@MikeMiller First I have to learn commutative algebra and then algebraic geometry. I haven't even finished Munkres (but I am at the end of chapter 13). I guess I should keep it slow :P I'll keep this problem at the back of my head and note your reference rather.

I don't think I am going to approach Gal(\bar Q/Q) anytime soon

@Ashwin Undoubtedly.

right after Z_p I have Gal(\bar C(z)/C(z)) at the list, and I have to learn Riemann surfaces first to think about it the way I want to, so....

@Ashwin are you an engineering student?

@Ashwin For me it's entropy is $$\Huge 0$$

@Ashwin I didn't read that document but....

@BalarkaSen May's stuff has nothing to do with those, for what it's worth. I'm glad you want to keep it slow; I think going quickly is a dangerous path, as you'll forget things you don't think about carefully for some time. (Experience talking here.)

@Ashwin That document is about finding two string with same MD5 hash.

@Ashwin That probably wont be able to lead you to original string.

@Ashwin Why, You fall in love with maths?

I think I might have sounded discouraging above and I didn't intend that. This sounds like a good project encouraging you to do a lot of math. Some things are almost certainly dead ends though (or not fit with the right ideas). I can do a better job of warning you off the things I know won't work; I can't help with what will.

@Ashwin Aditya

@Ashwin Don't ever get caught in maths trap

PS - if you want to realize something "geometrically", you don't want the etale fundamental group, as powerful as it is. It's almost a tautology that $\pi^e_1(\text{Spec }\Bbb Q) = \text{Gal}(\Bbb Q)$. I don't think this is what you mean by a geometric realization.

@Ashwin Why Mathematics? Don't you think engineering is a good profession?

@BalarkaSen that's what everybody thinks, till it does.

inspirational but not, I think, entirely true

@Ashwin And how is that related to maths?

How's life, @Venus?

Is this kosher notation? $$ \left\{ n + \frac 1n \geq 2 \mid n \in \mathbb{N} \right\} $$

@Ashwin Yes, I'm studying first year engineering!

@Alex I'ma put a puny bounty on your 2-groups question.

@MikeMiller which'n?

hm, nah. Was going to do it on the highly upvoted one. But the point of a puny bounty is to attract attn to questions nobody's seen.

@Ashwin Don Bosco Institute of Technology Mumbai

@MikeMiller ah yeah the reference request? I did have a bounty on that once actually and it ended up running out

@Ashwin GOAT Computer Science

@Ashwin Mathematics is just like a girlfriend to me! Whom I don't want to marry.

@Huy Fun. My grades are also good. Waiting for wonderful X-mas. You?

@Ashwin actually I'm trying to repeat to get into some $$\Huge\text{IIT}$$

@Ashwin Not yet. It's still one semester ahead

@Ashwin Yeah.... But...

@AlexanderGruber If I suspect that a person is operating two accounts on Math SE, what should I do?

@Venus Do you think WB is fun? See this,

@Venus: Had my last tutoring class in linear algebra today. Eventually. Such a relief.

@Integrator i suggest mixing iced tea and lemonade, maybe with a slice of orange

that was easy. went down my faves list and found something unanswered that I want answered.

I know, @Mike, I can get enthusiastic several times when encountered nice-looking advanced ideas (and especially big names ;)) but I'll eventually stop to look behind at what I have done and how much I have understood of it, mostly because of the warnings of you, Ted, Daniel, Pedro, Karl and Alex.

I appreciate them, and I'd always like you guys to give heads up whenever I try for big jumps, which will if successful would end up missing a lot of stuff in the middle that I should have done. I would definitely appreciate if you warn me with ideas that won't work and I welcome any ideas you have as well.

@Integrator having two accounts isn't illegal unless the two are interacting, e.g. upvoting each other or adding answers/bounties to each others questions. If you think the latter is the case, flag it and say why you think that.

