/mg/ = /math/ general

>astronomy
stopped reading right there

>/math/ general
>10 posts in and no math
If you're looking for beautiful math then knot theory has you covered, a seemingly banal subject that turned out to have great physical, theoretical, and biological application.

Stop bullying the gorilla and prove that for any [math] n \geq 2 [/math] the general linear group [math] GL(\mathbb{Z}^n) [/math] is generated by the diagonal embedded groups [math] {\Delta}_{1,i}GL(\mathbb{Z}^2) [/math], with [math] 1 \leq i \leq n [/math], where [math] {\Delta}_{i,j} : GL(\mathbb{Z}^2) \longrightarrow GL(\mathbb{Z}^n) [/math] is defined as
[math] {\Delta}_{i,j}\left( \left(\begin{array}{cc} a & b\\ c & d \end{array}\right) \right) = \left( x_{u,v} \right)_{1 \leq u,v \leq n} [/math] with
[math] x_{i,i} = a [/math], [math] x_{i,j} = b [/math], [math] x_{j,i} = c [/math], [math] x_{j,j} = d [/math],
and [math] x_{u,u} = 1 [/math] when [math] u \neq i,j [/math].
All the other entries in the matrix are [math] 0 [/math].

At first I was excited since I did my undergrad thesis (we have to write a thesis to graduate here) on astrodynamics (it was about the behaviour of periodic dynamical systems under perturbations of parameters with applications in celestial mechanics, to be more specific) but then I read the rest of your post and it's just a shitpost. Astronomy and Classical mechanics were surprisingly popular in my department, since they can be approached in an axiomatic, purely mathematical context (as per Clifford Truesdell and others).

Prove that [math] \textbf{Ab} [/math] and [math] \textbf{Mod}_R [/math] have no subobject classifiers.

ncatlab.org/nlab/show/subobject classifier

Finally, for what values of [math] k [/math] is [math] x(x^2 - 4) = ky(y^2 -1 ) [/math] an elliptic curve?
These 3 problems should keep you busy for a while.

>Finally, for what values of k is x(x2−4)=ky(y2−1) an elliptic curve?
over what field?

also did you mean ky(y-1)?

[math] \mathbb{R} [/math]
Nope.

>[math]\mathbb{R}[/math]
No such thing, user.

Get laid losers.

>Nope.

>elliptic
>cubic in y

>mfw I started a math major and was really happy about it
>mfw the professors were shit with the exception of one
>mfw I gradually starts to become uninterested in it
>mfw I start watching game of thrones for entire days until I finished it
>mfw I start to ignore the classes
>mfw my grades were awful in every class except for one
>mfw I get dismotivated and stop going to college
>mfw I'm too scared to say anything to my family about it
>mfw I keep lying to them and go out every morning saying I'm going to college but instead I just go to a park where I just wait for some hours to go back home
>mfw I'm doing that for 2 years now and no one suspects anything

Can I still unfuck my life? Don't get me wrong I still love mathematics but I think I just fucked up the little potential I had to make a good career. I just don't know what to do and I'm extremely tired of wasting my days.

>for 2 years now

well I'm not smart or good in maths but I found a book about surreal numbers and the idea of a different way of representing numbers is cool

Yes. Cubic in [math] y [/math]. I'm not sure what is it that confuses you. Do you need hints?

I hope this is LARPing and no one is actually pathetic enough to go to a park every day to pretend you're in college

I bet this guy is asian.

>no one is actually pathetic enough to go to a park every day to pretend you're in college
Asians are.

I'm serious, I know I'm fucked up and I'm pathetic, I'm 20 right now, is there still hope for me to have a good mathematical career or should I just give up?

>on stack exchange
>after asking so many brainlet questions, decide to give back to the community
>spot a hard question that I could answer
>spend a couple hours on it, texing it up takes a good 30 more mins
>my solution is complete, and parametrises all the answers to a particular diophantine equation
>post my answer
>somebody with shitload of rep points already posted a shitty answer, just gives a condition for a solution, posts a couple of trial and error solutions, and it was already marked by the poster as the definite answer

should i just kys?

dawg if you're only 20 you still have your life ahead of you, but you should get your standing with the university sorted out

Are you even any good at math? Something tells me you're not being honest (not even with yourself). In any case, none of us here knows you or the full extent of your circumstances. How in the world are we supposed to advise you?

