ENTITLE in ANY WAY SHAPE OR FORM that his proofs should be WIDELY ACCEPTED by a WIDER AUDIENCE until they are rigorously VETTED again by OTHER SPECIALIST.

1 or 2 people that supposedly understand it isn't sufficient enough to say everything he has done is correct.

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>>6944308

>It's a conspiracy!!

>People are trying to pull the wool over my eyes but I'm too smart for that!!!

lol

It's a work in progress. Many specialists have learned it and he's hosted several workshops. That report is from 2013. The ABC conjecture isn't the main interest of the research and even if there's a flaw with the proof of the ABC conjecture (which is currently very unlikely), there's still a lot of value in IUTeich.

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>>6944674

> (which is currently very unlikely)

What evidence do you have to support that?

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>>6944704

Do not mistake these for formally defined terms. Just that informally one would argue that most issues are discovered in the first year or two. This has been around longer.

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>>6940930

Doesn't anyone else find Tao's comment pretty funny?

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>>6944744

Check out this interview he did

http://thecolbertreport.cc.com/videos/6wtwlg/terence-tao

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>>6943937

it's a hentai

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>>6943875

You stated the following:

> i think the guy you quote meant that you should be able to express your thoughts clearly

> if i hand in a bunch of hieroglyphs claiming this is a proof without explaining the hieroglyphs, everyone will call me a retard even if what i meant is true

In other words, you said IUTeich was incomprehensible and Mochizuki didn't presented his ideas in a clear way.

I refuted with the following:

> But he explains everything through a series of papers. And others have already learnt it; even without his direct aid. Stop with this bullshit already, IUTeich isn't "incomprehensible" or "would take a decade for someone to learn". Read this again before going out there spreading shit: http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202013-12.pdf

In other words, I how it was actually pretty well written and explained and how people were already learning about it. 2 people said it should take a serious mathematician around 6 months to get through all of it.

And then you come and say "lol it isn't proved only two people learnt it!!!11!!! lol"

Are you a retard by any chance? I never claimed his prove was verified, I just refuted your post about it being incomprehensible, which it isn't.

I hope you are a troll, but in case you are actually this retarded and can't follow a simple discussion, I hope you get better.

Now get out of /sci/, please.

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>>6945190

Not the guy you replied to, but a fellow mathematician. The sort of hubris you exhibited in this thread is fairly abhorrent. Regardless of the person's views (the one you're arguing with), you handled it badly. If anything, people like you deserve to get out of /sci/. Just my 2 cents

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>>6944744

My favorite two comment ever in pic related

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>>6945336

How is that funny? Grown men are fanboy'ing over Tao as if he Justin Timberlake in the 90s. Tao could comment "I took a shit and I can prove it." and he'd automatically get 100+ upvotes/likes. This is one problem I have with the field of modern mathematics, that it is reduced to fads and celebrity worship.

For example, Joel David Hamkins suffers from this as well as evident by his blog post: http://jdh.hamkins.org/mathoverflow-the-eternal-fountain-of-mathematics-reflections-on-a-hundred-kiloreps/

He once joked that tenure/promotional consideration should take into consideration ones MO points.

Look at any top school in math. Most will be overrepresented with specialist in the same areas of mathematics, why? Because it is "sexy". When was mathematics ever about being sexy, cool, or a celebrity?

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>>6945345

>When was mathematics ever about being sexy, cool, or a celebrity?

It should be. How else do you suppose to close the gener gap? We need to get away from the stereotype of mathematicians being autistic basement dwellers.

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>>6945190

Not the guy you're quoting, but s/he raises an interesting and very important philosophical point. How many mathematicians need to confirm the proof before it can be accepted as truth? If only one or two persons read it and didn't see the error, then we can hardly accept it. What if 10 (100, a million, ...) people read it and none of them sees the error? The error will still be there. How can we verify that a proof is really free of errors? Math should be about correctness and not about authorities, so how can we accept a proof only on the basis of a few famous mathematicians saying "we read it and it looks okay"?