Thanks for the inspirational comment @AlexanderGruber but like Mike said, it's not quite entirely true. I know that what I am doing won't work for Gal(\bar Q/Q). The best I can do probably is Gal(\bar C(z)/C(z)). If it was that easy, Grothendieck would have done it way earlier ;)

@Integrator: How did you get that incredibly awesome football hat?

I only have candles :(

@MikeMiller No, that's not quite a geometric realization :) I am familiar with the fact (only the fact, not a proof neither what it means) but Spec Z is not really a geometric object.

Oh, I didn't notice your hat 'til now. Love it.

Hey, I didn't even say Spec Z - I said Spec Q. (Lots of folks would disagree with you about Spec Z, but YMMV.)

It also strikes me that what you're trying to do and what Grothendieck was trying to do are quite different.

@Integrator What WB? Anyway, why have you not posted your answer to my question?

@Huy That sounds good.

@MikeMiller You do? Well that doubles my suspicion that what I am thinking about is BS.

@Venus: We're having great weather over here these days. I woke up to this a few days ago: imgur.com/hNuhTWF

@BalarkaSen No - this is a statement out of ignorance. I don't think he was interested in the sort of 'geometric realization' statement you're talking about. I think he was interested in different questions entirely.

Don't take my comment too seriously.

He did think about a geometric realization in Equisse d'un Programme though

Grothendieck-Teichmuller theory is meant for that job AFAIK and was discovered by him in his later years of mathematics.

Maybe so! Again, a comment out of ignorance.

Wouldn't you considering embedding Gal(\bar Q/Q) in a braid group as geometric realization?

Probably not. But that's personal taste.

Might be so.

@Ashwin Oh, thanks.

(how do people know when my birthday is, lol)

@Integrator math.stackexchange.com/questions/782414/… <- I've done my part.

@DanielF How do those folks find old stuff to fix up? Only tools I know are the ones in the top right.

@MikeMiller Which folks, and what old stuff to fix up? The unanswered tab enables one to find posts where one can nag comment-posters.

That could have been more clear. About a third of the edits I see suggested are on posts much older than the past, say, week, and some of these edits are done methodically by certain users. Are these just questions they're running into and fixing up or something else entirely?

@Huy What's that? I can't visit the link you gave. My internet firewall suspects that's phising

@Venus: imgur.com is a popular website for hosting pictures.

@MikeMiller often they're in less popular tags for which you can go back months by just scrolling to the second page

ahh, that explains it.

@N3buchadnezzar Depends. It's a perfectly fine set of boolean values, $\{\text{True}\}$, provided you have $0\notin \mathbb{N}$.

@DanielFischer and I did mine :)

@MikeMiller One common way to find such things is to search for posts containing a particular misspelling (Schwartz where Schwarz was meant or so). That gives you a nice big list if you chose the right one.

It annoys me when people bump a whole bunch of those things.

@MikeMiller You're not alone.

It seems to me the exact same purpose could be achieved by commenting "The correct spelling of ____ is ____."

Well, I guess it improves searchability.

winterbash2014.stackexchange.com/naruto the hell is with this name ?!!! -_-

@Venus I have asked about that integral before. Have you seen the paper it was posted in?

@Venus try each separately first

If you dig through my questions you will find it.

@MikeMiller It's good to make such corrections immediately, when you just happen to come across the post. If you make a search and go badge-hunting, it's annoying.

Yeah.

@N3buchadnezzar No, I haven't. Where?

@robjohn K

One bumped question is nothing.

@Venus In reality it is a simple appliance of the fubbini theorem. However the restrictions for when it is legal to apply it is not met. However it works...

@Huy Complete 10 review tasks!

$$ \int_0^\infty \frac{f(ax) - f(bx)}{x} = \log \frac ab $$ If i remember correctly

@N3buchadnezzar It doesn't work because $f(\infty)$ diverges

@Venus If you ignore that you get the correct result

that is why I asked a question on main about it

Search for it... Do some research yourself =)

I have a billion exams atm

@Venus arxiv.org/pdf/1005.2940.pdf here is the paper... Example 3.7

@Venus LOL

@Venus that paper from @N3buchadnezzar is not that bad.

