@Karl I don't think I ever said but I wish you all the best.

Me too @Karl

@KarlKronenfeld Any idea where you might want to go?

Thanks @Mike and @Ted. @AlexYoucis I know it doesn't really affect my anonymity, but I'll pretend I am more anonymous by not saying.

@KarlKronenfeld Sure. If it's Berkeley, you should stop by some time and say hi.

@AlexYoucis Thanks for the invite; unfortunately it's not Berkeley.

@KarlKronenfeld Haha, I doubted so. There are quite a few schools in the world.

:D

Does anyone still use ber and bei when dealing with bessel equations? I'm working with a book written in the twenties.

@atomSmasher I have seen $J_n$ and $Y_n$, I think.

What do you mean "still use"?

As in notation?

@seaturtles Yer answer here

le wowed.

@Karl If we ever end up in the same place you should surprise me.

Does the great majority of undergraduate university students in mathematics happily read and do maths by themselves in their free times ?

do people still work on Bessel functions at all?

@Amateur Rhe great majority so nothing more than take their classes and get their bachelors.

@Mike Really ?

My students don't have the time, in general, but a number do that once they're rid of me :D

@Amateur That answer changes if you're referring to math undergraduates going to graduate school.

@Amateur From my experience, yes.

Ah, yeah.

Reading Akhil Mathew's blog makes me feel stupid

@Fernando Hahahaha

@FernandoMartin Don't google "Peter Scholze" then.

Don't google anything.

Just hide in a cabin in the woods reading post-modern books.

at least he doesn't write a blog

@Mike a la Grothendieck

@FernandoMartin No, but he writes papers, and goes to conferences, and visits my/your school.

@FernandoMartin There's a rumor, fairly faithfully substantiated, that Akhil might come here next year too.

That's just here say though.

hearsay

I don't know how those people even have time to do all that stuff

@AlexYoucis One thing's for sure: he never got the ability to name things well.

@Mike Hmm, oh, I see.

@FernandoMartin It is crazy.

"Perfectoid spaces". Come on bro.

@Mike Great name. It's perfect, if you will.

@FernandoMartin What people?

Akhil, Qiaochu, etc.

Taking words and adding -oid is dumb.

it's dumboid

I'm learning C* algebras earlier on my career than Qiaochu. beats chest

@FernandoMartin Do what? Study?

To learn all that stuff

Unless they started at a stupidly young age

but I doubt that

they started at a stupidly young age, @Fernando

Whenever I read stuff they post, I feel like quitting math.

Seriously.

even if I had started at a stupidly young age I doubt I would have got that far that quick

@FernandoMartin Also I think we should not underestimate the power of passion.

Well, dunno about Qiaochu, but yes Akhil.

@AlexYoucis I think it's time to chime in

I think I'm passionate about what I like, that doesn't make me as nowhere near as good as them

Have you read Qiaochu's blogposts?

They're really good, he has some accesible stuff

My good friend Alex Y once told me that one shouldn't quit math (or any subject) because someone out there is better.

I don't feel like quitting, I just feel stupid

@Mike Well, I'd like to contribute something to maths, that a reason why I study. Seeing all this, one wonders what one can possibly contribute. =)

But you're stupid.

FUCK

not stipid

oh my god that's a typo

I know @Mike

One shouldn't bother comparing themselves to others who are really good. At the end of the day, all you can do is strive to do your personal best.

You can't reach maturity without embracing your own stupidity

I should write a column on zen bullshit on some magazine right?

@Mike I should read Paul Arden's books again.

You should always want to be so good at math you're curbstomping someone: yourself 3 months ago.

Exactly

I feel really good comparing myself to 3-months-ago-myself

That's the spirit.

wtf happened to the chat?

Beat the hell out of January Nando

@Karl: Sorry, my fault

@Karl It turned into a self-help book.

I should go to math-prison some months.

"I'm a latino in a hardhat, but I'm also wearing a hat, so you know I'm a supervisor."

"We're college students listening to our professor, but the class is taking place.... OUTSIDE?!"

Priceless.

@FernandoMartin Fernando is slightly Canadian.

No, I'm just polite @Pedro

I don't see why you'd have to apologize for speaking your mind.

It was tongue-in-cheek, I wasn't actually apologizing

I never understood why "tongue in cheek" has something to do with humor.

lol

Ways to feel smart, part one: Say "Reasonable doubt, Your Honor!" with a thick stress in the "e".

@Mike I think I have figured out how to surprise you. :D

@Karl I hope it's not with assassins.

@Pedro There are two ES there.

@Pedro Want to know a fun fact?

reasona-BULL doubt..

I was thinking reasona-blay

That's un-American of you.

Well, un-North-American

I didn't say it was correct.

Just how I'm picturing Pedro saying it

ah lol

Reeeeeasonable

What's fun?

