/sci/ - Science & Math

The previous one is still in page 2, retard.

>>11581267
You are a moron. Go post there instead.

>>11581267
Bump limit

What other mathematically inspired hobbies do you have, /mg/?
I love making geometric origami. It's very fun and relaxing, especially if I'm trying to think through a problem while I fold.

>>11581270
>>11581275
unironically kill yourselves

>>11581280
I've made the 5 Intersecting Tetrahedra a number of times with a number of variations. It's always a nice puzzle to assemble.

>>11581289
You have to go back

Threadly reminder to work with physicists.

>>11581223
Not this guy, but I'd say there's more reasons not to take it than to take it.

>Name one reason not to take it as an axiom.
Properly capturing computational semantics of undecidable problems.
>>11581199
E.g. fix a language and consider the enumerable collection of all legal computer programs theirin (e.g. all the ascii strings that compile in C). Let [math] P [/math] be the predicate denoting whether a given program will halt.
E.g.
P("int main(){return 7;}")
should be true, since that program compiles and, when executed, return 7immediatenly.
And
P("int main(){while(3==3){} return 7;}")
shoudl be false, since that program compiles and when run actually never breaks out of the while loop.
https://en.wikipedia.org/wiki/Halting_problem
It's known since Turing that this predicate can't be turned into an effective procedure (it's ndecidable).
Now, by the LEM, for any program X it's "true" that [math] P(X)\lor\neg P(X) [/math].
It's dubious - unless you're a hard Platonist - what that latter proposion ought to express, given that by the solution to the Halting problem, we know that there's a for which we can't decide P(a) nor not(P(a))

Not adopting the law of excluded middle doesn't get us into the situation.

>>11581239
>proofs by contradiction, which are pretty useful
I suppose that point can be made, but it can also be contested.

It must be stressed that whenever Q is a propositition that's provable in the classical logic with the law of excluded middle, then there's statements Q' that are constructively provable, and which are classically immediatenly equivalent with Q.
https://en.wikipedia.org/wiki/Double-negation_translation
So it's not like adopting LEM enables you to prove more theorems (it just makes the proofs easier, as adding an axiom does.)
While, at the same time...

>Name one reason not to take it as an axiom.
There's axioms A, that are inconsistent with LEM, but not with the rest of one's theory, e.g. in Synthetic Differential Geometry.

>>11581317
CS faggotry is not mathematics.

>>11581296
This torus gets made out of about 500 little simple units. It's sort of fun to see how the angles that the pieces meet at are always constant, so you need to build larger polygons with them toward the center and smaller polygons with then toward the edges to create the proper local curvature. You get to see how it all balances out to 0. Sort of a first foray into the world of the Gauss Bonnet theorem.

>>11581331
>faggotry
Why the homophobia?

>>11581336
>homophobia
Why the homophilia?

>>11581336
>>11581338
have sex.

>>11581340
How?
And I mean with women, since I am not a faggot.

>>11581338

>>11581338
I was with you at first but now it's clear you're new. Bye.

>>11581296
>>11581335
And now I want to play with a 3D printer.

>>11581351
>I was with you at first
That was literally my first post in the entire thread.

>>11581346
>this dude talking about this being the most embarrassing thing he's ever admitted to someone
total fucking weaksauce
he's not even a gay furry

>>11581346
ew...

>>11581354
I was against that guy at first, is what I mean.

>>11581363
I literally have no idea what you are talking about.

>>11581359
Are you a gay furry?

>>11581352
>He doesn't have a diy 3d printer
They're pretty damn cheap. Not hard to assemble if you get a kit, lots of fun and great things you can make.

>>11581341
>How?
Pay them.

>>11581331
Whether we want to draw a line between logic, theoretical computer science and math is a question of its own.
Be that as it may, would you say that there should only be one foundation (axiom set, presumptions) of math?
I think one has to be able to study various axiom system for math to be able to do exactly what I describe there, namely be able to capture semantics of of computation.
In a sense, due to all the algebra-topology-logic equivalences, those systems are already subsystems of classical mathematical structures anyway, so one may as well describe them axiomatically (in the same way one can study groups without thinking of the group operation as a binary function, where a function "is" a particular set of pairs.)

>>11581375
I'm not sure how to respond to this one. Sorry.

>>11581370
don't reply to him, he's a schizo.
all of these posts are his
>>11581267
>>11581270
>>11581289
>>11581317
>>11581331
>>11581336
>>11581340
>>11581351
>>11581363

>>11581377
Sorry. I still have a shred of dignity left.

>>11581280
Physics

>>11581384
>don't reply to him, he's a schizo.
I'm not a "he".

>>11581376
I'll just use one in the library when I go see my parents the next time. Or, probably not. I will probably forget the whole thing anyway.

great start to this thread

How far along are we?

>>11581390
Dick already cut off?

>>11581378
From top left to bottom right: 0/36/72-35/71/99 (last 8 pics have a lower probability)

Rolling for 11

>>11581390
Yes you are you pathetic tranny. Stop shitting up all the threads.

>>11581384

>Direct proof
>Contrapositive
>Proof by contradiction
>Modus ponens
>Modus tollen
>Induction
Are those all the types of proofs out there?