@DanielFischer If you don't want to answer those questions then say it explicitly. I'll do that.

@robjohn someone has gone on bizarre editing spree, I guess he is trying to earn Archaeologist badge.

@Integrator Some I would not want to answer (too boring), converting comment to answer on others is fine. If you see one you'd like to answer, you can answer it without pinging me. For the others, ping and ask if I want to. I may or not. Just don't ping me in a too high frequency, not more than a couple per day, please.

@Venus I didn't get my 7 th Enlightened because of you. :(

@DanielFischer -sensei if you think that's too boring, maybe you can find my problem above challenging ^^

@DanielFischer I only pinged you for those question which I found interesting.

@Integrator Interesting enough to want to have a go yourself?

@Integrator Why me? math110 won't accept the answer that he doesn't like even if it's highly upvoted.

You may check his question posts

@DanielFischer Yes.

I've just answered question of this guy and then I notice that he is unregistered user. I delete my answer.

@Venus That's rude.

@Venus But why did you delete your answer?

@Integrator Then have a go, by all means. Just because somebody commented before doesn't mean you can't have fun answering it yourself. If you find the question more "meh" and would only answer it to get it out of the queue, then ping, but if you would enjoy answering it, enjoy.

@Integrator Why rude?

@HatMan I just don't like to give an answer to an unregistered user

@DanielFischer Thanks! Now you won't receive any pings from me.

@Integrator Are you sure you won't find any you'd not enjoy answering yourself?

@Venus This question at scientific fiction SE was answered by the screenwriter. And he is unregistered. Unregistered users can add value to sites.

Out for jogging

@DanielFischer You only get what you look for! :)

@Integrator Ah, I thought you went through the unanswered queue to get it shorter, not specifically to look for questions you find interesting.

@Venus May I ask why you don't answer to unregistered user? Just because it's highly unlikely that he'll accept your answer and cannot vote on your answer?

@Integrator In this particular case, it's not so unlikely, he accepted a good number of answers.

@HatMan Not many, only several of them. Mostly, they don't (IMO). Besides, that's my stance on the issue about unreg users.

@DanielFischer but it appeared that @venus only deleted her answer because OP was an unregistered user.

@Integrator Maybe.

@Venus so, reputation is the reason here. right?

By the way, there is a recent meta post on whether registration should be made mandatory (for asking questions) on mathSE. meta.math.stackexchange.com/questions/17244/…

@Venus If I'm not mistaken, it is $b^2-a^2$

@Integrator No. My motivation is written on my profile page.

Anyway, I got another hat for deleting my answer. Not bad. ^^

I've had anonymous users make vulgar edits to my posts on MSE before, I'm not to keen on letting everyone have a chance to participate...

@robjohn Yep! You're correct. Should I post that question on the main?

@Venus If you want to...

@robjohn OK, I'll do. Wait a sec.

Grr, I can't edit on mobile...

@TedShifrin hey there.

Mobile is fun :D

hi @robjohn ... So we have hat and moderator election bedlam :)

@Venus too many things are written there.

@TedShifrin don't forget to send me the final 2410 Final today :P

Why are people editing you vulgarly, @teadawg?

@DanielFischer from your profile at Stackoverflow, I see that your preferred programming language is Haskell. What do you recommend as a good mathematics textbook that covers prerequisites for learning Haskell?

Hi @Ted

Nice hat

@TedShifrin I dunno, trolls will be trolls I guess

@TedShifrin yep... on top of everything else. It is wild

Oh, @teadawg, I actually did typeset that for you a few hours ago. Hold on.

@DanielFischer I don't really care about the unanswered tab.

Thanks, @Mike. I think it's garish.

@Venus How do you know the answer?

@teadawg: Sent you two.

@Ted Well, get a better hat.

@robjohn My friend just said so

@TedShifrin Neat! I'll look at them once I get back from my appointment this morning :3

@Venus ah...

