Proof claimed for deep connection between primes

[Anonymous No.5046917]

>The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved.

>Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem.

http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378

[Anonymous No.5046948]

I'm not familiar with the abc problem, but at first glance it seems like it may just show like general lower bound stuff that's useful in many ways, but may not actually lead to stuff like prime number factorization that doesn't rely on an algorithm?

[Anonymous No.5046952]

>>5046917
enjoy the nsfw ban

[Anonymous No.5046953]

>>5046952
ok :3

[Anonymous No.5046954]

>>5046948
>but may not actually lead to stuff like prime number factorization that doesn't rely on an algorithm?
what? what we DO want is an algorithm. unless you consider guessing and checking an algorithm, in which case we want a very efficient one.

[Anonymous No.5046955]

Glorious if it works out.

>>5046948
It's a very strong bound that allows you to solve all sorts of Diophantine problems. The proofs are things like:
- you prove that x is an integer between 1.5 and 2.5, and therefore you can find x
- you prove that x is an integer between 1.5 and 1.9, and therefore show that there is no x satisfying your conditions

Plus you have the body of math that leads up to solving the problem, math which will surely be useful in solving other related problems.

[Anonymous No.5046957]

>>5046953
enjoy your emoticon ban

[Anonymous No.5046961]

>>5046957
ok :3

[Anonymous No.5046962]

>>5046961
enjoy your nsfw ban.
enjoy your emoticon ban

[Anonymous No.5046966]

>>5046955

That's what I mean, in the context of prime factorization, at best it will be used to make better bounds/guesses and make algorithms more efficient.

>>5046954
It would be better if we could just make an equation. An algorithm is kind of a worst case scenario.

OP, please delete your nsfw pictures, don't be a jerk.

[Anonymous No.5046970]

>>5046962
ok

[Anonymous No.5046977]

what's wrong with those titties?
looks good to me...

[Anonymous No.5046982]

>500 page

Proof by intimidation

[Anonymous No.5046983]

>>5046977
they're highly unscientific

[Anonymous No.5046998]

The abc conjecture is surely one of the most well-known problems in number theory, Mochizuki has been working in this direction for many years.

As for the abc conjecture specifically, it is the following.

Given e > 0 there is a constant C such that for all nonzero, relatively-prime a,b,c satisfying a+b=c:

max(|a|,|b|,|c|) <= C rad(abc)^(1+e)

where rad(x) is defined to be the product of the primes in x, without multiplicity.

This implies Fermat's Last Theorem in all but finitely many cases as follows.

Assume that x^n + y^n = z^n

By the above, we have that:

x^n <= C rad((xyz)^n)^(1+e) <= C (xyz)^(1+e)

and similarly,

y^n <= C (xyz)^(1+e)
z^n <= C (xyz)^(1+e)

Multiplying these inequalities together we obtain:

(xyz)^n <= C^3(xyz)^(3+3e)

(xyz)^(n - 3 - 3e) <= C^3

Taking the logarithm of both sides, it follows that:

(n-3-3e)log(xyz) <= 3 log(C)

and as log(xyz) >= log(2) since x^n+y^n = z^n, there holds that:

n - 3 - 3e <= 3 log(C) / log(2)

The right-hand side is a constant. Therefore, n is bounded from above. That is, there are only finitely many n such that FLT holds.

Pretty neat.

[Anonymous No.5047003]

>>5046948
Proofs of will probably not lead to faster prime factorization algorithms. If a theorem being true lead to a fast prime factorization algorithm people would simply assume it's true, and test it out have experimental results that the algorithm works quickly, even if you can't prove it should.

[Anonymous No.5047010]

>>5046998

Jesus Christ if you're going to bother to type all that shit use math/eqn tags.

[Anonymous No.5047020]

What would this imply? Why do we need to know all of the primes?

[Anonymous No.5047023]

>>5047003

This makes sense, I guess a solid conjecture lacking a proof/counterproof is in many practical applications just as good as the real thing.

[Anonymous No.5047025]

>>5047020
the difficulty of prime factorization forms the basis of modern cryptography

[Anonymous No.5047045]

>>5047025

Yes and no. It forms the basis to RSA encryption, which is the largest currently used cryptosystem out there, but there are others. El Gamal is another large cryptosystem.