>>11581403
>0/36/72-35/71/99
I like the effort you put into this

>>11581409
Just don't respond. It should be obvious that the person who did the lengthly anti-LEM shilling (me) isn't the same person as all the faggot talk (>inb4 why the homophobia)

>>11581410
There's a lot of syllogism
https://en.wikipedia.org/wiki/Syllogism
and many will be derivable in various systems.
Maybe this helps (also just one system)
https://en.wikipedia.org/wiki/Natural_deduction

>>11581410
I'm not sure where proof by exhaustion fits into that. Direct, maybe?
Also the most chad proof method of all
>p implies q
>not p implies q
>therefore q

>>11581410
Contradiction is more akin to handwaving than proof

>>11581425
this just shows that
[math] (p \lor \neg p)\to q [/math]

:^)

>>11581410

what constitutes the type of a proof is ultimately arbitrary

>>11581425
>>11581437

the law of the excluded middle has been thoroughly debunked

>>11581410

what you choose to call a proof technique is ultimately arbitrary

>>11581409
Nice try, schizo tranny

>>11581410
>Draw a diagram
>Says it's "obviously" commutative
>Conclude whatever
>Here's your proof bro
Is this a direct proof?

What's the use case of expressing complex numbers in Cartesian form?

>>11581468
Addition is easier in that form.

>>11581468
What have you tried?

>>11581468

there is none, it's just a thing that you can do

>>11581473
I'm just reading a book and it made me think.

>>11581492
really simple to do geometry that doesn't involve circles, really simple to do linear algebra, etc...

>>11581468
It probably is preferable to store them that way when doing computations on a computer.

>>11581504
STFU CS NIGGER THIS IS MATH GENERAL NOT COMPUTER GENERAL OR WHATEVER FUCK OFF TO /g/

>>11581511
>CS
?

The brainlet Poincaire
>>11576545

Me, an intellectual
>>11581495

>>11581468
It's conceptually simpler for beginners

>>11581520
all the more reason to avoid it

>>11581518
Retarded. Mathematics is the study of structures.

>>11581511
>NIGGER
Why the racism?

>>11581468
every single thing that complex numbers are used for??? because Cartesian form is equivalent to any other equal representation???

>>11581523
Mathematics is the study of things mathematicians like studying formally. Prove me wrong. Protip: you can't.

>>11581526
>racism
Why the anti-white rhetoric?

>>11581528
>implying all mathematics is formal

>>11581504
Nah, when we do image processing the polar form is the most common

This just arrived, what can I expect?

>>11581534
>the polar form is the most common
But it is numerically a bad choice, granted, accuracy is of little relevance in image processing.

>>11581536
a meme

>>11581528
I'm a mathematician and I like studying physics formally, but physics isn't math so you're wrong.

>>11581533
It is if you want to publish it. Or at least it should be

>>11581523
very vague without telling me anything. what the hell do you mean structure? like a building had a structure?

>>11581541
>physics isn't math
There are those who disagree

For me, it's exponential form.

>>11581536
jesus imagine reading those books the whole way through. its really not needed to make it through gradschool, definately not undergrad. people seem to take to these books as if it were some religious devotion to science, as if they were monks rhuminating over scripture, hoping for some divine blessing of intellect to wash over them for their pious study. To some limited extent i suppose it really does bless you with knowlege, but really...those books should be nothing more than reference manuals for when your own intuition and pre-knowlege hits the brakes.

>>11581548
Mathematical Structures™

>why yes, of course I do all my complex arithmetic using 2x2 real matrices
>is there any other way?

>>11581565
>Flashbacks to a quantum computing class where we had to multiply 64x64 complex matrices by hand
Triggered

>>11581573
>where we had to multiply 64x64 complex matrices by hand
unless your matrices were 98% zeroes this is physically impossible, that's like half a million arithmetic operations

>>11581565
>complex numbers? You mean equivalence classes of [math]\mathbb{R}[X]/<X^2+1>[/math]?

>>11581536
The best book currently in Algebra

Btw, how much did you pay?

>>11581589
They were, the matrix were like a bunch of hadamard gates tensored out, so there's a whole lot of zeros, multiplying some vectors. It was really easy to make errors

>>11581594
>The best book currently in Algebra
This is not Algebra, by Serge Lang

>>11581541
Science is the branch of maths which creates objects and rules which work in an approximate way to the different empirical systems are observed to behave.The objects and rules are considered scientific iff they can predict outcomes of real world 'games' within the specific acceptable error margin (ie ballistics is only scientific if you can score the epic three throw nearly every time.).

>>11581598
That's a graduate textbook, Aluffi is an intro for undergrads

>>11581598
>This is not Algebra, by Serge Lang
Lang is a meme.

>>11581610
>reading undergrad books
NGMI

>>11581615
Don't bully the anon. People need to start somewhere.

>>11581612
Lang is the best living mathematics author

>>11581594
>The best book currently in Algebra
*ahem*

>>11581559
This book has pretty much all of the basics in algebra, I worked through most of it from a pdf copy and I keep coming back to it for reference, so I thought it was worth the purchase, since I prefer physical books.

>>11581594
£78. Bit expensive, but I have the money, and I use it enough to be worth the investment. It's unfortunate Atiyzah/Macdonald is so expensive (same price as this) for a 120 page book, since that's another one I keep coming back to.

Just imagine if people were raised to learn a base 26 system in which each number was a letter in the alphabet? Imagine how trippy it would be to read books: maybe we would discover some secret connection between language and maths by being able to naturally decompose every word into a number.
question:
is 26 a good number for a base?
abcdefghijklmnopqrstuvwxyz = ???

>>11581635
>£78
No man, just no, it's not about having money or not, most people have, it's about having values, we need to stand up against those abusive prices, not keep buying them, by doing what you did you're fucking over all of us who are making a stand, stop being a slave to Springer and co., Tell them to fuck off, had you hired a bookbinder to produce that book I bet you'd pay less than £78.

>>11581657
>stop being a slave to Springer and co
Aluffi isn't published by Springer

>>11581635
yeah, i have at times enjoyed reading a hard copy myself. there is a certain enjoyment one can get from it, just like im sure monks could enjoy the beauty of the doctrines they translated, but for me such labours should not be done by rote as if it were a strict commandment from your bishop (professor) to be observed.