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We are human...after
2014-12-13 10:36:29
Post No.6945363

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>>6945345

To reply on the "question": It's funny/cool if you don't know that those two guys are on MO. If you already know, then it's not unexpected.

But regarding the main point, I agree with you.

There is this (good) 200+ votes thread by Bill R.I.P. Thurston

http://mathoverflow.net/questions/38639/thinking-and-explaining

and in the comment some guy says

>What I am really thinking is that, if you had posted this anonymously, this question would have been closed in five minutes.

Thanks for the link. It linked to the Jon Skeet blog, and the fact that I know him and what he does, despite never having written a working C-program speaks for itself.

I've seen Qiaochu "born to do abstract algebra" Yuan also saying that he sort of considers SE/MO reputation a factor when applying for positions - people see others think you know your shit.

The fact I can use names of people like that here and others maybe know who I mean already shows that this creates personalities. On 4chan, we see "mathematicians" and "physicists" threads too, I mean Grothendieck, Feynman, even Wildberger (kek), or here Mochizuki-Shinichi is the topic of a thread. But then again, I recognise that those threads have more responses too, and if I just make a thread with a abstract question I'll not get any replies. Threads like this survive.

In some ways, I'd like SE to be more like 4chan - so that people vote on answers without knowing the rep of a user. I have actually spent thousands of rep on bounty there - I feel when you get 5000+ rep, you actually get sucked into the game and waste too much time with stuff you don't learn from.

The rep system is pretty shitty in any case, independent of that problem. An earlier critique of negative point from the programming site is

http://michael.richter.name/blogs/why-i-no-longer-contribute-to-stackoverflow

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>>6945356

Good points, >>6945190 seems to be arguing that 'so and so people read it and say it's ok' thus it isn't incomprehensible and thus is correct. Then dismisses the notion that the ABC conjecture is even the point, and the mathematical theory that proves it is the meat (almost as if to say 'don't on these open problems, just learn the new math').

As evident by the people that reviewed the papers, there were errors. Even if these errors have been fixed (the claim) then who is to say there isn't more patch work that needs to be done? What if it is patch work that even if resolved doesn't prove the theorems?

Regardless, point is and ego aside. This proof needs to be widely vetted against. Right now as it stands, the "proof" isn't a proof in the mathematical sense (even if it is later shown to be valid).

Another problem in math is it seems like mathematicians/people confuse abstruseness in symbols/concepts for rigor. There is a difference between the two.

I could write:

" Θ±eNHS-Thorn related to a given Θ±elate_{Z}-Peterson theater by means of a non Legendrian knots/scheme-theoretic horizontal arrow of the Huygens arrows cross elate-knots."

Say it is a new mathematical field. Say it proves correct results and then leave it up to you to figure out. It seems impressive because of the symbols/language but who is to say that what I wrote isn't gibberish, or something really simple made complex to seem sophisticated?

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>>6945363

>In some ways, I'd like SE to be more like 4chan

Yeah, I too would love to call people faggots and retards over there, redirect them to the paranormal board and post unrelated reaction meme images.

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>>6945363

I am familiar with those individuals, as anyone in the field would be. I have a set of my own 'cool' MO points and a thread that was highly upvoted/seen over 1,000 times. I don't speak from jealousy or any of that, I speak from what I see is a problem with such online communities.

>It linked to the Jon Skeet blog

Not familiar with Jon Skeet. Who is he and what is his connection?

>An earlier critique of negative point from the programming site is

http://michael.richter.name/blogs/why-i-no-longer-contribute-to-stackoverflow

I'm glad someone else feels the same way I do about it.

>Your comments on Thurston (RIP)

That commenter is absolutely correct. Whenever you get 'big shot' mathematicians involved in an online community you'll want to make them feel welcomed. I've seen several such topics like Thurston's closed within minutes as being too 'soft'. Thurston got a break due to his fame.

In this respect it reduces math to 'gaming the system' so to speak. It isn't about studying the area of math you find interesting 'just because' but about studying areas of math that are 'fashionable', one that will give you an intellectual medal for just saying that you 'study it'. It is reduced to celebrity worship, fashion and nonsense.