[Anonymous No.5047104]

Guys, I breafly read the first of his articles, just one question:

HOW the fuck could he manage to afford all this fuckload in his brain ?

This is goddamn formulae, formulae, groups, frobenoids, cusps, theta-data OMG

Even Perelman's article was smaller, yet also difficult to understand.

I read several books on GR and QFT and even they were easier to grasp.

[Anonymous No.5047116]

>>5047104
Because Mochizuki is a first class mathematician who has worked on these results for a long time.

These are not formulae or difficult words which he is forced to remember, but ideas and concepts with a beauty all of their own.

[Anonymous No.5047117]

>>5046955
>integer between 1.5 and 1.9
>integer

[Anonymous No.5047118]

>>5047117
Did you even read the post?

[Anonymous No.5047120]

>>5047104
Unlike other fields, once you understand a concept in mathematics it's common sense. If you're using rote learning and memorization then you are doing it wrong.

>>5047117
>squinting really hard to see the integers in between

[Anonymous No.5047124]

>>5047104
He's Japanese, and therefore smarter than you

[Anonymous No.5047127]

>>5047120
Oh come on. I've forgotten so much stuff that I understood, it's not even funny.

[Anonymous No.5047133]

In what way is this useful to anyone besides a mathematician?

[Anonymous No.5047140]

Which concept ?

Of a frobenoid ? But what for ?

E.g. does it really matter, call
we Lorentz transforms a Lorentz group or just
assume these rules and then calculate ?
Same way call I Laplace transfroms a some special group, what
does it give me ? Say, I have then a concept of a commutator subgroup,
abelianization etc. But again for which reason ?

Guys, I have nothing against it, but for my vision abstract maths ve gone too far.
I was tought in spirit of the old school, its like functional analysis, complex analysis,
vector and tensor calculus, but I had enterily no group theory or other abstract shit and I
completely dont understand what is a real advantage of it, except just calling usual things
"groups", "module" etc.

And this shit works ye know. I research control systems and its like much about maths, but I completely dont need these concepts.

Even GR and QFT can be completely understood without group theory.

It reminds me the old controversy about normal "german" maths and "jewish" abstract maths.

[Anonymous No.5047154]

>>5047140
>Even GR and QFT can be completely understood without group theory.
HAHAHAHAHA

[Anonymous No.5047158]

>>5047154
prove me wrong first,
demonstrating you are retarded - go to /b/

[Anonymous No.5047160]

>>5047127

Actually, I have too, but I had a lot of shit happen in my life and ended up leaving mathematics for 6 years (till now since I just got registered into a Uni for the winter semester).

I still remember a lot of shit conceptually, but if you were to ask me to apply stokes theorem I wouldn't even know what the fuck. Really need to get back on the horse.

[Anonymous No.5047168]

>>5047140
the advantage of abstraction is that it allows us to see the structure of things more clearly. For example, all the different methods you learn in ODEs to solve them (1st order, 2nd order, bernoulli, variation of params, etc...). All of these are actually the same method, but you can only see it if you start viewing solutions of ODEs as Lie groups.

[Anonymous No.5047171]

Let me tell you something, when I come to 4chan, I come for quality discussions and trolling, not for dirty pictures to stimulate myself. If I wanted to stimulate myself, I would have gone to somewhere else for my weekly stimulation. But no, you shitwads want to just keep on posting NSFW pictures as if the rest of the world wants to see it. Protip: Not everybody wants to feel stimulation in their pants while they browse an imageboard.

Now before you say something along the lines of, “But if you didn’t want to get fucked up don’t go on 4chan", well of course that is the most safest route, but why should I do that when I could just go to SFW board? SFW means safe for work, but nooo, you fucks think it means not safe for work. There are quality SFW boards that are an interesting place to lurk and post at: like /v/, /vg/, /g/, /a/, /jp/, /lit/, /mu/, /sci/ and so many more. The content there is quality discussions, but some faggot always go ahead and post some ridiculous NSFW picture that definitely does not pertain to the thread’s topic. Also using a post or thread hider is useless, since its thumbnail has already been downloaded and shown to people before even being able to hide it.