Where is the hat shop, @Mike?

You've gotta earn 'em, @Ted. Here's the (public) list.

That's the one I was given.

@Mike Did you earn the "Fascinating, Ma'am" hat yet?

Of course, @teadawg1337.

I wouldn't be much of a hat baron if I didn't.

Well, I have to go get my final started. I'll ponder millinery later.

@HatMan Are there any prerequisites? If you want to go deeper, you need some category theory, but to learn to use it at a reasonable level, I'd say you only need a little experience in abstract thinking. It flows naturally then - if you're already used to some other programming paradigm, that may sometimes be a hindrance, since many things are done much different in a lazy (non-strict, really, by definition, but the implementations are lazy) functional language.

@Mike Indeed, indeed

At present, I'm at a bit of a hat standstill.

@MikeMiller, become a Treasure Hunter :P

I don't think it's actually possible for me to get a gold during bash.

@Venus I just return back to write you a thought (and then leave)

@Venus if you integrate by parts, all gets reduced to computing integrals of the type $$\int_0^{\infty } \frac{x^s}{2 k x \cos (a)+k^2+x^2} \, dx$$ but recognizing the denominator, and using the proper series, you may get the result.

Actually, I guess I could get one on Math Educators, if I upvoted wildly for about a week.

But that seems more than a little crass.

@DanielFischer I am trying to learn. I don't feel okay with monad and similar things and I read one or two people telling that once you know the abstract definitions of monad etc, things are really simple. So I am thinking about learning some category theory.

Out for jogging now.

@HatMan Hmm. People are different of course, but I think that's overselling category theory a bit. Of course having some familiarity with the concepts helps understanding them in Haskell, but just knowing the definitions not so much.

I've just posted on the main @Chris'ssis @robjohn @N3buchadnezzar.

@DanielFischer I see. Thanks.

@robjohn As far as I remember, I have asked the similar question to you about this type integral. Do you use double integral to evaluate it?

Can anyone help me with this? "The sum \sum_{n=2}^{\infty} \frac{\binom n2}{4^n} ~~=~~ \frac{\binom 22}{16}+\frac{\binom 32}{64}+\frac{\binom 42}{256}+\cdots has a finite value. Determine that value."

@HatMan I see you are wearing a hat atop a hat ! B)

@MathyPerson write $\binom{n}{2} = \frac{1}{2}(n^2 - n)$ and think about differentiating a geometric progression :)

I wonder if I sounded ultra vague :O

kind of @r9m

@Mike: Seems that both @Pedro and I have had playful, humorous comments taken out of context and been accosted therefor. If we can't pick on you and @Hippa, then I'll just quit.

@MathyPerson do you know how to find closed forms of $\sum\limits_{n=1}^{\infty} nx^n$ and $\sum\limits_{n=1}^{\infty} n^2x^n$ ?

@Venus I differentiate half of the integral (that is what I meant by do each separately), then put them together.

Is Venus chris'ssis's twin?

@r9m ye, but kind of need a refresher on it

*yes

@MathyPerson okay .. as long as $x \in (-1,1)$ .. $\sum\limits_{n=1}^{\infty} x^n = \frac{x}{1-x}$, so differentiate both sides wrt x, you get $\sum\limits_{n=1}^{\infty} nx^{n-1} = \frac{d}{dx}\frac{x}{1-x}$, and multiply it with $x$ and diff both sides again you get $\sum\limits_{n=1}^{\infty} n^2x^{n-1}$ ..

@TedShifrin What do you mean by comments taken out of context? I think the people you're worried out might not be worth paying attention to.

I meant Alec castigating me for teasing Hippa and somebody-or-other saying Pedro was an unfitting moderator candidate because he was teasing/joking with you. Sigh.

@r9m: Even easier, write $\dfrac x{1-x} = \dfrac1{1-x}-1$ :P

@TedShifrin aye aye .. you are right sir ! ... hick ! ^^'

how would i apply generating functions to the problem? @r9m

Yes, i remember those. I stand by my seconed sentence.