>>11581657
I've downloaded every single textbook that ive needed through libgen anyway, this is just a caprice (?)

>>11581663
Can't you read? When I said co. I meant all other publishers who follow the Springer trend of publishing low-quality binding and printing book with abusive prices.

>>11581671
>all other publishers who follow the Springer trend of publishing low-quality binding and printing book with abusive prices.
The AMS does not use print-on-demand bindings. Everything in the GSM series has a sewn binding and a professional print job.

>>11581670
Me too, then I just print them

>>11581679
Well, that's a little better, but their paper is not good quality as far as I know, charging £78 for it is still not justified.

>>11581681
>but their paper is not good quality
The fuck do you mean "not good quality"? Have you ever even picked up an AMS hardback? GSM paper is literally the best quality I've ever seen in any textbook I've opened.
If you want to be a jew about the prices then go ahead, but don't try to make excuses for it. The AMS is basically the only publisher left whose books AREN'T a steaming heap of shit these days.

>>11581670
Be it -gen or -rary, lib is the thinking person's choice.

Hi /mg/bros. How can you show that this graph does not have a hamiltonian path?

>>11581730
>How can you show that this graph does not have a hamiltonian path?
What have you tried?

>>11581654
here is the alphabet number for anyone intersted.

>>11581736
I have tried drawing smaller rectangular grid graphs like that that have no hamiltonian paths because I thought the relatively easy structure would make it easier to notice why it has this property. I wasn't able to prove it though, that's why I'm asking here.

>>11581745
that nub on the top right, that isnt a node is it?

WHAT A GREAAAAAT DAY TO STUDY SOME MATHEMATICS AM I RIGHT BROS LET'S GIVE OUR BEST TKDAY YEAAAAAAA

>>11581671
>publishing low-quality binding and printing book with abusive prices
The PDFs I download of libgen have a pretty good quality though?
Nicely typeset and all...

>>11581654
That would allow us to speak of perfect names, as you could find the factors of a name. You are mistaken, though. There are 29 letters, you forgot å, ä and ö. Using the proper number, one obtains a prime base, a nice observation.

>>11581761
They're not like that on the physical paper, especially Springer books in general, their binding is glued, their paper is the worst and the printing is all blurry.

>>11581755
>WHAT A GREAAAAAT DAY TO STUDY SOME MATHEMATICS AM I RIGHT BROS LET'S GIVE OUR BEST TKDAY YEAAAAAAA
That would be tomorrow. Too tired to think at all today.

>>11581764
The two Springer books I own don't seem to have that problem...

But they are both in German, so maybe the based springer bros are just scamming mutts?

>>11581755
why bother? i will achieve nothing in this life. today is sunday, so i will rest instead. hopefully i can enjoy life enough today to stave off my suicide for another week...

>>11581763
>29 letters
You're smart but wrong. Those are phonemes not letters. Letters are technically a multiplicity and in standard English are context dependent. These phonemes are absorbed into the standard parlance and so not included in the alphabet. if you wanted to make a base 44 system in which each number was a standard English phoneme then i say all the better.

>>11581763
>you forgot å, ä and ö
å isn't real, but ü and ß are missing.

>>11581789
ßässed

>>11581763
of which 44 is 4 x 11 which is cool because you can have 4 prime quadrants.

>>11581763
Those aren't used in written english, and they're not letters of the alphabet, they're letters with diacritics. [math]\"i[/math] would've been a better example, as in [math]na\"ive[/math].

>>11581801
Stupid 4chan tex engine.

>>11581802
tex is such a waste of time. its better we get everyone acclimatised to shitty command line tier presentation because we are now in the digital world.

>>11581778
>so maybe the based springer bros are just scamming mutts?
In my (fairly wide) experience, it's not Springer, it's the North American Amazons that are the problem. I've purchased books directly through springer.com for sales before and while they're still printed on demand, they're really well done. I would not even have noticed they were POD if Springer didn't tell me.
Ordering one from Amazon.ca or Amazon.com is literally just flushing money down the toilet. You get this comically shiny plastic rectangle with a completely flat spine that's like 30% fatter than a real copy of the book, the paper is rough and so stiff it will spring back if you stop holding it down, the cover is glued onto the endpapers so loosely you can get a finger (sometimes two) in between the spine and the cover, and the first few times you open them the big wad of kindergarten glue they call a binding makes this fucking loud crunching sound. And they used to come half the time (I'm not exaggerating the number) with egregious printing errors like entire pages blank or printed at a 30 degree angle, but this has improved.
Eventually I just stopped wasting my time even trying Amazon.

But European Amazons oddly do not have this quality issue. I've got at least half a dozen Springer books from them and they were all at minimum passable.
Shipping isn't that expensive, sometimes the cheapest way to get a usable copy is really to import it from the UK or wherever Amazon.

>>11581765
Gonna need a sauce on that one pal

>>11581827
Enforcing quality standards is communism

>>11581783
>i will achieve nothing in this life
You idiot, it's not about achieving something or not, it's about putting up a fight, no matter the circumstances, no matter if you win or lose in the end, if you keep fighting that's enough. Victory is merely a detail, humans live not by achieving victory every single time, but by doing their hardest, by fighting their hardest, then even if they lose in the end they'll still lose with no regrets because they know they did the best they could and this feeling of trying no matter what is what matters, not victory or defeat.

>>11581399
new
>>11581405
new

>>11581849
>Everyone who isn't transphilic is new

>>11581846
fag

>There are people PAYING for math books in 2018

>>11581857
general culture
lurk more

>>11581846
stupid platitudes. while it's as subjective of an opinion as any other, it's widely agreed that life's meaning is personal and subjective. what you're saying might make you feel good but it has no impact on me; for me a significant part of life was to learn and research cool things in my field of study. but i can't do it, most of us can't, and no one had the pity to take us aside when we were 10 and tell us that there was no point in trying because some chinese dude called tao could do in one week what would take us a year to achieve.