Now how hard is it to not post a NSFW image and just post some SFW image of some fucking sort? Hell,even a My Little Pony picture would be more appropriate.

I swear it feels as though 4chan’s userbase has shrunk in thinking. I guess that is to be expected with the influx of kids from /b/. No wonder people say technology is dumbing down society, you guys can’t even critically think about others' situation.

Long story short, fuck you all posting NSFW pictures on SFW board. I hope you all go to hell, good day.

[Anonymous No.5047175]

>>5047168
Okay, okay. It makes sense.

But lets recall to the definition: Lie Group is a smooth manifold + a smooth operation.
Okay, but isnt it too general ?

I have nothing against but even without these general def-n i would say, sol-s of ODEs
are smooth and could be smoothely multplied by each other.

No complaints, just trying to look from another viewpoint.

[Anonymous No.5047177]

>>5047171
Here are some boobs to help you calm down.

[Anonymous No.5047182]

>>5047158
>prove me wrong first,
Tell me how you can do gravity without a functional on the Levi-Civita connection of space-time with values in the Poincare group.

Tell me how you can do quantum field theory without vector bundles with a connection. Tell me how you can formulate electromagnetism without GAUGE TRANSFORMATIONS.

By DEFINITION both of these theories REQUIRE group theory.

Do you even know what SYMMETRY means? How old are you? Your cognitive defects are an insult to SCIENCE. Get the fuck out of the SCIENCE board, you imbecilic moron.

[Anonymous No.5047184]

>>5047171
there is so much wrong with you.

[Anonymous No.5047191]

>>5047168
>>5047175

I'm kinda inclined to agree. Whilst from an abstract standpoint it may be nice to know that all solutions to ODEs are connected, I fail to see how this knowledge helps in carrying out the procedure of solving them. It doesn't matter if the different methods you know are connected if you don't know what they are or how they work.

[Anonymous No.5047192]

>>5047182
>Your cognitive defects are an insult to SCIENCE. Get the fuck out of the SCIENCE board, you imbecilic moron.
My sides!

[Anonymous No.5047197]

>>5047140

>analysis...old school
>implying algebra isn't older than analysis
>implying abstract algebra isn't the basis for modern computer science

[Anonymous No.5047200]

>>5047197
CS is neckbeared horseplay with shitty category theory - it is not SCIENCE. You will not defile SCIENCE with anti-intellectualism, shitposting asshat.

[Anonymous No.5047204]

>>5047182
Vacuous argument. Feels like you re just a student. Question to question is not an anwser.
I put a question - you anwser. You dont know ? Then
just forget, screaming demonstrates your poor intelligence.

> you can do gravity
what do u mean ? Say, I have a connection, some transformation rules, which preserve the proper time, what does the NOTION of a group give me ? Can u understand the question ?


Learn how to make a discussion form him >>5047191

[Anonymous No.5047205]

Amerifags, I don wanna harm you, but it is just the way, YOU were tought,
"New math" if I'm right.

I can understand your malice, but they way you argue with eurofags
doesnt make you a credit.

[Anonymous No.5047208]

>>5047171
>>5047171

Fag? Much?

[Anonymous No.5047209]

>>5047205
*shrugs*
that's only because we tend to send democracy via bomb bay doors

[Anonymous No.5047211]

>>5047182

You should have stopped replying after the "prove me wrong" part. Instant disqualification.

[Anonymous No.5047214]

>>5047197

Abstract Algebra (including Linear Algebra) is pretty much the basis of anything nowadays.

[Anonymous No.5047216]

>>5047205
I understand that 4chan boards are pretty much the ugly side of whatever topic at hand, but god damn.

All of the people claiming to have taken complex analysis and group theory in the 7th grade or whatever while talking down to everyone else just sickens me.

How does it make you feel to know that there are people who know more about those subjects than you ever will, but at the same time they aren't elitist about it at all? You should feel ashamed.

[Anonymous No.5047218]

>>5047200
Math isn't science either. CS is actually more scientific than math, with sometimes having to run "experiments". Both are perfectly logical and acceptable areas of study though.