You blame your professors but maybe you lost interest because you're no good at it. I too barely went to classes during my undergrad. Because I practically lived inside the university's library. There is really nothing in your story I can relate to so I can't even begin to guess at why you fucked yourself up like this and how to fix it.

Like, you say you're willing to apply yourself if there's still a chance you might "make it". But do you really mean it? Did you study any math by yourself during these 2 years? (I suspect you did not.)
And why in the world didn't you take a gap year?
Your issues run deeper than your mathematical potential, that much is clear.

I have a problem with procrastination, that's just it, I really like maths. The problem is that I barely opened any books during the classes. Had I studied correctly everyday, then I would have got good grades.

About the professors, one of them just walked into the class with his clothes and a pen on his hands, the fucker didn't even bring any books or papers, he just walked in and started writing things off his head, sometimes he even forgot about explaining some subjects. Once my friend even asked him when was going to be the days of the tests and he said something like 'just decide among yourselves and give me a date', everyone in the room just laughed. There was also another one, a woman, who had barely any idea of how to teach. There was another who prefered to talk about soccer everyday than teaching his class.

I didn't ask anything about your professors. It's not just that I don't care at all about them, but also that it doesn't in the least matter how they conducted themselves. This is [math] your [/math] problem.
From my end, your whining about fuck all. What's so odd about the students deciding the date of the exams anyway? It's common practice here. Professors that fixed the date themselves were the exception, and they did it mostly due to extraneous circumstances, like having to leave for some conference after a certain date etc.

If a right triangle existed with a hypotenuse of 10 and an altitude of 6 (I know this can't happen), would the area of the triangle be complex?

>good at math
>making no headway at solving any of the millennium problems
Honestly I'm thinking of giving up and pursuing finance
If it takes me two decades to solve even one problem (and in the worst case solving this problem does not immediately solve the other problems as a consequence) I'll be netting a measly 25,000 dollars per year, after taxes.
It doesn't take a genius to know that two decades of compounding interest could whisk me away into a world where I make that much money in a single week.

>If a right triangle existed with a hypotenuse of 10 and an altitude of 6 (I know this can't happen)
why not? couldn't the base just be length 8?

You're already in the wrong when you want to solve a millenial problem be ause of the money you'll get.

What's her ethnicity?

Is it any different from professors who solve non-Millennium problems for their salary?

so what noble goals do you have after spending a significant fraction of your life on something?

>I will hit you with this stick otherwise
How about I hit you with my penis instead?

>who solve non-Millennium problems
Ew...

I will solve a millennial problem because I want to prove to everyone that anyone, even the most ordinary of people, can do it if they put their minds into it.

Do you have more images of anime girls and mathematics or with books or in a library?

So you've got a low sense of self-worth and have invented a chip on your shoulder? That's no reason to waste your life for peanuts (and probably fail anyway, considering that the people you'd consider "ordinary" haven't solved such problems)
Maturity is realizing that everyone is ordinary, regardless of their upbringing, socioeconomic position, and intentions. We all die eventually. And more importantly, we all have to eat.

This is probably the most delusional and pathetic post I've seen in these threads. And that's saying a lot.

Lombard.

I will not fail.
>Maturity is realizing that everyone is ordinary
???
Gauss was definitely not ordinary, nor was Euler, Pascal, Newton, Gödel. They've been immortalized by their minds, but I'll be immortalized by perseverance and efforts alone.

Yeah, people said that about Cantor also, people love humiliating other people who chase their dreams.

I'm studying real Analysis right now, but I'm mad at your suggestions, Veeky Forums.

>hurr Rudin is the only god-tier book you need

No fucking way you disgraceful autist, it's poor in explanation, and the exercises are too hard and they'll take me a year to solve. I need a book that likes to chew and explain every single thing.

I'll use Rudin for the exercises, but that's it.

Any other recommendations? I really need this.