HELP .. $f:[0,1] \to \mathbb{R}$ is differentiable, such that $f(x^2)+f(y^2) \le f(\sqrt{xy})$ for $x,y \ge 0$, then $\displaystyle \int_0^1 \sqrt{x}f(x)\,dx \ge f(1)-f(\frac{1}{e})$ ..

@Pedro

so let's say you've got a C* algebra. Like before, this is just a Banach algebra with an adjoint that satisfies $\|AA*\|=\|A\|^2$.

So let's pick an element. It's called normal if $TT^*=T^*T$.

We'll often be interested in C*(T) - the algebra generate by T. That is, the smallest algebra containing T that's norm-closed, adjoint-closed, addition-closed, multiplication closed...

More down to earth it's just power series in T and T*. From closure under adoption and multiplication and adjoint you get the elements that are polynomial whose inputs are T and T* - norm-closed gets you pier series.

Well, it turns out that C*(T) is isomorphic to the continuous functions on the spectrum of T.

So we can pretty much just pass to working with functions.

closure under adoption? never heard of that one

Functions are nice.

addition, @Fernando, they're not allowed to pick up little baby operators that aren't theirs

What's the spectrum of T?

@mike

Oh, right. In this case our algebra has an identity so this makes sense. It's the same as for operators: $\{\lambda \in \Bbb C : \lambda I - T$ is not invertible $\}$

Can you say something about the topology of the spectrum?

It's compact and non-empty. (Former isn't too hard - latter is suspiciously hard.)

can you say something about connectivity?

It's hella disconnected. It's discrete almost everywhere.

If if accumulates anywhere at all, it only accumulates at 0.

Cool

So our functions are really nice @Fernando

Here's a standard application. A positive operator is a self-adjoint operator whose spectrum is contained in the non-negative reals.

This isomorphism between C*(T) and the continuous functions on the spectrum carries T to the identity function.

So, since $f(z)=z$ has a square root (remember, $f$ is defined on the spectrum, which is contained in the reals)

So does $T$. :D

do you have some sort of functorial thing going on?

Nah, I don't know about the class of subsets of C that can be spectra.

We just have an isometric isomorphism between C*(T) and the continuous functions. So virtually everything we can do to functions, we can do to operators.

it gets a lot of use. one just has to remember that this is only operators in C*(T) - not all the operators in our original algebra - so we have to be careful not to overstep what we can do.

kinda sorta reminds me of localization

except in localization you don't manage to join together a whole bunch of fields of math in the process :D

also, that isomorphism gives us a nice helpful fact: pick a self-adjoint element; carry it to $f(z)=z$ by our isomorphism; then since A*=A, $\overline{f}=f$, so the domain it $f$ is real; self-adjoint elements have real spectrum.

@Karl It's crazy, innit? the whole field is a bit too analytic for me to do long-term, but I'm glad to be wowed for now

I just read by. Sleepin now

@AlexanderGruber Somebody changed the name of the layer in the MSE chat dwellers map to "Sujaan Kunalan".

After looking that up, I am pretty sure I know the culprit. :)

@Karl Hmm, I have a guess from the initials.

Someone changed what @KarlKronenfeld ?

@AlecTeal See the menu on the left here.

Menu on the left?

Menu wasn't right. The panel with the list of names and whatnot.

I'm just doing a terrible job at this. I meant to link here: mapsengine.google.com/map/edit?mid=zg6p6CxQUjpY.ktFFDHMUvfso

/me 'd rather not click

@AlecTeal How about this

No, but only because this laptop has awful speakers

Like "removed from novelty birthday cards" quality.

@AlecTeal An excellent piece of humor that does not require speakers. Not directed at you or anybody--not even relevant--just funny..

@Mike Whadyou bing me about?

that website is amazing @karl

this one is an absolute classic

Lol @AlexYoucis good one.

Someone using Bing :P

@AlecTeal I meant ping, but being such a ravenous consumer of other people

's attention, I accept your compliment.

@FernandoMartin Is that the one with the floodlight?

/me is really starting to hate Microsoft.

Why?

It's the one where he tries to pay his bank with a spider drawing

@FernandoMartin I meant the same guy, and yeah I found it.

Ah yes

@AlecTeal I like Windows, lol.

27bslash6.com/halogen.html

@WillHunting I loved Halo 1, 2 and 3. Then came Wars (crap), ODST (crap), Reach (Crap), 4 (not bad, but they so aggressively use LOD that anything beyond 3 feet looks awful), then make a new console with the required Eye Of Sauron, and EA inspired DRM.

Didn't this used to be called something else? Letters from an asshole?

Then they U-turn 4 times, which is 720 degrees - mocking us further.

I have used Linux for many years, it has many problems.

I don't want to talk to my console, I don't even want to have to stand. Let alone raise my arm and shout fire (Ryse son of Rome), or tell it to turn on. Turning it on/off from the pad is the dream!

@WillHunting like?

@AlecTeal Sometimes pixellation, sometimes no internet connection, sometimes can't play a VCD or video, etc. Sometimes the problems can be resolved with a simple Google, other times no.

