@leslietownes yeah and then at the end write in bold: I solve the Twin Primes lol

I think arxiv requires a sponsor, but I stopped publishing research before arxiv started.

I'm probably shooting my mouth off before I've self-verified, so don't get your hopes up yet

You know the chances that you have proved it are very very small.

i think many people reflexively stop listening to mathematics, including conjectures and experiments, if they learn it is part of an attempt to solve a notoriously difficult problem. that might be unfair in some moral sense but it is just the economics of how people spend their time.

Not true, I believe elementary math is more powerful sometimes in some regards than higher-level rigid math

I saw so many crackpot angle trisection proofs.

i don't try to outrun cheetahs, i'm probably not oging to listen to somebody's proof of the invariant subspace conjecture. although i did have a academic far more senior than myself buttonhole me at a conference and make me listen to half of his argument. i just can't. other people are similarly parsimonious with their time.

It is a matter of trust to some extent. And you have to start earning it somehow.

Well, I will write the paper, but not lay it on too heavy when I ask people on MSE or wherever to view it

Hopefully it is not your day job.

I have 17k rep on the site. But I'm no fat cat like Qiachu Yuan.

Bit of difference in known horsepower.

who has like 300k rep

And Qiaochu never finished his PhD.

Because he's a genius

I never finished my BS in CS

And probably never will. I'm too asocial atm

There are people with way more rep than me who know far less math than I do. Rep isn't that meaningful. But, yes, Qiaochu knows a lot.

He probably has published himself, right?

Not that I know.

i think my reputation is in direct proportion to what i know. i am a rare exception to the rule

I'm not a researcher yet, but I'm getting there guys!

Wish me luck!

Mathematics is a tough field for professionals.

Math4life

Cross your fingers that proof of twin primes is proffered

Haha

So many people earn tens of thousands of rep with worthless crap.

@StudySmarterNotHarder yes

It doesn't mean you can't. it does mean the chances are tiny.

I don't rely on Zhang's results or anything like that. The researchers wrote on Wikipedia anyway that $2k = 6$ is the lowest they can hope for for infinitude of gap pairs

with those results

@LeonhardEuler are you related to Euler irl?

Hmm... maybe you could help / guide me :>

None of us here presently know anything at all about this, as far as I know.

Well yes, but actually no

lol

we are all brothers and sisters

You are his $10$th generation or something

Everyone is related to each other

Well, no.

I am a relative of Elizabeth

But a very very far relative

;)

What about Emily Noether? Maybe you could channel her and figure out if my ring is Noetherian or not

Emily? Geez, man.

Emmie?

Eli?

I forgot :/

@TedShifrin Thanks for the suggestion. The Prime mobile is warming up.

Someone suggest me a nice name

I am a victim of twin primes yes, but I will make them my b*tch one day

For my computer algebra system

BananaCats

AfterText

euler's branch of the mathematics genealogy tree is very swiss and dutch and french and stuff. i have german roots.

My roots are not germane to my math.

^_^ They all mated in an orgy and had babies. We're all related mon

:-)

I have a very bad name for my computer algebra system

lol, I had that same project name before on one of my coding projects!

long long ago, and forgotten

you're gonna have some trademark genericity issues. i would choose something more marketable. build a brand.

It is wine o'clock here. Kona is come out to play.

Actually it can't do much rn

It computes bernoulli number and zeta

And simplifies expressions

I am building it

That's a lot actually

And what I need are algorithms

Probably I'm guessing 60 code files by now

Yea something like that

@LeonhardEuler are you in Accademia?

No

You're like me! Bros

:)

Let's be algebrothas together

You will be labeled a crank if you push too hard.

Everyone's a percentage crank anyway

you may be right about that. my phd advisor had what might have been a crank theory about the twin prime conjecture. he never published it or publicized it.

my crank theories will follow me to my grave

My crackpotteries are endless in my domain of automata.

There are many people who don't publish there works

How come Qiaochu Yuan is listed on math.berkeley.edu/people/past-phds ?

Because he has 300k rep and they know that

j/k

Does not happen like that.

i have no idea, but i was listed there for at least a few years after i left. i even had an office. someone used my name as an 'officemate' to get office priority, and nobody noticed that i had graduated.