Agreed ...

@MathyPerson I don't have much clue ! can someone help mathy person plz ?! :)

@TedShifrin >.>

Tu t'en plains, @Hippa?

@TedShifrin Non non ça va :)

@MathyPerson Put "$" to enclose your LaTeX

While using generating functions

Hello @DanielFischer!!!

$The sum \sum_{n=2}^{\infty} \frac{\binom n2}{4^n} ~~=~~ \frac{\binom 22}{16}+\frac{\binom 32}{64}+\frac{\binom 42}{256}+\cdots has a finite value. Determine that value.$ @Hippalectryon

@r9m I'm pretty sure you can answer this one ^

@robjohn I've found another way to evaluate it after seeing your answer ^^

@Venus Post your answer.

why am I not wearing a hat in chat?

@Hippalectryon sorry atm I might get banned from chat if I talk ...

@robjohn I just did

@r9m ??

@robjohn Why might @r9m get banned ?

@robjohn Why not?

@Hippalectryon I'm in a terrible mood :( I might say something not nice .. :P thats all :|

Ah ok

@r9m What happened?

@robjohn Nice hat. You look so funny ^^

@JasperLoy I don't know... I was asking. My main profile has a hat, and I refreshed my chat profile from the main one.

Ah, there it is.

Perhaps it is none of our business.

@JasperLoy just angry at myself ... (common post teenager problem)

Post teenager? Who? looks around

:P

@robjohn The answer should be $a^2-b^2$, your answer must be rectified.

If you get banned @r9m I will never return.

I got banned from chat 5 times.

@MathyPerson $$\sum_{n=0}^\infty\binom{n}{2}x^n=\frac{x^2}{(1-x)^3}$$

I have been banned from chat $0$ times

@robjohn ??

@skullpatrol Where's your hat from here?

@robjohn : nvm

From raider nation @Venus

@MathyPerson so $\frac4{27}$

Are you still here @r9m? I am on your side.

@robjohn: you mean 4/27?

@robjohn Ah, sorry. I didn't see your question in your answer.

@robjohn Any idea for this one?

@skullpatrol :O ! you are too kind :-) (I was just saying its possible that a chain of events might lead to me getting banned if I talked too much atm .. just to describe the kind of mood I am in .. that's all)

Ok pal.

@r9m: srry to hear that! i am in a sort-of-crabby mood as well xD

@Ashwin You should think carefully, then just act according to your plan like I said. Take what others say into consideration, but make your own decision ultimately. Good luck! Also, you don't need to listen to me, for I am only a banana.

@Venus which question?

@robjohn: thank you

@Ashwin At least see a psychiatrist for two sessions and a psychotherapist for two sessions before giving these up totally, like I did.

@MathyPerson "crabby mood" you should get the imitation crab hat then.

@BalarkaSen hahah

If you feel like anybody is ganging up on you and trying to bully you in here @r9m you can count on me to be on your side

@robjohn This one

Click the link

@MathyPerson The general formula for that sum is actually on the ChatJax installation page :-)

I have 6 funny hats ^^

I only have 3.

@Ashwin I do not know what problems you have, but there is no harm seeing a shrink like I said. Only four sessions.

@robjohn: oh, hahah xD

@Integrator Where are you? Have you got the answer for my OP?

@Ashwin Sometimes.

@Venus I dislike using the term OP somehow. It just sounds weird, but many use it.

$How many cubic (i.e., third-degree) polynomials f(x) are there such that f(x) has positive integer coefficients and f(1)=9? (Note: all coefficients must be positive---coefficients are not permitted to be 0, so for example f(x) = x^3 + 8 is not a valid polynomial.)$ any hints?

Yes you can always repair yourself, that's what believing in yourself is all about @Ashwin

@skullpatrol there is no problem here :) .. just a bad mood (likely to disappear If I get a good night sleep ;) ..)

@JasperLoy What should it be then?

@Venus I am just saying I dislike it, not that it should not be used.