Fashion can hurt career advancement as well 'why hire this dude that studies logic when I can hire another K-theorist?" -- Stuff like that shouldn't even happen. Also, to further the logic example, when is the last time you seen a mathematician that studied logic win the field medal outside of Cohen?

Regardless, I stopped using sites like MO. I now just hang around my professors and pick their brains anytime I truly get stuck on a problem. I am usually more enlighten that way. Plus, I know many solid mathematicians that haven't even bothered being on MO. Doesn't seem like myself/them are missing too much.

This is why I like 4chan. No rep systems, completely anon.

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>>6945365

>>6945356

>>6945221

For fuck's sake, I'm not arguing that his proof is correct, I'm arguing that is understandable! Here's how it went:

A) Mochizuki's proof is incomprehensible, nobody can understand it so it isn't a proof. It's like hieroglyphs. It isn't clear!

B) Actually, it has been understood by 2 people through Mochizuki and by 3 others through Yamasita. It should take about 6 months for a professional on the field to study IUTeich and get a good grasp of it. His theory is far from incomprehensible and unclear; it's well detailed and people out there have already read and understood it in half a year.

B) LOL just becuz 2 people read it it doesn't mean it is proved! u retard xD

I never claimed it was proved, idiots. I was arguing against the retard saying it was incomprehensible and unclear. Learn to read.

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>>6945412

Okay, it is generally understood to be 'learnable'. This doesn't then mean it is correct. What progress is being made so that western mathematicians can also learn and verify his theories? Why isn't he lecturing in the US yet? Why has this been going on for years with no real wide scale progress?

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>>6945416

>Okay, it is generally understood to be 'learnable'.

Some retards on this thread were saying his papers weren't; I was arguing against that, nothing else.

>This doesn't then mean it is correct

Of course. I never stated otherwise.

>What progress is being made so that western mathematicians can also learn and verify his theories?

What the hell are you talking about? What prevent western mathematicians from learning it? Are you implying only eastern mathematicians have access to it or what? Stop with this privilege bullshit. Anyone can learn it, just read the papers that lead to the proof. If you are talking about the lectures his giving at japanese universities, anyone can attend. And just for your interest, Mohamed Saıdi is an associate professor in the UK. Nothing prevent "western mathematicians" from learning it.

>Why isn't he lecturing in the US yet?

Are you proposing he lectures on foreign universities before doing so on his own and others nearby? Why's the US special? Check your privilege, fatass.

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>Not familiar with Jon Skeet.

http://meta.stackexchange.com/questions/9134/jon-skeet-facts

>Whenever you get 'big shot' mathematicians involved in an online community you'll want to make them feel welcomed.

Yeah, same thing happened when 't Hooft showed up on PhysicsSE when people complained about his Wolframian "Strings for universe as a state machine" papers

http://physics.stackexchange.com/users/11205/g-t-hooft

He doesn't really get the format and used SE post just to talk to people, having 5 answers in one thread, and still each got 20 upvotes

>...one that will give you an intellectual medal for just saying that you 'study it'.

But I fear that's how it goes in general.

I recently read (here actually) that Neumann didn't get into subjects overlappling with Turings work - just because Turing was a good mathematician. Grothendieck got mad, apparently, at Delinge when he used his shit to prove the Weil conjectures, and not himself.

>It isn't about studying the area of math you find interesting 'just because' but about studying areas of math that are 'fashionable', ...

And people always talk shit about the value of other peoples subject. I think it's even worse in subjects where there's money in it. I don't know, biology, industry,...

Tbh. even students will give me shit if I put time in (re-)learning and looking into a subject which I don't "need" anymore.

>Also, to further the logic example, when is the last time you seen a mathematician that studied logic win the field medal outside of Cohen?

Yeah, I happen to like Konsevic and Lurie because the work is close to my interest, but I was thinking honestly to myself and concluded that them being in the jury of the prices of the sort they won is pretty unfair. Of course, the works they understand and like will again go in their direction.

>This is why I like 4chan.