I got a tshirt and a mug at 100k :-).

Personally, I like the number reached more.

Have a coffee!

Tea.

Ikr

I think there were two grad students with that name!

A UC berkeley Math professor almost killed me once.

Okay, well I will keep you guys posted but not in an overdone, needy way. I'll show you the proof very softly :|

Yes, Lancos stuff.

if you're referring to the unabomber, he was a former professor.

I am. I know.

@copper.hat that's interesting, maybe his sheaves were perverse

Oh, nvm. That's serious. Sorry to joke

Okay, I'm out of things to say, so will leave chat open for a while, and leave eventually

i was kind of annoyed by that. sometimes the undergrads who gave campus tours would bring him up around evans hall, which AFAIK the guy never occupied. like, plutonium was discovered about half a block from here, maybe go there and talk about that.

Two Yuans listed. The one who finished was applied.

and not some asshole who blew up a CS lab

It was my computer terminal.

was this the one in soda hall?

or... terminal computer?

Cory. Mezzanine.

Soda was not around then.

oh, right. i was mixing my halls

hah hah

i had a calculus section near there. that sucks. i understand the investigation was fairly intrusive because they had no idea who was behind it. some of the people i knew in the math department were bothered for quite a while about it

well, it is to be expected. i would rather they find the perpetrator.

i was interviewed many times by different investigative units.

that's a long time ago now.

yeah, wow

more interesting was the frat lad who put micky mouse hands on the campanile clock

but did not bring a rope long enough to get to the ground.

by the time i got there, i'm not sure any frad lads knew what a clock was. times change.

it used to be you could walk to the top if you wanted.

i got in on the tail end of that. that seems to have gone now.

well, if you knew someone :-).

then there was humphrey gobart.

you could ride to the lawrence hall of science for lunch (for free).

they had something similar to MSRI when i was there, but it did not have the whimsical name. the spirit of the 60s and 70s slowly vanished as time went on. now it's an underfunded, in-need-of-earthquake-retrofitting firetrap.

no offense to anyone who is still there

they did some interesting stuff there.

but probably one of my favourite berkeley places was cody's books.

i heard they painted over the hippy murals on the upper floors of evans hall. i hated those murals but something in me died the day i heard that.

we were talking about cody's the other day! and moe's. and shakespeare & co.

moe's is still around. i used to go to the med opposite until a few years ago and after my quesadilla & a chat would pop into moes and buy more math books.

i still have a dover edition of shilov's linear algebra that i bought in cody's. it's survived five interstate moves. and several non-interstate moves. it's not that good of a book. but it was cheap and i bought it at cody's.

it was a brilliant shop then, the books were top rate plus you would often meet top folks in relevant fields there.

death by amazon unfortunately.

i'm as guilty of inducing that as everyone else. even by grad school i was mostly buying from amazon. until something didn't come in time for my qualifying exam, then i was over to cody's real quick. i don't think i even got the refund from amazon.

i started with amazon where they were a hard to find books place, long before the amazon of today. you could talk to someone on the phone.

i'm going to tell my grandchildren about what it was like to talk to people on the phone

we used to have a phone that you wound the handle on the side to contact the operator :-).

My daughter (20) can communicate in Morse code.

that's cool. we had a rotary phone but not the one with the crank on the side. that's something special

not really, just funny when you look back from today's perspective.

i grew up in a family of writers, so we had a lot of typewriters around. i remember being in my dad's newsroom when it was full of typewriters. carriage return and line feed are separate manual operations to me, not just byte codes in a document.

that is my one connection to the past

i used to send teletype messages for my dad.

have churned butter & separated milk with a hand powered centrifuge :-).

we had a manual coffee grinder. not because i'm old but because my dad was just cheap. it sucked to operate but the coffee came out of this cool drawer at the bottom.