[Anonymous No.5047219]

Anyway I hate to be a nigger and I know you math types enjoy solving these problems just for fun...


But does this have any potentially "practical" applications? Cryptography perhaps?

[Anonymous No.5047225]

>>5047204
>Then just forget, screaming demonstrates your poor intelligence.
Clearly you don't understand "why" this formalism is used. I'll try to clarify.

>Say, I have a connection, some transformation rules, which preserve the proper time, what does the NOTION of a group give me ?
That is the entire point of Lie groups in physics. Gauge transformations are morphisms that preserve the configuration space. Gauge groups define the structure of this configuration space. The action functional is a function of gauge transformations, right? The only invariant that works is this theory. Your argument is equivalent to saying that you can call a topological group either a topological group, or some topological space with continuous group structure. It's semantics.

Connection and curvature define gauge fields - http://en.wikipedia.org/wiki/Curvature_form#Definition

The field strength is then encoded with a Lie algebra valued differential form which is consistent with gauge transformations and symmetries of the underlying manifold. This provides a Lorentz-invariant structure that preserves both local and global symmetry and geometrically looks like a fibre bundle attached to every point on a base manifold.

There's empirical evidence that these fields exist - http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect

There is no known other way to do this in a theoretical framework that is consistent with observation. If you can find a means to recover all means of transformations that act both on field configurations and observables that makes better predictions, you'll probably win a Nobel prize.

If you want more, get a book on AQFT.

[Anonymous No.5047223]

>>5047219
No. Pretty much this.
>>5047003

[Anonymous No.5047233]

Whats with all the people on this board so hung up on maths for its practical sake only? cant people just appreciate that a famous conjecture has perhaps been proven without complaining about the lack of current applications?

[Anonymous No.5047236]

>>5046982
Yeah, I'm calling minor arithmetic mistake on this one.

[Anonymous No.5047241]

>>5047233

Have some compassion for the engineering fraction.

[Anonymous No.5047242]

>>5047233
Most of us are not Math nerds so we don't inherently see the joy in it.

[Anonymous No.5047244]

>>5047233
This board is filled with engineers. They cannot see beauty in formal systems

[Anonymous No.5047261]

>>5047208
Yeah, of course you can't say anything even halfway intelligent. As expected.

[Anonymous No.5047265]

>>5047219
>>5047133
This helps solve many Diophantine problems. Diophantine equations are typically easy enough to explain to a child but crazy enough to take millenniums to solve. No, no matter how sophisticated computer science or physics get, they will probably never become sophisticated enough to solve a Diophantine problem.

>>5047233
It's because of all the innumerate sciencefags who we share the board with. Our retarded mod doesn't help either.

[Anonymous No.5047288]

>>5047225
wait, wait, wait. Again this is a structure to define alternatively the connection, which is
just a *rule* for cov. derivatives, right ?

U completely dont understand my question. Nobody is arguing that
gauge transfroms are have to be defined properly. But u can say either
these transforms preserve proper time *thus* they form a Poincare group, *or* a
definition of this group naturally flows from these physical facts.

AGFT - is just one approach to give rigorus mathematical basis for QFT axioms. Its strictly methematicians' problem. U re misunderstanding again.

[Anonymous No.5047331]

I wonder if this is where I left my SFW...
Nope, not here.

[Anonymous No.5047334]

do people really read 4chan from work?

with their boss/coworkers looking over the shoulder?

[Anonymous No.5047339]

>>5047334
and you don't?
What are you, an /r9k/?

[Anonymous No.5047343]

>>5047339
Actually I do. But I'm a sysadmin so I know to SSH tunnel back to home first. And not to do it while the boss is in the office or someone is reading over my shoulder.

[Anonymous No.5047353]

>>5046970
enjoy you're ban

[Anonymous No.5047359]

>>5047334
>2012
>having a job where anyone gives a shit what you do on the internet when you do good work
>ishygddt

[sage No.5047362]

>>5047359

some offices have female employees.

[Anonymous No.5047451]

>>5047362
So they feel insulted when one looks at better looking women on the internet?