What I don't like is he idea of talking with people that I wouldn't like otherwise (engineers, unfriendly autists, etc.)

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>>6945431

There is a reason his 'proofs' haven't been considered valid yet. Mostly due to his autistic insular way of handling it (which is non-standard). Sounds like you are slightly autistic yourself. Unfortunate.

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>>6945434

There is an interesting point Friedman made on this topic. I'll just quote him directly:

"This is the **crucial point** about the Fields Medal for me. It definitely has this enormous influence. The committee is made up human beings, who inevitably carry their own biases and ignorance like everyone else.

Furthermore, their high status in the profession inevitably leads to reinforcement of these biases and ignorance. Since, as you say, the process

"tells us what the leaders of our profession consider important and promising," these biases and ignorance then get reinforced throughout the profession - especially since mathematicians still by and large (as you say) like the Fields Prize."

First of all, I think it is somewhat clear that the typical person on the Fields Committee probably is unfamiliar with even propositional calculus. However, they probably think they are competent to judge high level work in logic and f.o.m. in comparison to high level work in core mathematics -partly because they are commissioned to do so, and have agreed to do so. Yet the subtleties involved in doing so are of quite a different nature than the subtleties involved in judging the relative merits of high level work in core mathematics.

Even if there were to be some Committee member who had some knowledge of logic that included propositional calculus, that does not make up for the rest of the Committee who doesn't. And knowing something about the propositional calculus is really not near enough to be able to judge work in logic and f.o.m. at the highest level.

And even explicitly picking a senior logician to be on this Committee would not really help."

>>

>>6945458

"I don't think core mathematicians are incapable of understanding, say, the

propositional calculus and its reason for being. It just doesn't fit in too

well with what they normally like to think about, and logic and f.o.m. (and

the importance thereof) has to be carefully explained **interactively** in

order to be noticed. The process I outlined above will facilitate this. If

not the first round or two, then in later rounds. For then, there will be

an *acumulation of material* that is accessible. I.e., the logic/f.o.m.

people will, by trial and error and reflection, figure out how to explain

this stuff to the very sophisticated people involved in deciding the Fields

Medals."

More can be found here: http://www.personal.psu.edu/t20/fom/postings/9809/msg00099.html

>>

In 2014 they gave the medal for a brazilian and for woman.

This made it the first time a woman and a Latin American got a Fields Medal.

I wonder if they weren't influenced by all the privilege bullshit we see these days.

>>

I think Grothendieck would have never taken part at SE or MO. He would have been above it. I think SE and MO diminish mathematics. It is something really really wrong. It's just my feeling I am not even a pure math fag.

>>

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>>6945465

But you're right. Problems like this are probably worst in industry and fields where the 'money' is at. It seems to be less of a unique problem in the math community when thought of this way and more a sociological problem/problem with human nature wanting to be recognized and validated.

I choose to study math not because it is sexy, but because it is interesting. I don't even have a 'goal' to win any big awards. I'd be happy if I just learned a thing or two and maybe proved a thing or two.

>>

>>6945469

SE and MO are great sites to make autists do my homework for free. This way I don't need to post it here on /sci/.

>>

>>6945458

I only read a few f.o.m. mailing list entries but the people there generally seem to be aggressive as fuck. I've learned some logic in the last 2 years - there is no such course in the physics curriculum, and understanding the syntax-semantics interaction have helped me tremendously to judge possibilities and spirit of math.

On that note, I'll post a basic question on modal logic on /sci/ after sending this.

>>6945466

>brazilian

Hey, afaik there is a strong school of logic in the south of the world. I know of this guy and then some

http://en.wikipedia.org/wiki/Newton_da_Costa

Maybe the logicans might eventually get some.

>>6945470

I work at a NASA'esk institute and in those fields, where there's lots of money involved, there is no arXiv. People don't just post their shit on the web.

One should be happy, seriously ;)

>>

>>6945495

Please stop avatarfagging.

>>

>>6945495

I do math, but am switching over to theoretical CS.My undergrad university that had logicians in in the mathematics department. You could find a few in the Philosophy department as well (that taught math logic in Computability theory & Model theory). I also got some dosage of it in the CS department as well, as there were people doing research in AI using various forms of logic.