:-). i liked older stuff partly because it could be maintained and lasted for a while.

i think our grinder dated from the 30s. all of the stuff we had growing up was bought at the st vincent de paul in berkeley and was probably 30 years old by the time we owned it

but that does not work with tech. you need a new phone every 2 years now to keep up the the javascript garbage.

now things break and you just bin it and get the new one

yeah, i hate that.

i'm hanging on to a 5 year old phone. it crashes if someone messages me while i'm on the phone. i'm sticking with it. yes, it's causing problems at work, but no, i don't want a new phone

i have only had two cars in my 40+ years in the usa.

well, that is technically a lie but i'm too tired to explain :-).

me too although i could not legally drive for about a third of that time

the advantages of youth...

my current car has had a very busy year, sitting in the garage and going to and from the grocery store a 5 minute walk from here. i think i'll get a good 20 years out of it

well, so, right now my family has 4 cars and 3 people living in the house.

i cover more miles per week on my mountain bike.

i don't like modern cars with their internet connectivity.

i do like reversing cameras since my neck is stiff :-).

my car has something resembling bluetooth, it doesn't work. i used it to play an mp3 on my phone exactly once, in 2015, before the android update. my wife's car has something internettish. it knows what streets we're driving on and has a map. that's creepy.

a guy i used to work for was late for a meeting because the software on his Fiat was updating.

i was in the early bluetooth committee meetings :-).

i'm a patent attorney, i imagine i will be deposing you sooner or later. i'll say hi now so we're friends.

i have a few patents. good for vc check lists.

did you ever hear about the cadence vs avanti case?

my next door neighbour is a patent attorney.

i have yet to be deposed :-).

i've heard of the case. i don't think we were involved with it although god knows a number of firms were.

i have some very close connections to that case. my friend was sent to state.

the semiconductor industry seems to bring out the worst in people. i was on a call just today about that.

that';s my industry (well, really eda).

i was an early cadence employee.

whenever you have rafts of money depending on a small amount of things, i guess that's a recipe for disaster. i don't know.

?

the real money is made in legal.

when i was in math i never worked in anything IP intensive. one of my friends went into semiconductor designs, and it's like, everything is the crown jewels with him. he can't trust the people he works with.

yes we do bill for our services. happy to pick up the phone at any time. :)

i know, last century i had to call my friend to stop his para charging my $600/hr for photocopying.

please see our bus ad, los abodagos magnificos

se habla espanol

are you serious or pulling my leg?

i have many partner friends.

we do not have a bus ad. i do fantasize about advertising that way.

we are los abogados magnificos

but not in an advertised way

i used to get my patent work done in India, then someone in the us would do the filing. worked out much cheaper and easier that way.

$600/hour for para photocopies is greedy. i'd say, maybe, i dunno, $450. and if you complain, you'd just compare to what it would cost for an attorney to do it

that's the smart money

somehow that kind of turned into tex for some reason, i don't understand that

well, the big name helped early on, but it costs.

india is an extremely good place for legal services and legal-adjacent services.

well, the folks i was dealing with knew the general area and were not shy of hard work.

when i got one done here it was incredibly expensive and slow and the people i worked with hadn;t a clue

there's just a lot of sources to choose from, and the billing is low. and they do better than people in the states who kind of phone it in because they see it as more of a cookie cutter thing.

exactly

for example, one done in the us was eventually close to $15-20k, the India one was $5k.

dollar signs, that's what does it

I mean the MathJax as in $\mathbb{R}$.

in retrospect that makes a lot of sense. not the 15-20k, but the dollar signs.

wow, its midnight here, and i haven't started my kona

time to get drinking.

there is an enormous amount of unrealized potential in india. i think the next 10-20 years will see the market pivotiing away from the more costly options simply because of the zip code of where it's coming from.

we do almost all of our prior art searches, at least initially, through indian firms. nobody in the US can match the quality

eventually this will lead to me being paid less, so i have mixed feelings

:(

:-). i wish i got paid like lawyers...

it's better than teaching calculus

actually, i wish i could charge like lawyers.

my time that is.

there's something general about institutions loving to pay top rates for solving problems after they happen. nobody wants to pay smaller rates to prevent the problems from happening.

cleanup always costs more.

yeah, it's never the cheaper option.

lookup the line from brendan behan about sex for money.

often the CEO is culturally similar to the person who wants to sell the corporation insurance. the CEO is not culturally similar to people in his own organization who could prevent insurance-coverage-implicating events from happening.

so it plays out like that.