>>11581862
>2018
Son... you've been sleeping for 2 years...

>>11581859
Stop using language like that.

>>11581866
>general culture
new

>>11581868
Tao is Australian you racist

>>11581862
>2018
I WISH

>>11581869
Can you prove that nobody purchased a math book in the year 2018?

>>11581870
Stop making posts like that and I won't have to

>>11581846
Fighting is hard. Fading into blessed nothingness is easy.

>>11581868
I'm having a hard time believing you're older than 10 with opinions like
>tell us that there was no point in trying because some chinese dude called tao could do in one week what would take us a year to achieve.

>>11581873
you know what i meant, i don't care where he was born nor do i care for his ethnicity. he could be an eskimo born in swahili and my point would remain the same. compared to this intellectual beast of a man, we are worthless filth.

>>11581870
Stop using trans/fag normalizing language.

>>11581873
>Australian
He is crypto-white scum colonizing indigenous spaces.

What the fuck are you niggers doing in my thread?

>>11581882
im not saying that you're not allowed to disagree with my outlook, but i think you'll agree that most of us were never told that being "smart" locally (in your high school or uni for example) means jack shit globally. there are entire countries who don't produce in 10 years the research that tao produces in 1.

>>11581871
>>general culture
>new
new

>>11581893
>there are entire countries who don't produce in 10 years the research that tao produces in 1.
Granted, if you aren't from a mayor European country you might as well kill yourself right now. But there are no niggers here, right?

>>11581879
Stop making posts like that and I won't have to.
>>11581884
No. Being yourself is normal.

>>11581899
>Everybody who disagrees with me is "violating general culture"
lol

>>11581904
>Being yourself is normal.
Does that apply to rapists, mass murderers and fag genociders too?

>>11581904
>Stop making posts like that and I won't have to
This is incoherent in response to the post you're quoting. This board is intended for 18+, please try to engage on a level higher than a 6-year old "no u"

>>11581893
So? Is your objective doing research on math or being more intelligent than Tao? You know research in vast, right? You can chose any field to specialize in, even one where Tao doesn't know anything about, and you'll still discover new things if you manage to go beyond a PhD.

It seems to me that you have a very naive view of what research is about, and since you can't be 'number 1 mathematician', 'the best mathematician alive' you somehow think you should just give up everything, like... what?

>>11581905
When you respond to a "I'm not a he" post with rude language, you are outing yourself as someone who hasn't been on /mg/ for very long. This is because in the distant past, when people responded with the "I'm not a he" meme, they didn't get any responses at all besides the occasional joke. But now, every single time someone says the meme you have the same old tired 4chan rhetoric in response. No one is fucking serious. The person posting it isn't transsexual. They're just a random long-time /mg/ poster posting a random long-time /mg/ meme. Every time you take it seriously, you out yourself as new.

>>11581926
>they didn't get any responses at all besides the occasional joke.
So me making a joke about it makes me new?

Let me get this straight. You claim I am new because I do *exactly* what has been done in this general for quite a long time?

>>11581908
no, of course not - a very very very small percentage of people are those things, while a relatively large percentage (30-40%) of people are not placeable into the tired "cis straight" box of gender and sexuality.
some people are closeted, that doesn't count as straight.

>>11581933
You don't understand what kind of jokes I'm talking about.
The joke you made was a pathetic attempt at 4chan bottom of the barrel humor.
I'm talking about subtle responses that show an understanding of the meme format.

>>11581935
>while a relatively large percentage (30-40%) of people are not placeable into the tired "cis straight" box of gender and sexuality
lol

>>11581941
>You don't understand what kind of jokes I'm talking about.
In fact I do.

>The joke you made was a pathetic attempt at 4chan bottom of the barrel humor.
Hating trannies has been a 4chan meme for about a year, it's absurd that you think that everybody who jokes about trannies is automatically new...

>I'm talking about subtle responses that show an understanding of the meme format.
LOL

>>11581910
it's perfectly coherent. the person told me to stop making posts telling him to use proper language, and i told him that if he didn't make posts using improper language, then i wouldn't have to tell him to stop.

>>11581923
"Specializing in a field" is one thing, but if you're not good enough it turns into "studying irrelevant garbage math which no one cares about, because that's the only area where you can come up with something new"

>>11581944
I'm not talking about being new to 4chan you fucking moron. You're obviously not new to 4chan. I'm talking about being new to /mg/.
Please stop trying. It's embarrassing.

>>11581949
You're such a fucking pill. Stop responding to me this way. You have no fucking respect.

>>11581949
If you care enough about something you will find new results in it eventually

>>11581951
>I'm talking about being new to /mg/.
So, someone, who evidently posts elsewhere on 4chan, who makes a post which clearly resembles general 4chan "humor" is "new to a general" because of that?

Are you retarded? Can you not see how retarded your arguments are?

>>11581961
>Are you retarded? Can you not see how retarded your arguments are?
new

>>11581966
>new
new

can you guys stfu with ur shit flinging... its 2020 and no one cares whether a lady is born with the wrong lady bits or not

>>11581974
>no one cares whether a lady is born with the wrong lady bits or not
The fags who cut of their dicks certainly do.

Aside, can you imagine a worse torture then what trannies go through?
Imagine having a mental illness and instead of getting treatment, you get prescribed life ruining medication and your dick gets cut off...
LMAO, the people who through of that must have been the biggest trans"""""phobes"""" out there.

>>11581974
Just report them

How is any of this related to maths ?