On the slim chance that you do solve these problems, you'll be immortalized for your mind, not your efforts. The computer that assisted in the proof of the four color theorem was an example of effort. The current millennium problems can't be solved through effort (you're fucking around with infinity) so your only option is to be extremely clever. You have to be more clever than any mathematician currently living. If you solve the problem, you're not ordinary. Take that as you will.
If you're trying to prove that determination [math]\implies[/math] results you will certainly fail. Everyone will misinterpret the cause of your success.

>you'll be immortalized for your mind, not your efforts.
No, because, different from other genius, I was nothing exceptional during school. My grades were good but I wasn't solving any IMO problems. I once even scored 10 out of 100 in a trigonometry test because I hadn't studied anything for it. I will definitely be seen as a person who persevered despite not being a genius.
> The current millennium problems can't be solved through effort (you're fucking around with infinity) so your only option is to be extremely clever.
Do you have proof of that? This sounds like a losers speech, you sound like you already give up all your dreams and expectations of solving them and didn't even try.
>You have to be more clever than any mathematician currently living.
You just have to be more determined than every mathematician currently living.

>(you're fucking around with infinity)
What did he mean by this?

stein shakarchi
or zorich

Academic record depends on more than just raw intellectual ability. Since you don't seem to realise even that, there's an extremely high chance that you're a brainlet, so you will never solve any important problem.

>Academic record depends on more than just raw intellectual ability
But there's certainly a correletion between them, because if you read the biographies of the so called genius of mathematics you'll see that all of them had exceptional grades during their school days.

>Since you don't seem to realise even that, there's an extremely high chance that you're a brainlet, so you will never solve any important problem.
Keep 'em coming, I will just accept every humiliation, but your words will not affect my determination at all, because I'll definitely solve a millennium problem and prove to the world that anyone can do that.

Allow me to elaborate
If, say, you wanted to prove the Riemann Hypothesis, you'd have to prove there were an infinite number of zeroes on the critical line.
There's no way to prove this via exhaustion, because we've assumed there are an infinite number of them.
At least one person in this thread thinks that there's some way to use a proof by exhaustion and that no cleverness is needed in such a case.

>I will definitely be seen as a person who persevered despite not being a genius.
No, you'll be seen as a genius who slacked off in school and then read a shitload of books, filling your enormous but previously empty mind with mathematics. Assuming you solve it.
>This sounds like a losers speech, you sound like you already give up all your dreams and expectations of solving them and didn't even try
No, I definitely tried. Maybe I didn't try hard enough. But that's because the solution wasn't simple enough. I'm not exceedingly clever. Perhaps I could reach an epiphany if I buried my head in the notes of dead mathematicians for two decades, but in the meantime I would starve and become a genetic dead end. And when I inevitably failed to solve the problem I would also be a memetic dead end.

>I'll definitely solve a millennium problem
Hey which one are you taking? Cause I'll definitely solve a millenium problem myself and it'd pretty awkward if you and I solved the same one

Just stop posting already. It's annoying. You're full of hot air.

try Folland

> but in the meantime I would starve and become a genetic dead end.
So you're OK with abandoning your dreams because you're afraid of death and that society will not see you as a prestigious person during the time you'll spend trying to solve it? Your dreams should be above anything in your life, if it means to spend 20 years trying to prove the Riemann Hypothesis while you're slowly rotting and starving , then what's the problem?

>If, say, you wanted to prove the Riemann Hypothesis, you'd have to prove there were an infinite number of zeroes on the critical line.
You should know more about what these problems actually are before commenting about them, if that was the Riemann hypothesis then it was solved almost a century ago.

I'll try those, thank you :3

>I will not fail.
Sooner or later you'll be giving your shotgun a blowjob.

I have an interest in the Riemann Hypothesis, but if someone proves it before me, I'll just move onto another one.

I should have also included "and there aren't any that aren't on the critical line".
It should be trivially obvious that you can't prove that by exhaustion either.

But you caught me; I don't give a shit about Riemann Hypothesis. I was deep into Twin Primes and Goldbach conjectures.