:-)

behan put it very well. i don't think CEOs will listen.

not their job :-).

hi everyone

wow nice 1 hour since the conversation began

hello @satan29

i have a question

good night folks, my glass is almost finished...

consider the function f(x,y)= xsin(1/y)

consider the limit of f, as (x,y)-->(0,0)

now the way I approached it, was since sin(1/y) is bounded, as x approaches zero, the product should definitely approach 0

the limit is indeed zero. Now whats bothering me:

if the limit exists, trhen the limit for all paths through 0,0 must exist, right?

but for the path y=0 we run into a problem..

yes. and as you've noticed, |f(x,y)| <= |x| is helpful here.

mm, i wouldn't see that path as existing in the domain of f

oh hmm

there's very much the issue of, do we want the domain to include all paths to 0, or do we stop if there are forbidden paths simply excluded by virtue of what the domain of f is and we don't care about them.

i think at least some textbooks have resolved this issue differently. but that's what you're noticing.

i think the bourbaki books resolve this differently from my multivariable calculus book. i don't remember where this memory comes from. it just bubbled up out of the void.

alright

if you approach the origin within the domain of f, i think there's no question that f does go to 0.

the question is whether this qualification, 'within the domain of f,' is an obstacle to defining the limit there.

If $f(1)=10$ and $f^{\prime}(x) \geq 2$ for $1 \leq x \leq 4,$ how small $f(4)$ can be?

right, so I guess I ll modify my statement: "if the limit exists, it must exist for all paths existing within the domain of f"

I think minimum value should be 10 only ?

(f(4) - f(1))/(4 - 1) is f prime of something something.

if (f(4) - f(1))/(4 - 1) >= 2 then f(4) >= 2(4-1) + f(1). it is probably not hard to realize the equality. maybe linear functions

what if f(1) = 10 and f'(x) = 2 for all x. then f(x) is a line with slope 2 whose graph goes through the point (1,10) and (4, ??). worth investigating

got it thank you

:)

@MikeMiller Is a real number a complex number?

How many "types numbers" are there? I know of positive integers, negative integers, reciprocals, imaginary integers... what else is there in this series? Using 2 as a starting point, you have, 2, -2, 1/2, 2i, ...

Are there any others?

Combining them, you have, 2, -2, 1/2, -1/2, 2i, -2i, i/2, -i/2, ...

What could be added?

This is not just for @MikeMiller. Please give your two cents worth, whoever you are.

Does this set of eight types of numbers 2, -2, 1/2, -1/2, 2i, -2i, i/2, -i/2 have a name? Are they the dyadic rationals?

*These are not just for @MikeMiller.

I was told that for commutative ring $A$ and $N,M$ is $A$-module, then Hom_A(M,N) is also $A$-module because we assume $A$ is commutative. If $A$ is not commutative, then Hom_A(M,N) is not A-module?

(I mean Hom_A(M,N) is defined in a natural way for commutative case)

@love_sodam No, when A is not commutative that only has the reasonable structure of a set. After all, make an attempt to define the module structure. How does it go?

disagree

it still has the reasonable structure of an abelian group

You're right

Fascinating

people have got some really useful applications of mathematics

This application has helped more people than I ever will

js violates math

it says 2 + [] is "2"

@love_sodam if M is an (R,S)-bimodule and N is an (R,T)-bimodule then Hom_R(M,N) is an (S,T)-bimodule

note that any abelian group is automatically a (Z,Z)-bimodule and any left R-module is an (R,Z)-bimodule

Hello, can anyone help me on finding the infinitesimal generator of Ornstein-Uhlenbeck process? I include my thoughts in this post. Thank you.

Are real numbers complex numbers?

yes

arxiv.org/pdf/1210.2961.pdf

The "Seven Samurai" paper

Can't tell if probability, geometry or algebraic number theory

@BalarkaSen why is it

because seven authors lol

why are they samurai

why isn't it the "Seven Deadly Sins" paper instead

@MatthewChristopherBartsh you get 1 because 2/2 = 1