>>11582000
How is your post related to math.

>>11582000
>How is any of this related to maths ?
This is just a homophobe containment thread.

>>11582005
>phobe
Nobody is afraid of some fags...

>>11582004
has the word math in it

>>11582015
No. It had the word maths in it.

>>11581280
making neat looking complex functions

>>11582067
noice. i just like making the most retarded broken ones.

>>11582067
>rainbow colors
REEEEE THE GAAAAAYS!!!!

200 posts in 5 hours, the fire is rising AHHHHHHH

>>11581949
What makes one 'not good enough'? No having Tao's intelligence? You think everyone doing research has a genius level IQ? You honestly believe average IQ people can't do find but irrelevant results? Again, I'm having a hard time believe you're not a teen, your mentality just screams that.

>>11581949 #
What makes one 'not good enough'? Not having Tao's intelligence? You think everyone doing research has a genius level IQ? You honestly believe average IQ people can't do find but irrelevant results? Again, I'm having a hard time believe you're not a teen, your mentality just screams that.

>>11581949
What makes one 'not good enough'? Not having Tao's intelligence? You think everyone doing research has a genius level IQ? You honestly believe average IQ people can't find anything but irrelevant results? Again, I'm having a hard time believe you're not a teen, your mentality just screams that.

I dont feel like doing anything would math help me fix that?

>>11582143
based

>I'M KUMMING

>>11582200
funny

https://en.wikipedia.org/wiki/Isometry#Examples
The 3rd example there says unitary matrices are the isometries of C^n.
Aren't translations in C^n also isometries?

>>11582316
No because thy're not linear transformations, but affine ones.

Applied Category Theory.

>>11582342
Applied English.

>>11582342
>Applied Category Theory.
So, all math?

>>11582144

Is 0 a natural number?

>>11582399
not in most definitions of that set
in some, yeah

>>11582399
There's nothing natural about zero

>>11582399
see the standard ISO 80000-2 (https://www.iso.org/standard/64973.html)) for an authoritative voice on this issue :^)

>>11582385
You're not funny for posting antisemetic ass shit.

>>11582433
>pretending to be antiracist when you can't even spell semitic

>>11582385
Based and funny

>>11582454
oh yeah that spelling makes way more sense

>>11582416
>Symbol is bold N
>Nobody uses a bold N, everybody uses a blackboard bold N
Nice "standard"

>>11582385
based. fuck the jews and fuck jannies

>>11582498
might be related to previously TeX not being as available

>>11582399
Only when it is useful

>>11581448
>the law of the excluded middle has been thoroughly debunked

How? Things can only be 0 or 1.
Any further complexity can always be encoded in a longer string of 0s and 1s.
There is literally nothing non-binary in this world.
That's why those-who-shall-not-be-named hate math and mathematicians.

I was recently talking to a guy I know doing a PhD in pure math. What is it like to realize that you are only proving obscure intestinal appendixes of logical consequence writing papers about things that will never have a single applied use case?

>>11582539
>those-who-shall-not-be-named
Who? Voldemort?

>>11582548
>What is it like to realize that you are only proving obscure intestinal appendixes of logical consequence writing papers about things that will never have a single applied use case?
pretty great mate
fuck applied fags

>>11582539
>Any further complexity can always be encoded in a longer string of 0s and 1s.
only if you allow infitie length strings, no?

>>11582548
Your world is an illusion, your 'applicabilities' have no real stand over anything abstract other than satisfying your own petty needs.

>>11582399
If you want to make sure, everyone understands 0 is included, use [math]\mathbb{N}_0[/math].
If you want to make sure, everyone understands 0 is not included, use [math]\mathbb{N}\setminus\{0\}[/math].
If it doesn't really matter, use [math]\mathbb{N}[/math].

>>11582399
Natural numbers are the ones used to count AND order. There's no "0-th" position.

>>11581346
lmao
for real though, grant was MUCH hotter than I thought he was going to be...

>>11582548
Number theory was created over 2000 years ago and was seen as useless until a few decades ago. Now it's the basis of cryptography.
Some fags on the 19th century tried to mathematize origami because they are bored, now their theory is the basis used to project folding solar panels for satellites among other things.
At roughly the same time other group of pure mathfags with too much free time started to tinker with the proprieties of knots and tied strings, now knot theory is used to model protein folding and other similar stuff.
In the 19th century some guy with too much free time created symbolic logic, now it's the basis for most digital technology.
Some German autists created a theory of generic geometric objects that don't behave like any geometric object you can make in our world, but their theory is the basis for relativity.
Some swiss lad made a theory of incidences that would latter become graph theory, which was for over a century considered to be a useless diversion. Those days every computer engineer knows his graph theory, because it's actually very useful.
You don't know what you will need eventually. Maybe most pure math is useless, but it's impossible to know.

Follow up question for mathers. Just how bad is it trying to get an academic job in math?

>>11582584
Getting an academic job at anything is pretty bad those days

define "mathematics"

ok I'm going to self study real analysis. I've been meaning to do this for 10 years. I have no delusions about going back to school or using this in anyway... I just have to get a taste of what mathfags are into before I die.

>>11582558
I do the same thing but for [math]\subseteq[/math] and [math]\subsetneq[/math].

I need a sequence of non-negative numbers [math](a_n)[/math] such that
[math]\sum_n^\infty a_n < \infty[/math]
but
[math]\sum_n^\infty a_n^2 \log(1/a_n^2) = \infty[/math].
Ideas?

>>11582619
Take something that converges conditionally but that lacks square convergence and see of it works. Like (-1)^(n)/sqrt(n)

>>11582628
Forget, I'm retarded, didn't see the non negative part

Why are the smartest people from top PhD programs going into financial trading? It's so sad seeing people with genuinely amazing publications and then a few years later disappearing to crunch numbers for a wall street firm.