Windows sucks at everything. That sounds biased but there is nothing it does well, Filesystem "LOL NTFS!" networking is a joke, the registry, running things it shouldn't (you can load files in Microsoft word that run code from the file - how does that even happen)

There is only one reason I don't use Windows, it is not FOC, lol.

Then they had Windows 8, and the Gnome developers were like "Gnome 3!" and I cried a bit.

@AlexYoucis No, it's always been 27b/6. Two different assholes.

lol these are so good.

Oh OK I hate GNOME 3 too.

@AlecTeal I am going to stick to the MATE desktop.

I have no idea what problems you have been having @WillHunting but yeah, that sounds like the OSs fault, if there's sometimes no internet connection.... (this is sarcasm, if it were a kernel thing, it'd either work, not work at all, or consistently break when you do something)

@Mike Is he the one that emails people on craigslist too? I guess it's not shocking there are multiple people with the same schtick.

@AlexYoucis Thwres a letters from an asshole where a guy is a dick to people on craigslist.

@Mike Ah, that is also funny.

I don't know why asshole came about, all asses have holes.

Thts an act, I think. This is just who David Thorpe is.

Find the one where Simon tries to get him fired.

Then you have MSSQL server, "OMG TABLES IN RAM!" this isn't new! MySQL has had the MEMORY database engine since before it had VIEWs

Secure boot.

We have an Alex and an Alec, confusing.

Halo live action series! (just let it die....)

This one.

Hello all. In the spirit of recreational-mathematics (...curiosities, ... "just for fun"), I submitted this: [(Just for fun) Please vote on your favorite Children's Math Book title(s). [on hold]](math.stackexchange.com/questions/762526/…). I didn't get the reaction I expected.

I'm told "take it somewhere else". This is the only mathematician community I know of. I asked if anyone knows a good community elsewhere, but it seems that once the question got put on hold, people stopped talking to me in the comments. Thoughts? (I don't need to conduct a poll. I just wanted to share and have some fun.)

I think that's a better question than the vast majority of stuff we get (people posting their homework and looking for answers). I do agree it's probably the wrong place for you question though. Here might actually be a good place: link to your poll in here occasionally!

@TravisBemrose you're interrupting their personal mathematical conquest!

(wry) :-)

@TravisBemrose Interesting idea +1

@TravisBemrose my favorite: Dummit & Foote's algebra. Start 'em young...

Oh!

@TravisBemrose Maybe Mathematics Educators.SE would be receptive.

@TravisBemrose I've got one

@skullpatrol is that your face?

no

torture^

Looking at that tag description and this question, I thought it would be accepted here.

@TravisBemrose it's ... not a popular question because maths trivia books suck.

@Mike I'm confused a bit. It looks like you meant to include a link behind one of your "Here"s?

I'm never going to read any of those, they're not really useful. After A-level when one discovers proof....

@AlecTeal @AlecTeal Trivia books?

You should ask kids to prove $1 + 2 + \dots + n = $ formula

@Travis Actually, I meant in this chatroom. :)

OH I misread

Heh

Crap!

Sunrise!

GRR!

@Mike Ah. So you mean just paste all the submissions in here (no fancy poll formatting) and let discussion ensue?

@skull I don't think MESE would appreciate it much.

I think there should be a fun kids book, where the main characters use phrases like "I think I'm in love because our fundamental groups are isomorphic", or "me over you taken to infinity equals 1". Then at the end the antichrist comes in and starts demanding rigorous proofs from all the people, and math was never the same :'(

@AlecTeal HA! I had to open that pic in another window to read the grey text. I'll share that with my advisor.

@TravisBemrose There are polling sites on the internet, set up a poll and link it here.

@Mike Just a suggestion.

When I was younger and saw that on TV I honestly thought "Year 4 spellings"

Khan Academy is probably full of kids-teach-themselves stuff @TravisBemrose

@EnjoysMath When I first heard of Khan Academy, I went there hoping to find Abstract Algebra.

@TravisBemrose "The adventures in John P's attic" (about P-adics)

rofl

27bslash6.com/bieber.html

@Mike When you say "students that are struggling with math" do you mean this is a remedial class and at what grade?

@skullpatrol In my most recent question? This is at an adult education school, for students who didn't get their high school diploma. They haven't thought about math in years. I'm told by the person running the place that they have trouble grasping all the math topics they have to learn.

Hmm...

I don't know much about their actual skill level. I haven't met any of them yet.

@Mike About how many?

20 in the class. We won't just be doing math

English and history too. Xi can do those more easily :)

@Mike Have you heard of the book PreAlgebra: An Accelerated Course?

Since they are adults.

I haven't. Do you think it would help for learning teaching style?

BTW - if you have ideas, you should post them as an answer :D

That is my best idea :-)

Well, post it, with a little explanation why you think it would help :)

Take them through that book step by step.

imo

I upvote all answers to my questions unless they're made in bad faith (e.g. someone telling me to beat the kids up :P)

icic