>>

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>>6945510

>>

>>6945507

The pic looked too much like the one the guy posted, I had to.

>>

Why do I have such a hard time to understand Kleene's T predicate and all that shit that refers to coding and numbering of machines?

Is it worth reading into the arithmetic and analytic hierarchies? It feels like knowing that stuff makes you judge possibility that somethings are true are not, but it's also a little too messy for me. (Sick of diagonal lemmas?)

And are you the guy who said that ... when judging if functions are computable, convergence of series is subtle and depends on some strange unintuitive things I don't understand.

>>

>>6931488

He said 'hopes'. It just looks like it could be true, and from what I can see (which isn't much) there's no reason other than the ones he gives that he can extend his work from theta functions to the Riemann zeta function. I'm no expert though.

>>

>>6941861

Because the Clay Institute thought that 7 was a nicer number.

>>

>>6944674

>there's still a lot of value in IUTeich

Why?

>>

>>6945348

>It should be

Not only is that impractical, it's undesirable.

>>

>>6946617

It's a new approach to number theory that allows us access to asymptotic bounds that most other methods don't. In particular it is one of the most significant results to come out of the anabelian geometry corner of number theory.

Perhaps more interesting (I haven't gotten far enough in the papers yet to say) is that he specifically makes use of "the universe" in which things occur. This will most likely be reformulated in topos theoretic terms in due course, but that reformulation should lead to a much greater understanding of topoi.

IUTeich is valuable because it (hopefully) provides new insight into some of the most powerful mathematical structure.

>>

>>6945495

I think the Brazilian guy made some contributions to his field at least, he has won prizes in it before the Fields Medal. I don't know about the woman. For what it's worth, this blog post (and others on the blog) are somewhat relevant to the above discussion:

http://owl-sowa

dot

blog spot

dot

com/2014/08/and-who-actually-got-fields-medals.html

(had to type weirdly to avoid spam filter)

>>

>>6947034

yeah I saw that some months before and read some of the anto-Gowers posts.

Seems pretty crackpot to me - from what he argues, he must hate the whole proof formalization stuff too.

I like Gowers projects, the tricki.org and also the Elsievers boycott stuff, so I'm kinda in favour of him.

>>

>tfw too retarded to explore the mathematical multiverse with Shinichi Mochizuki

>>

>>6951786

iktf ;_;

>>

>>6931488

This pic looks like a reaction image

>>

This has to be one of the oldest existing threads still around at this point.

>>

>>6952806

It's not even 10 days old

>>

Mochizuki seems like he'll be the Weil of this century - revolutionizing algebraic geometry in a complicated way, leaving a lot of work for everyone else to do for the next 100 years on cleaning up the theory/abstracting it further.

>>

>>6953953

I don't think so. Andre Weil and Oscar Zariski got everyone interested in pursuing algebraic geometry rigorously, but in the end no one used their weird formalism (from what I've read, I may be wrong). Apparently Zariski and Weil's treatment of algebraic geometry relied on having a field in the background, which, of course, is not the case with schemes.

>>

>>6951798

>le math man meme :^)

>>

>>6954306

And now Mochizuki will get everyone excited about pursuing inter-universal geometry seriously by proving some long outstanding hard conjectures, just as Weil did with zeta functions.

>>

>>6953164

Now it is. This thread is the longest surviving thread out of any in the current catalogue.

>>

>>6955246

But people aren't excited yet and there is no sign that they will be.

>>

>>6955246

Got Langs algebra again today, because I needed to look something up, and found it funny that he actually mentions the abc conjecture in the foreword.

To restate what the guy above said, afaik not many dare to invest the time to read mochizukis stuff.

>>

Awesome 90's website this guy has

It's missing a Friends Ring at the bottom

>>

>>6955643

I am, if only i could read those dam papers, thats my goal right now. to understand what he wrote.

>>

>>6934221

This.