>>11582646
if you're good at something, why not maximise the amount of money you get for doing it?

>>11582556
What are you referring to?

>>11582619
ln(1/x^2) < x^2 for x > 1, so your new sequence is less than a_n^4 which is less than a_n for all suficiently large n (because a_n converges 0 < a_n < 1 and thus 0 < a_n^k < a_n for k > 1), so there's no such sequence

>>11581426

lmao ma nigga contradiction is the most powerful and efficient form of proof get the f*k outa here ma nigga

>>11582734
No, that doesn't work because a_n < 1 so the first implication fails. But there's no positive x such that x^2ln(1/x^2) > x, so the convergence of the original sequence still forces the second sequence to converge.

What really is an elliptic curve?

>>11582802
An algebraic variety of degree 2

>>11582770
yeah precisely

>>11581468
Formal autism

>>11581448
>using the LEM to prove it has been debunked
lmao

>>11581523
cancer

>>11581548
structures are how pretentious faggots pronounce "graphs"

>>11581536
read the table of contents, skim the problems at the end of each chapter, then read the chapters

>>11581730
solve a smaller version of it then incrementally make it bigger until you have the answer.

>>11582843
Absolute retard. Kill yourself, for your own good.

>>11582646
>why do people like money

gee i dunno

>>11582865
cry more tranny no amount of homoalgebra is going to add points to your room temperature IQ

>>11582882
>I can't understand math with a higher level of abstraction than undergrad courses: the post

Is Lang really a meme?

>>11582896
He's very divisible, some people swear by him and other absolute despise him. So try it by yourself and see what happens.
Do note that his undergrad books are all pretty good, it's the ones people use on gradschool that usually are a problem

>>11582899
wtf I love lang now

I recently read a group-theoretic proof that [math]\mathbb{R}/\mathbb{Z} \cong S^1[/math], where the first group considers sum and the second multiplication.

Is there any way I can make sense out of this intuitively? What the fuck am I looking at?

>>11582888
>he doesn't know that categories are directed labeled hyper-graphs

lmfao. delicious tranny tears.

>higher-level of abstraction

you do realize there is nothing more abstract than a graph right? you can't get simpler than a fucking dot and a line. lmfao you stupid pretentious faggots are so impressionable and dumb that you actually believe categories are somehow "more" abstract than graphs. nigga they are graphs. lmfao fuck you're so dumb you don't even know what the words you're using refer to you just mindlessly regurgitate ad hoc techniques from the textbook without any awareness of the fact that it IS ad hoc and not in any way as abstract as you think it is. fuck eilenberg literally talks about categories being ad hoc and you still think you're doing something truly abstract despite how incomplete and literal it usually is.

>>11582896
don't listen to trannies and pretentious retards on /sci/, if it works for you then use it. everyone calls rudin a meme but a couple of my buddies kick ass with it. i'm ambivalent towards him.

>>11582912
S1 is the unit circle buddy

>>11582912
S1 is the full circle, so the element from R/Z represents a percentage of a full turn.
a = b in R/Z if they both take 1 to the same place after you spin the circle for the amount they represent

>>11582929
holy cope. Did a category theorist fuck your gf or something?

>>11581785
Who talked about English?

>>11581789
>å isn't real
https://en.wikipedia.org/wiki/%C3%85

>>11581801
They are the last 3 letters of the based alphabets.

>>11581835
Kami Nomi zo Shiru Sekai.

Now good night.

>>11582912
the map is a -> exp(ia). exp maps sums into product. As other anons mentioned, adding in the argument just make you turn more. topologically, you can also see that the mod ZZ identifies 0 with 1, meaning you are closing the segment [0,1] over itself, making a circle.

>>11582953
lmfao it comes off like that doesnt it.

no i don't actually hate category theory just the people who unironically believe shit like "real math is about structures" or some other hand-wavy holier-than-thou bullshit that need to be kept in check.

Do you think in images? Do you have a voice of the mind?
Do they affect your ability to do math?
I have both but I heard that people who doesn't have a voice of the mind can process things faster.
Related:
https://en.wikipedia.org/wiki/Aphantasia
https://www.youtube.com/watch?v=u69YSh-cFXY

>>11583017
FUCK HE'S BEAUTIFUL

>>11583017
I'm pretty sure the "no inner monolog" thing is bullshit, at least if it ought to mean, as this asian woman implies, that she can't even imagine producing the idea of spoken words in her head.

>>11583104
>asian
>no inner monologue
how is this incomprehensible to you? watch asian twitch streamers for a few hours and you'll understand my incredulity

>>11582843
>using the LEM to prove it has been debunked
who are you quoting, I don't even know what the quote is about. what is "it"?

>>11583104
My friend told me that she can actually picturing someone speaking in her head, but using that to actually think is mentally tiring.
When she thinks, it's all about concept, feeling and images pierced together.

>>11582843
>using the LEM to prove it has been debunked
who are you quoting, I don't even know what the quote is about. what is "it"?

>>11582539
>How? Things can only be 0 or 1.
That sentence claim is just a restatement of LEM.

see also that post
>>11581317

>>11583120

You are using the LEM to debunk the LEM. I have yet to see "a logic" that doesn't use the LEM. I really genuinely don't think you understand what the LEM does. With no LEM you wouldn't be able to distinguish between things. We couldn't be having this conversation because you wouldn't be able to distinguish between any of the words I was using, because you wouldn't even have a conception of words because you wouldn't have any conception at all. That's what "logic" would be like without the LEM.

Fuck paraconsistent/"non-classical" logic is so fucking stupid. Literally no one thinks about the words that they're using when they fucking speak and it makes me sick.