[Anonymous No.5047457]

>>5047451
...don't get out much, do you?

[Anonymous No.5047459]

>>5047451

no, they report you to HR and you and your boss get a spanking.

[Anonymous No.5047640]

So, I see, mathfags sick dick again trying to substantiate, that they are needed

[Anonymous No.5047656]

>>5046917

she has a nice pair of primes...

[Anonymous No.5047676]

>>5047459

i must have missed a century or two... sorry...

[Anonymous No.5047707]

Gender identity.

Is it the society that shapes men to be less emotional, aggressive and have the more dominant role through spoonfeeding us with the ideal of a man and the norm, so that's why we become who we are?

Or

Is it mostly reliant on our biological heritage, our genes, hormones and genitalia?

Discuss.

[Anonymous No.5047720]

>>5047676

they are both potentially offensive.

why not treat ppl like you would have them treat you?

[Anonymous No.5047721]

>>5047720
If I treated women how I wanted them to treat me I'd get arrested

[Anonymous No.5047723]

>>5047720

what people, exactly, am i treating?

you seem to be oozing politically correct nonsense. that has to hurt your pores.

[Anonymous No.5047724]

I like sci changing themes so suddenly :3

[Anonymous No.5047726]

>>5047721

now THAT's funny, i don't care who you are!

[Anonymous No.5047730]

>>5047724

we're so much smarter than your average... board.

say... /b/ or something of that nature.

[Anonymous No.5047733]

>>5047730
No, I dont like ur b, its even more stupid than ours

[Anonymous No.5047736]

>>5047720

when the picture of a human, clothed or not, becomesw offensive to a race that has been around for, oh let's say half a million years, then that race no longer truly deserves to be 'at the top of the food chain', because that race would have, obviously, missed some crucial link in becoming fully sentient.

can you follow that or should i couch it some 2012 gabble and follow it with a graph in order for you to understand how completely silly it is for an individual to apply their mores across a broader social spectrum than their simple, yet probably misguided, spectrum of existence?

logic. it truly sucks. emotional nonsense. now THAT'S the future.

[Anonymous No.5047738]

>>5047733

i didn't mean, like you know, for literally or anything like that you know.

i just pulled a forward slash and a random letter and another forward slash out of my butt and, like, typed it on the paper you know.

except it'snot really paper, like, but a screen that i guess acts like the paper if there was paper where the screen was, like.

oh, it's all very scientific.

you know.

[Anonymous No.5047753]

>>5047738
You try to look retarded, dont you ?

[Anonymous No.5047752]

>>5047724

we must continue to remain light on our feet in order to guide this insanity along lines both respectable and intelligent, or as ever the need arises for us to continue with inanity or introspection, whichever may occur first, or should have if that's the case, or in whatever order you would have to make this seem spontaneous and somewhat lackadaisical in nature, unless of course that is your nature in which the simple use of structure would probably appear to you as if all were chaos and complete disjointednous on this board.

yes, that was a real sentence.

[Anonymous No.5047754]

oh hey this thread is still here

[Anonymous No.5047763]

>>5047753

i don't TRY to look retarded... i AM retarded...

and that you noticed really REALLY hurts...

[Anonymous No.5047775]

>>5047763
Then I make a guess, that you are this saem-person-
faggot:
>>5047154
>>5047182
>>5047192
>>5047211
>>5047225

[Anonymous No.5047789]

>>5047754

JUMPIN JESUS ON A POGO STICK !!!

you CAN'T post shit like THAT here... the titty nazis will come and take you away!!! you wouldn't want to be taken awayh, now would you?

well, WOULD YOU?

you may only post the appropriately religiously moralized versions of any postable type posting material...

i believe the picture you would LIKE to post resembles something along the lines of this.

[Anonymous No.5047795]

>>5047789
too much skin. you may enjoy a ban.

[Anonymous No.5047805]

>>5047775

i may be a faggit (?), but at least i have the intelligence to a) use proper grammar and punctuation (did i leave out sentence structure and spelling on purpose? very possibly) and b) not bother to show up at the science board with an IQ about the same as your shoe size...

unless of course your shoe size is larger than, say, an eight (narrow).

oh, and no, i'm not the same one. why would you ask?

