/mg/ = /math/ general

HAHAHA MATHFAGS BTFO

I wonder.

lads unless you know you are getting tenure theres no point for grad. We have the internet and we can easily communicate with other mathematicians. As a last resort. you can always go to college and pretend to be enrolled there and get feedback (never tried it) do something more financially productive and just study math in your free time if you truly love it. that is the last test of your love for math. not grad school .
If you are no John F Nash, u dun goofed.

Why would you not want tenure? It's not hard, and being a professor is comfy af.

>mfw I found a math textbook written by a physicist that covers algebra, topology and analysis (with some proofs) under 500 pages
>mfw I won't tell you the name

>having to talk in front of 20-100 people every day is "comfy"

Nah, fuck that. I'm too autistic, and the students would make fun of me.

What's wrong with letting people smarter than mathematicians write math textbooks?

good luck disproving it, faggot
there are at least [math]g_{64}[/math] zeroes

>Having a PhD and caring about what people who don't have PhDs think of you.

Do you seriously think that somehow matters? I pity you.

The vast majority of physicists are barely smart enough for mathematics.

From thumbnail colors I thought it was just her usual dress.

>did you read any interesting problems, theorems, proofs, textbooks, or papers recently?

The vast majority of adults are barely childish enough to wet their beds.

what are you looking at doing for work?

>tfw recognize pic
I gotta stop hanging around fourchin so much

we know where you hang user

>did you read any interesting problems, theorems, proofs, textbooks, or papers recently?
arxiv.org/abs/1609.02080
>Proof mining in [math] L^p [/math] spaces
>Let [math] \rho \in T^X [/math] be an admissible type. Let [math] B_{\forall}(x,u) [/math] be a [math] {\forall}-formula [/math] with at most [math] x [/math], [math] u [/math] free and [math] C_{\exists}(x,v) [/math] an [math] {\exists}-formula [/math] with at most [math] x [/math], [math] v [/math] free. Let [math] \Delta [/math] be a set of [math] {\Delta}-sentences [/math].
>Suppose that:
>[math] \mathcal{A}^{\omega} [X, \| \cdot \|, \mathcal{C}, L^p] + \Delta \vdash \forall x^{\rho} (\forall u^0 B_{\forall}(x,u) \rightarrow \exists v^0 C_{\exists}(x,v)) [/math]
>Then one can extract a partial functional [math] \Phi : S_{\hat{\rho}} \longrightarrow \mathbb{N} [/math] whose restriction to the strongly majorisable functional of [math] S_{\hat{\rho}} [/math] is a bar-recursively computable functional of [math] \mathcal{M}^{\omega} [/math] such that for all [math] L^p (\mu) [/math] Banach spaces [math] (X, \| \cdot \|) [/math] having the property that any associated set-theoretic model of it satisfies [math] \Delta [/math], we have that for all [math] \rho \in S_{\rho} [/math] and [math] x^* \in S_{\hat{\rho}} [/math] such that [math] x^* {\gtrsim}_{\rho} x [/math], the following holds:
>[math] \forall u \leq \Phi (x^*)B_{\forall}(x,u) \rightarrow \exists v \leq \Phi (x^*)C_{\exists}(x,v) [/math].
In the span of a few years we have went from conceptualising space mining on asteroids to mining proofs in abstract spaces.
Robots are underrated.

>penultimate theorem line
should be [math] x \in S_{\rho} [/math]

Uh, can I get that in English?

What kind of jobs can a BS in Stats get that a BS in Pure can't?

statician

real answer: if you're getting a BSc in pure math you better be planning for further study. BSc in stats sounds more easily marketeable for business or whatever

Which part trips you up?
The result gives conditions for producing theorems that hold in [math] L^p [/math] spaces. [math] \mathcal{A}^{\omega}[X, \| \cdot \|, C, L^p] [/math] is a formal system for them.
You can also always read the full paper. All the details are introduced.