>>11583120
Simply because it cannot be decided, if [math]P(x)[/math] or [math]\neg P(x)[/math], doesn't mean neither is true.
Those are two completely different things. And, since the problem is trivially semi-decidable, it should be an indication for [math]\neg P(x)[/math].

What's a book on graduate-level group theory? I already got Rotman

>>11582646
If you're good with numbers, you'd be a total retard not to go into finance

>>11583325

>>11583384
this isn't lang

>>11583440
He/she didn't ask for a meme.

>>11583524
>He/she didn't ask for a meme.
I'm not a "he/she."

>>11583325
Gorodentsev
Rotman is a reference book, not a textbook

How advanced does trigonometry get? I haven't particularly heard about people advancing or researching trigonometry, or studying/reading/writing advanced trigonometry books, or taking trigonometry classes beyond high school (or freshman college if 'tarded). Obviously trigonometry can be applied to more advanced things, and can be used in calculus. But does trigonometry itself get more advanced than the basic stuff covered in a precalculus textbook?
Not really looking for resources to delve into it or anything, just curious.

>>11583671
Trigonometry is mostly just formulas and more formulas. Once you get to complex analysis it gets much easier to get trigonometric identities plus there are a bunch of trigonometry based methods to write down polynomial roots, but that's about it really. Trigonometry has a name and a bunch of named functions because historically it's practical importance (to navigation) was immense, much bigger than it's theoric importance and surely much bigger than theory itself as a field.

>>11583683
Thanks for answering
>Once you get to complex analysis it gets much easier to get trigonometric identities
What do you mean by 'get' trigonometric identites? 'Get' as in derive? Or understand? Or what?

>>11583692
Derive, I just didn't write derive to not make it sound like derivative.

Is it true that neutrons decay into hydrogen?

>>11583696
okay ty for answers

>>11583671
As >>11583683 said, trigonometry is mostly about formulas. That doesn't say there's a lot of interesting things about it, the Andreescu's book 103 Trigonometry problems from the USA IMO team is a very good source for that.

Since nothing can travel faster than light, can't events in the so called past, such as those from stars billions of light years away, be said to happening in the present scientifically speaking?

>>11583769
I'll check it out thanks

>>11583556
I'm not you.

>>11581730
Anyone?

>>11583868
I'm taking graph theory this semester, give me 4 months and I'll answer

>>11582972
>>å isn't real
It was a joke, I obviously know that it is a "real letter" in some alphabets, it just isn't a real letter in the alphabet of my country.

>>11581763
You forgot ą,š,č,ė,ę,ū,ų,į,ž

should i continue studying math even though im stupid?

>use 26-base system
>everyone needs to learn 26x26 multiplication tables

Good morning. Have a productive day!

>>11584021
Those don't count. They are ugly.

>>11581654
>is 26 a good number for a base?
It's not particularly divisible (26=2*13, so it's exactly divisible by 1,2,13 and 26).
Multiples of 12 are generally a good start.

>>11584137
12 looks way too blue to be a good number, the best numbers are yellow like 8

>>11584139
What numbers are yellow to you?
Powers of 2?
I like those very much as well, but the problem with those is, that while there are never numbers with more prime factors smaller than them, the unique arrangements of those are way fewer than for numbers smaller than them.
Take 16: 16=2*2*2*2, so the divisors are 1, 2, 4, 8 and 16.
But 12 already has more: 12=2*2*3, so the divisors are 1, 2, 3, 4, 6 and 12.

I'm too stupid for this stuff.

>>11584162
same bro.... i think im just gonna off myself

linear algebra and functional analysis >>>> rest of math >>> dog shit > complex analysis

>>11584187
This was supposed to be a nice hobby, but no.

>>11584188
what about C*-algebras?

>>11584188
>t. too dumb to understand anything else than linear algebra

>>11584187
Let me assure you: That doesn't add up.

>>11584213
how come?

if you commit suicide, the jews win. don't let it happen

>>11581622
No.

>>11582807
lolno. It is a smooth projective variety of dimension one, genus one, and a distinguished rational point. That is of course the worst way to define it (unless you try with schemes, which is even worse). Maybe you prefer to say it is an abelian variety of dimension one.

>>11584055
Protip: every mathematician was considered stupid by his/her own standard until he figured everybody is clueless most of the time.

>>11584241
Lol nononono, you don't know what an elliptic curve is

>>11584254
joke on you I actually know

>>11584245
It actually does feel like this sometimes. Thanks, anon.

How do I stop having suicidal thoughts each time I encounter challenging problem/concept?

What's the best LaTeX editor?

>>11584362
im using texmaker its pretty nice

>>11584363
What you guys think of this list?

https://itsfoss.com/latex-editors-linux/

>>11584245
>everybody is clueless most of the time.
That's seriously the one insight more people need to have.
And it's by far not limited to mathematics.
I genuinely feel happy, when I'm pointed out mistakes on my end.
That's something I can work with. Improve my effectively clueless self towards a less clueless self.

>>11583868

SOLVE

A

SMALLER

VERSION

OF

IT

Fuck. It's literally a fucking grid with a square missing in the top corner and an extra leg on another. You couldn't make it any easier to rescale a simpler problem.

>>11584362
vim/emacs/vscode

>>11584363
Pretty mediocre, unless you really need a clicky GUI to put in symbols.

>>11584373
Terrible.
LyX is unusable. The rest usually are missing very basic features, like a non-obnoxious color scheme, reasonable auto completion, snippets, etc.

I also think the author is severely mentally challenged, somebody who writes:
>Texmaker is considered to be one of the best LaTeX editors for GNOME desktop environment.
or
>If you perform PDF conversions often, you will find TeXmaker to be relatively faster than other LaTeX editors
has ABSOLUTELY no idea what is going on.