>>

How to understand IUTeich from the bottom up:

- Algebra (Israel Gelfand)

- The Method of Coordinates (Israel Gelfand)

- How to Prove It: A Structured Approach (Daniel Velleman)

- Kiselev's Geometry - Planimetry and Stereometry

- Trigonometry (Israel Gelfand)

- What Is Mathematics? An Elementary Approach to Ideas and Methods (Richard Courant)

- A Course of Pure Mathematics (G.H. Hardy)

- Linear Algebra (Kenneth Hoffman and Ray Kunze)

- Elementary Differential Equations (William Boyce and Richard DiPrima)

- Topology (James Munkres)

- Calculus On Manifolds (Michael Spivak)

- Principles of Mathematical Analysis (Walter Rudin)

- Real and Complex Analysis (Walter Rudin)

- Functional Analysis (Walter Rudin)

- Partial Differential Equations (Lawrence Evans)

- Analysis On Manifolds (James Munkres)

- Abstract Algebra (David Dummit and Richard Foote)

- Algebraic Topology (Allen Hatcher)

- Introduction to Smooth Manifolds (John Lee)

- Foundations of Differentiable Manifolds and Lie Groups - (Frank Warner)

- Galois Theory (Harold Edwards)

- Linear Representations of Finite Groups (Jean-Pierre Serre and Leonhard Scott)

- A Classical Introduction to Modern Number Theory (Kenneth Ireland and Michael Rosen)

- Introduction to Analytic Number Theory (Tom Apostol)

- Modular Functions and Dirichlet Series in Number Theory (Tom Apostol)

- Riemannian geometry (Peter Petersen)

- The Theory of the Riemann Zeta-Function (Edward Charles Titchmarsh)

- An Introduction to Teichmüller Spaces (Yoichi Imayoshi and Masahiko Taniguchi)

- A Course in p-adic Analysis (Alain Robert)

- Foundations of p-Adic Teichmuller Theory (Shinichi Mochizuki)

- Mochizuki's papers at http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html

>>

>>6956712

have you read all of these?

>>

>>6956714

No, but I'm on my way. Should still take some years to finish it.

>>

>>6956716

>on my way

wow

>>

>>6947804

His stance is probably the way it is for cultural reasons, but I would agree with him on proof formalization as having problems. Ultimately, you can't make people agree that semantic correctness implies logical correctness on all issues, or some statement similar to that.

>>

>>6956712

You don't need to read all of them

>>

>>6957684

that doesn't matter much. what matters, the idea, is that you make computerized mathematics, or at least computer readable notation, so common that papers like mochizukis are (by humans) already formalized and written down so that they can be autormatically or assistedly checked.

>>

>>6957700

What good would that serve? The idea of why it is true is still not understood.

>>

>>6957700

Mathematicians generally have some faith, or let's rather say they don't care in detail.

>>6956721

What does X^log mean, how does it relate to a log?

When do the different universes come into play?

Why are 2-cats relevant, and on what level do we deal with 2-cats and at what level do we pass between universes?

I lack the language for most of this and all of this "Lok" stuff, so I don't get far.

In what form do the theorems come in this theory?

>>

>>6934112

>handed him a field's medal

Field's medal is isn't given to anyone over 40, that's why Wiles didn't win one.

>>

>>6957687

Can you make a more concise list please? That one really put me off even though I already knew some of those books.

>>

>>6945356

I really, really like this picture.

>>

>>6957778

Hartshorne's Algebraic Geometry, a few analytic and algebraic number theory things and probably some of Grothendieck's work (EGA, SGA). Ask an expert in the field of arithmetic geometry, they would know more than me. But I do know that most of that list is irrelevant for understanding the important parts of his work. Math is more about understanding things than reading things.

>>

Can someone give a cliff notes explanation of the Riemann Hypothesis to an idiot like me? Is that even possible? The most math Ive taken is 2nd year college calculus.

>>

>>6957944

Thanks

>>

>>6956721

Also, what role do moduli spaces play in this theory. Teichmüller theory is all about them, right? But then again, isn't Teichmüller theory not about complex Riemannian surfaces. That's weird, I don't see how this theory would be analogous.