I told you to stop posting. It's obvious you have no idea what you're talking about.

don't worry he doesn't ever need to know what he's talking about
he's DETERMINED

Ok, I'll stop, but what do you mean with >It's obvious you have no idea what you're talking about.

>It should be trivially obvious that you can't prove that by exhaustion either.
I wouldn't say that's trivially obvious at all, hypothetically someone could prove there's an upper bound on how large a non-trivial zero off the critical line could be, and then the proof could be exhaustive. Just like how the four colour theorem was reduced to looking at ~2000 maps and then proved by exhaustion despite there being infinitely many maps that the four colour theorem applies to.

>someone could prove there's an upper bound on how large a non-trivial zero off the critical line could be
And you wouldn't consider that to be extremely clever?
Christ, how much does it take to impress you?

>And you wouldn't consider that to be extremely clever?
I certainly would, did I imply otherwise?

My mistake; I thought you were implicitly defending Captain Perseverance's plan to solve the Riemann Hypothesis without cleverness.

What do I mean by it? Let's see: can you calculate [math] {\sum\limits_{n \in \mathbb{N}} n^{-3}} [/math]?
Another genius. Why are you talking about the RH when you don't even know what an elliptic curve is?

>Why are you talking about the RH when you don't even know what an elliptic curve is?
What does RH have to do with elliptic curves?

A great many things.

>A great many things.
Go on...

Can you calculate this?

Here's two hints: Sato and Tate.

>generalizations of Sato-Tate imply analogues of RH for elliptic curves
I only spent 5 seconds googling but I hope I'm missing something, I was expecting something a little more direct based on your posts

I'm 98% sure you're full of shit

I will tie anime posters of math general in chairs in a basement, and come down to feed you and inject some feminine hormones into your veins periodically. Then I will put you in girly clothes, like skirts and stripped socks, and start drilling your asses with cute sex toys of all colors and sizes, and I'd use my own penis to dig through your mouthes and asses. I'd force you to have sex with each other and then join. Then I tie you back in the chairs, leave the basement and only come down every now and then, either to feed you, inject hormones into your veins, torture you, or fuck you.

please stop

...

>I will tie anime posters of math general in chairs in a basement, and come down to feed you and inject some feminine hormones into your veins periodically. Then I will put you in girly clothes, like skirts and stripped socks, and start drilling your asses with cute sex toys of all colors and sizes, and I'd use my own penis to dig through your mouthes and asses. I'd force you to have sex with each other and then join. Then I tie you back in the chairs, leave the basement and only come down every now and then, either to feed you, inject hormones into your veins, torture you, or fuck you.

why don't 3d women look this beautiful?

Is there any way to prove a function is surjective iff it has a right inverse without Choice?

Should I mention math general and anime in my speech when I win my fields medal?

>Should I mention math general and anime in my speech when I win my fields medal?
Why aim as low as a Fields Medal? How about you give that speech when you win the first inaugural Gorilla Trophy?

>I'd use my own penis to dig through your mouth
Feel free to try. I'll bite it off.
>I was expecting something a little more direct based on your posts
Why?

>Why?
Because you randomly brought up elliptic curves when the topic was RH, and then claimed they were related by referring to an conjecture which remains to be connected to RH in any way

This is some pretty decent fanfic.

Don't fuck wid Infinity he a hardass nigga.

i don't get it.
how can these diagonal embedded groups generate GL(Z3) if entries like x3,2 are always zero?

Then I'd remove your teeth one by one and replace it with a silicone prothesis so it looks like you have teeth but can't bite. I'd do it in the most painful way possible so you can learn your lesson.

I have a serious question for you anime posters. Are you virgins? Have you ever gone to parties or had any friends? I won't make any fun of it. I'm just curious.

Don't you have
[math]\Delta_{3,2}(\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix})=\begin{bmatrix} 1 & 0 & 0\\0 &1 & 0\\ 0& 1 & 1\end{bmatrix}[/math] which has non-zero x3,2?
?

What I was getting at is that the RH is a much more difficult problem than the one posted upthread (which for whatever reason tripped you up), yet you opine on it anyway.

>how does matrix multiplication work?