>>11581745
>>11583868

I'm re-reading what you wrote. Correct me if I'm wrong it sounds like you are saying you know what the solution is but you can't prove it? What experience do you have writing proofs? Are you stuck on a certain line of the proof? Please be specific.

>>11584055

Yes that's actually one of the best reasons to study it.

>>11584399
>vim/emacs/vscode
Those are text editors not LaTeX editors

>>11584406
>Those are text editors not LaTeX editors
LaTeX is written in plain text any text editor is also a LaTeX editor.

>>11584412
But why would any of those be better than editors focused solely on LaTeX like the ones in the list?

>>11584416
>But why would any of those be better than editors focused solely on LaTeX like the ones in the list?
Many of the editors on that list are barely maintained software which means they are usually very basic, buggy and are lacking a lot of features I mentioned.
It is *hard* to write a good text editor, but it is significantly easier to write a good extension to an already existing editor.

If you do not need a clicky GUI to choose which symbols to use, then VSCode with the appropriate LaTeX extension, will be flat out better in pretty much every single regard.
It is a pretty good code editor, into which, I would guess, at least 100 times the effort was put into, compared to every piece of software on that list and that really shows.

If you are unhappy because VSCode is non-free (as in freedom, it is gratis to use and download) you can use VSCodium which is free software.

>>11584426
I found this article http://opensourceawesomesauce.blogspot.com/2012/10/latex-editors-emacs-vs-vim.html?m=1

What do you think of it?

>>11584440
>What do you think of it?
Both vim and emacs have a relatively steep learning curve (and some time investment to set up correctly).
I personally think that vim's "keybindings" are absolutely great, but, thankfully, you can use vim keybindings in a lot of things. Like emacs or VSCode, so that is what I am doing right now.

For the article specifically, I see little wrong with it, it is a subjective comparison of two text editors.

Variables in math are basically just addresses, lexical scope is implicit.

>>11584362
Sublime Text works very well for me, I like using it for LaTeX.

>>11582646
Like who? Most quants are people who never got academic offers

>>11584362
Seconding Texmaker.
If you need to collaborate with (a single) someone, use Overleaf.
Sublime Text is a decent editor, but in the end it's nagware, and I'd never use it for Latex while there is Texmaker.

>>11584551
>and I'd never use it for Latex while there is Texmaker.
You shouldn't use it for anything since there is a totally free alternative with equivalent or better features, namely VSCode/VSCodium, which coincidentally has a LaTeX extension with all the features you could ever want except a clicky GUI to insert symbols.

>>11584554
You know, I'm glad I have managed to escape the MS ecosystem.
Especially memories of Visual Basic send shudders down my spine.
Fool me once, shame on you. And there won't be a twice.

>>11584591
Thankfully MS doesn't really have as much of a hand in the thing.
It IS open source and VSCodium is even free software, which includes no Microsoft branding, but is otherwise the same.

>>11584591
>>11584596
And, I mean, I say this as someone who genuinely hates MS and pretty much everything they do.

>>11582581
>Is impossible to know.

In your examples given, we have
>Number theory
>Origami folds
>Knots and strings
>Lorentz transform
>Graph theory

I dont think it takes hindsight to see the potential of all of these except the last one or two(and even they are epic from any point of view). the first three are all directly applicable from the moment they were founded, thus can be seen as worthwhile even in their age.

Saying that these contributions are the same class of discovery as those of the classical and post classical era is a stretch. modern contributions are a diminishing return results wise. such is life.

I for one think you are correct, but the timescale on which it applies is potentially longer than the lifetime of the universe. Some things will never be associated or applied with reality, as the sun is destined to swallow us.

>>11584630
>as the sun is destined to swallow us
Sorry for the OT, but the sun won't swallow anyone in this thread, and I don't think it will ever swallow human kind as a whole.
The actual doomsday clock is the rising entropy, that will eventually prevent life from generating the energy that it needs to be.

>>11584362
Microsoft Paint/MS Wordpad, anon. Unironically. Im super serious right now. MSpaint is the most streamlined tool invented for writing scientific papers. yes it isnt neat and flashy, but it is a million times easier to get literally anything done.

>Want to write some weird symbol youve no idea what its tex is?
JUST DRAW IT ON THE PAGE WITH YOUR MOUSE.
>want to make a table with annotations etc
PASTE THE GRAPH INTO PAINT AND TYPE THE ANNOTATIONS IN A TEXT BOX
>want nice hyperlinks to direct your reader through the text and to the bibliography
MS WORD GOT YOU COVERED

if you are an absolute rebel like me then you will see that MSpaint is the real GOAT for ease of use and intuitive function, and should be used fo 90% of formatting.

>>11584646
>he thinks humans can in2 space.
You are a danger to the american people, NASA is make work jobs for snake oil salesman. i wouldn't support the space meme until you get the subterranean lizards out the government first.

>NASA IS THE GREAT FILTER

>>11584734
I have been starting to think that we are past the "GREAT FILTER".
Look, people have been thinking they were experiencing the end times of the human race for as long as humans were a thing.
I won't deny I have had experiences that made me feel similar things, but so far it's always been going on. Further than ever before.
It can easily happen that we will suudoku ourselves rather sooner than later, but I hope not. What gain is there in betting on the opposite anyway?

>the subterranean lizards out the government
You mean politicians out of government? America has done the first step towards that, and I highly appreciate your efforts.
Democracy needs to mean democracy, and not aristocracy.

>>11584767
>>11584767
>You mean politicians out of government?
No i mean the secret subterranean cousin of humanity who secretly rules earth from Shangra-la.
They are perpetuating dense globe theory and trying to break the firmament and end causality,

>>11584767
>Look,