[Anonymous No.5047810]

>>5047795

dammit! i couldn't make the brush size any smaller in order to do the fine work around the eyes...

My! you HAVE covered yours up pretty well, haven't you?

i am jealous!

[Anonymous No.5047831]

>SFW 4chan board

[Anonymous No.5047837]

>>5047831
it's in the rules retard. fuck off.

[Anonymous No.5047852]

Anyway, back on topic.

I'm doing my Masters in cryptography and I'm more concentrating on quantum cryptography at the moment. I'm failing to see the connection between Fermat's Last Theorem and the abc conjecture proved here. Does anyone have an understanding on how the abc conjecture implies FLT?

[Anonymous No.5047854]

>>5047837

is retard a scientific term? i've heard it bantered about quite a bit, especially on this thread.

one can only assume it relates to the square root of religious moral degredation of the thespian atom when mixed in a duroxide of ammonium nitrate and couple with a close order schema...

or so.

retard.

[Anonymous No.5047857]

>>5047852

MY...GAWD...

are YOU lost...

[Anonymous No.5047869]

>>5047854
I am not a retard. I am aware of the rules. Take your nonsense back to >>>/b/ retard

[Anonymous No.5047879]

>>5047854
That post was really dumb. I know you were trying too hard to be funny. But this was just epic fail.

[Anonymous No.5047897]

>>5047805

So, "proper grammar and punctuation", but not sentence structure or spelling? What, exactly, do you think grammar is?

Also, about that "proper grammar and punctuation" of yours...

[Anonymous No.5047917]

>>5047171
If you get that uncomfortably aroused by thumbnails, you're the one with the problem bro..

[Anonymous No.5047925]

>>5047288
May I jump in? All math is analogy, at its heart; a very careful analogy to be sure, but analogy nonetheless. When I say, "life is like a bowl of cherries" we can make certain isomorphisms with the pit and how sweet it is, and how nice it is to find a girl who can tie up the stem with her tongue, but the analogy brings with it a lot of connections that don't make sense as well. Group theory, and other structural bookkeeping make sure we don't ADD or IMPLY anything that isn't true to our analysis; it makes sure our analogies are so good, we can use them to predict the future.

[Anonymous No.5047929]

>>5047869

no... YUR the retard.

and /b/ was just some bullshit letter, or don't you understand THAT yet either?

i repeat... YOU'RE the ...

[Anonymous No.5047931]

ghfrbf I can't wait to spend all day trading insults with someone on a different continent hbbbcxfhkmbtuiokvb

[Anonymous No.5047936]

>>5047879

i'll try harder for you mrs. loopner... i promise! we'll get that chuckle out of you yet. maybe even a guffaw.

[Anonymous No.5047942]

>500 page proof.

It's going to take a long time to verify it.

[Anonymous No.5047945]

>>5047879

{sobs} but i WAS trying so hard {sobs} and then YOU came along and made {sobs} FUN of me and all the hard work {sobs} i did.

and i did it {sobs} JUST for you...

i'm going home now {sobs uncontrollably).

[Anonymous No.5047947]

>>5047897

titty nazis AND the grandma police...

shoulda known not to come here on my days off... these people are fucking SHARP!

dammit.

[Anonymous No.5048022]

>>5047854
A person can have mental retardation, or be mentally retarded. Retard is a shortening with negative conotations, spic vs hispanic is another example

[Anonymous No.5048032]

>>5047947

Well, to be fair, HE was the one who bragged about his grammar. So, really it's like he was a power-tripping Syntax Store security guard that got caught pretending to be a an officer of the Grammar Police in an botched attempt to make someone else look stupid. Kinda like I'm doing now for illustrative purposes.

[Anonymous No.5048362]

>>5047925
Do you mean, in this sense these abstract constructions act like some kind of restrictions ?

> it makes sure our analogies are so good, we can use them to predict the future
E.g. AQFT. Which predictions does it make itself ?
Which prediction could be possible based on a proper structure put on some known
things, say physical facts ?