>jobs a BS in stats can get that a BS in pure math can't
None exist. Statistics is a joke. doesn't know what he's saying. Statistics students are the reason why math majors have lower average IQs than physics majors. They drag everyone down with their piss-baby shit.
You will most likely have some probability theory and statistics courses as a pure math major anyway. There is no reason to be majoring in statistics unless you're a brainlet.

I'm getting a BS in math because my schooling is free, it's comfy to study, and many programming jobs don't require a CS degree (if any), so I decided to go with Math. I agree with what you say about Stats being more marketable, but the difference in classes is slight (even more so if I were to pick Stats electives as a pure math major), and I'm wondering if my potential employers will know that. Thank you for the reply!

>You will most likely have some probability theory and statistics courses as a pure math major anyway
This is why I'm adverse to majoring in it. I imagine I could market myself as a 'statistician' if that's what a potential employer wants to hear too.

So does that allow us to automate theorem proving in [math]L^p[/math] or something? Will this allow us to produce theorems that are "new" but provably true?

It's like you don't know anything about physics.

>So does that allow us to automate theorem proving in [math] L^p [/math] or something?
Partially. It delineates a set of theorems of the "for all such u there exists some v" kind.
>Will this allow us to produce theorems that are "new" but provably true?
Yes. Providing anyone bothers to implement the metatheorem in some automatic prover.
We should be able to get some pretty convoluted fixed point results with it.

>We should be able to get some pretty convoluted fixed point results with it.
Actually no, this depends on this combined with another proof mining result. Let me see if I had that one bookmarked somewhere.

Right, the produced results aren't constructive is it? It would only state that such-and-such statements are provably true but wouldn't give you any hints as to how to actually prove it, right?
Why even do this again?

> brainlet political scientist
Will do the MIT linear algebra course in the next weeks when I've finished Stanford's Machine learning course. I know some of the concept from stats but it's too patchy overall.

No, it gives you actual proofs. It's an upside-down search. You start with a proof pattern (here [math] \mathcal{A}^{\omega}[X, \|\|, C, L^p] + \Delta \vdash \forall x(etc) [/math]) and look for all statements that can be proven in a similar way, or more specifically you try to determine to what extent this is possible (here the role of [math] \Phi [/math], which is non-exhaustive, in the sense that there might be other statements in that are provable in a similar fashion but which are not accessible by way of [math] \Phi [/math]).

there might be other statements that are provable in a similar fashion

lmao nerds

You don't have to, there are quite a few books like that, hell there are some books that go a lot further than just topology, analysis, and algebra, those subjects (at least part of them) are pretty standard in most math phys classes, in fact they probably don't go far enough for many theoreticians.

>tfw barely passed calc 2
>tfw still hate it and will probably forget it in 3 months
at least I can act smart on /g/ about it and call them brainlets

Currently reading pic related.
It's quite nice, I was pleasantly surprised.

>see high schooler asking for book recommendations on mathoverflow
>someone recommends Bourbaki

Who the fuck reads Bourbaki in this day and age?
Set theory is old and busted.
Seriously.

I love this general because it has everything and everyone I love. Thank you for existing.

Show your love by posting some math.
Or something about math.
Thanks.

How does one go about learning geometric constructions using a compass and straightedge?
I can't find anything on this because I'd imagine those techniques became obsolete, but I'm still interested in them.

Read Geometric Constructions by George Martin for a primer.

Thanks. I will look that up.

there's a thorough treatment in Rotman's Galois Theory appendix C. surprisingly you can characterize constructible numbers as a simple field extension.

Unfortunately, the theory is above my level, and it's not comprehensive, but I'll keep it in mind.

I'm having some problems with part (b) of this exercise. It's fairly easy to show that if [math]\Pi_1, \Pi_2, \ldots[/math] are the cosets of a subgroup of [math]\mathbb{Z}[/math], then such a partition is compatible with +, but I don't know what to do next.
I suspect that these are the only compatible partitions, and if so, I was trying to prove this using the result from exercise 8.12 (if S is a subset of G and the cosets of S partition G, then S is a subgroup of G). But I'm not getting anywhere. How do I do solve this problem?