>>

>>6946647

>people are doing good and useful work in mathematics

>but they're cooler than me so I hate them

>>

The 2 week old thread that refuses to die is still here.

>>

>>6959607

You'd like to think:

>There are people doing math

>I don't understand math

>Thus I hate them

When really it's:

>Hey it's autistic people doing autistic things

>>

>>6958921

A moduli space is a space that parametrizes a family of distinct objects (e.g. the triangles in the plane, distinguished up to rigid motion). Teichmuller space is the moduli space of all complex structures on a given space (e.g. a torus), up to homeomorphism (in the connected component of the identity). This itself turns out to be a complex manifold. The case of the torus (i.e. elliptic curves) is the easiest to start off with, if I recall correctly this is given by the torus's lattice in $$\mathbb{C}$$ modulo rigid motions.

>>

>>6959607

Why is that an argument in favor of the statement "math should be sexy"?

>>

>>6945466

What the FUCK are you talking about? Both of those people are fucking geniuses. What Mirzakhani did was nothing short of astounding work. Who the fuck are you to talk shit about such people?

You're a fucking neckbeard, 4chan-dwelling retard who hasn't accomplish jackshit, talking shit about the best mathematicians of our day.

>>

When will this thread be pruned?

>>

>>6961505

>What the FUCK are you talking about? Both of those people are fucking geniuses. What Mirzakhani did was nothing short of astounding work. Who the fuck are you to talk shit about such people?

>You're a fucking neckbeard, 4chan-dwelling retard who hasn't accomplish jackshit, talking shit about the best mathematicians of our day.

What the fuck did you just fucking say about me, you little bitch? I’ll have you know I graduated top of my class in Triple Integration Theory and I’ve been involved in numerous secret math classes on triple integrals and I have over 300 confirmed triple integrals computed I am trained in triple integration and I’m the top triple integrater in the entire US. You are nothing to me but just another target. I will wipe you out with precision the likes of which has never been seen before on this Earth, with barnett's identity. Mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting jacob barnett so we can kick your ass. The storm that wipes out the pathetic little thing you call your ego. I can be anywhere, anytime, and I out triple integral you in over seven hundred ways, and that’s just with my bare hands. Not only am I extensively trained in mathematics, but I have access to the entire arsenal of geniuses like jacob barnett and I will use it to its full extent to wipe your miserable ass off the face of any math competition. You’re fucking owned, kiddo. Consider yourself triple integrated.

>>

>>6962722

>no mentioning of IQ or -1/12 or 300k starting

meh, too lazy, I'll give you a 3/10

>>

>>6962725

Math major

>300k starting

>>

>>6962154

until the Inter Universal Teichmuller theory is verified of course

>>

What Mochizuki is claiming is that he has a new set of techniques, which he calls “inter-universal geometry”, generalizing the foundations of algebraic geometry in terms of schemes first envisioned by Grothendieck.

>>

This is the thread that refuses to die.

>>

>>6956712

someone should bundle that list into a torrent, download link or upload those books into that sticky link

>>

Holy fucking shit

Please let this die already.

"Anonymous 14 days ago"

>>

>>6963819

I hope this thread stops getting pushed up to the top with each comment soon. This thread has ran its course.

>>

>>6963819

>wants it to die

>bumps it

lel

>>

>>6963998

>it was most likely to be bumped anyway

>I may have contributed to its death by eliminating the need for a future poster to post saying the same thing

>>

It would really rustle my jimmies if someone bumps this thread again.

>>

>>6964042

me, too.

>>

>>6964133

same

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>>6964142

ya what is bump

>>

>>6931488

Oh, what an asshole. Have he stated, from where he got his "inspiration". He should consider, what happens after people get what damage this could cause. Stealing without understanding eh?

>>

And to add it. He "found" nothing more than the fact, that we had this solution since the universe begun. It is freaking awesome, that it took that long to discover this "super uba easy" algo. It's normal to produce primes with this. But I doubt he really understand what he is doing.

>>

>>6931488

Bumpin' this 2 week old thread.

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