Even more specific, is the definition of Poincare group based on physical facts about proper time, or Poincare group predicts Lorentz transform etc. ? I'm not sure about the history of the subject, but I would suggest, that this group was formulated based on
the notion of proper time and Lorentz transfroms.

We're goin into the old controversy between pure maths and physics+engineering sciences. It senseless.

BTW what would you say about such analogy: abstract constructions in maths = classes in programming

[Anonymous No.5048405]

>>5047925

pure mathfags would probably argue that real life is just an analogy of mathematics.

[Anonymous No.5048414]

What is wrong with /sci/ today...?

I'm going to leave, and when I come back tomorrow all these shit posters better be gone.

Holy shit all I wanted to do was get some /sci/ence news and you kids are >implying>implying>implying with fucking namecalling and fallacy.

what is this?

[Anonymous No.5048437]

>>5048405
easy, dont harm their feelings
these guys also wanna look like they are needed in modern world of technology
and applied science LOL

[Anonymous No.5048476]

>>5048414
>implying >implying
faggot

[Anonymous No.5048488]

>>5047104
He's 43 years old.

Imagine that you starting studying math at princeton at age 16, and continued rigorous study for 27 years.

There's an insane amount of knowledge in his head

[Anonymous No.5048498]

>>5048437

Actually, pure mathfags not only don't care if the world needs them, but they don't need the world. Never do advancements from other branches lead to advancements in mathematics unless they're done originally by mathfags in multiple fields (in which case the math part comes first).

[Anonymous No.5049475]

>>5047288
>Again this is a structure to define alternatively the connection, which is just a *rule* for cov. derivatives, right ?
Yes. In "experimental physics" the point of gauge groups/algebras is just a structure to hold the transformation law for the connection under gauge transformation - so you know how local trivializations change as one moves around on the base manifold. It's the natural framework that emerges from the symmetries of the system.

Because all the symmetries in a group form a manifold; you have the appropriate means of frame, connection, and curvature to define fields and field strength now. Perturbations in the connection are the particles we see in colliders.

Again, you have a configuration space <span class="math">\mathrm{Conf}[/spoiler]
<div class="math">S:\mathrm{Conf}\to\mathbb{R}</div>
under some action functional <span class="math">S[/spoiler] that is invariant under a bunch of symmetries that are associative and closed (mathematicians called this a group <span class="math">G[/spoiler]) acting on <span class="math">\mathrm{Conf}[/spoiler]
<div class="math">\forall g \in G, \phi \in \mathrm{Conf}: S(g(\phi))=S(\phi)</div>

>AGFT - is just one approach to give rigorus mathematical basis for QFT axioms. Its strictly methematicians' problem.
That may be the case, but investigating things axiomatically is beneficial in the sense that you can see there exists no other framework that could "replace" gauge groups.

>U completely dont understand my question.
Let me just remind you what I'm arguing over again. In >>5047140
>But again for which reason ?
There is nothing else. It doesn't matter if you call it "a collection of transformations which leave the system invariant" or a "group". Therefore
>Even GR and QFT can be completely understood without group theory.
is wrong.

[Anonymous No.5049478]

>>5048362
>E.g. AQFT. Which predictions does it make itself ? Which prediction could be possible based on a proper structure put on some known things, say physical facts ?
If you're talking about the framework of QFT, well, it turns out, thanks to combinatorics and the fact that spontaneous symmetry breaking is experimental, that there are a limited number of possible gauge groups that represent every possible universe. AdS/CFT then allows a computational technique to sift through all of these and find a couple that fit experimental data. The more data we get from the colliders, the more vacua we can eliminate, the closer we get to a theory of everything without ever needing to probe the Planck scale.

>Even more specific, is the definition of Poincare group based on physical facts about proper time, or Poincare group predicts Lorentz transform etc. ? I'm not sure about the history of the subject, but I would suggest, that this group was formulated based on
the notion of proper time and Lorentz transfroms.
Yep. The Poincare group is the group of all transformations which preserve flat spacetime. Unitary representations turn out to be the familiar elementary particles we all know and love. They all naturally come out of transformations which respect the spacetime interval/metric/proper time/whatever.