>I suspect that these are the only compatible partitions
what about the trivial partition where each part is a single integer?

That's the cosets of {0}, a subgroup.

>No, it gives you actual proofs.
Interesting, so it's sort of like automated theorem proving in Euclidean geometry via Groebner bases, but weaker.
Can't imagine why mathematicians would try to make themselves jobless though.

I didn't say anything about physics.

>Euclidean geometry
It's decidable though. Most of the math people do isn't, so they won't be losing their jobs anytime soon. But I'm working on it.
>Can't imagine why mathematicians would try to make themselves jobless though
I'm currently trying to accomplish this mainly for fun.

That's a very noble goal. Good luck.

What is the universal property of anime?

>Who the fuck reads Bourbaki in this day and age?
Lots of people
>Set theory is old and busted.
Bourbaki's Set Theory was already old and busted when it was written. It has nothing to do with set theory as studied by logicians. Also, there's literally nothing wrong with sets.

Them digits tho

Nice try, Rene L. (((Schilling))).

Do cute boys post on /mg/?

If we rewrite the KZ monodromy [math]d\Psi = \omega\Psi[/math] in an iterated integral [math]\Psi(\gamma(t))= I + \int_\gamma \omega \Psi(\gamma(s))[/math] we can write Witten's knot invariant as as formal series [math]Z(K) = \sum_{k = 0}^{\infty}Z_k(K)[/math] (or a limit [math]\lim_{k \rightarrow \infty}Z_k(K)[/math] if [math]K[/math] is non-singular) where
[eqn]
Z_k(K) = \frac{1}{(2\pi i)^k}\int_{t_1

i mainly chose to major in math so i can understand all these fancy symbols.

wewlad

>Tfw all axiomatic systems that could possibly constructed are busted in some way or another.

Who are you quoting?

Are you mentally challenged?

He asks as he posts an anime image.

You seem to be new here. All the *chan websites are born out of anime culture.

>anime and culture in the same sentence

if I have a sequence of length n, how can I compute the expected length of the longest palindrome centered at index i? I'm counting the single element in the sequence to be a palindrome of length 1.

I imagine that the length of the longest palindrome centered at index i is dependent in some way on the length of that at index i-1.

And by the way, I'm not asking for an algorithm, I'm trying to calculate the expected runtime of an algorithm.

What should I even read up on to be able to conceptualize and solve problems like this? Is it Combinatorics?

I do not like Patchouli, and I do not like Yukari. I think we should post more Cirno.

...

Going to take a shit.
BRB.

MATHEMATICS!

brb pewdiepie

ok im back

Any good tutorial on doing maths in latex?

>Not following Tao's blog
terrytao.wordpress.com/

Cirno has nothing good to say though.

nah mate literally get to it. start solving problem sets with it, googling stack overflow for how to do stuff. it sticks after a while and you'll be writing fast soon enough

I follow Baez's.
golem.ph.utexas.edu/category/
Haven't been reading it since he ignored my email tho.

share latex and overleaf both have tutorials and are really easy to use.

I have this asserted belief that any serious person would not be animefag. Either I am wrong or you are not serious person.

Salut Andrei. When are you going to join the homotopy type theory master-race?

Does Villani not count as a serious person?

Tough math problem you got there mate.

twitter.com/al1d/status/544490249121177602
Villani confirmed animefag

Villani confirmed proving existence of anime.

>Villani confirmed proving existence of anime.
But what about uniqueness?

>monolinguals
That's twitter-contracted French for "Cédric Villani hosts (a) session (on) #education".

Also, Villani being awarded the Fields is solid proof that the medal is a joke.

>Also, Villani being awarded the Fields is solid proof that the medal is a joke.
elaborate