/mg/ -- Blocks Your Path Groupoid Edition

Because they have, in some sense, less restrictions.

They fell for the abstraction meme.

Would the homotopy category be concretizable if we relax the restriction that Set must be wellfounded?

the homotopy category of what

it's a very beautiful subject. everyone already knows the most elementary connections between algebra and geometry (analytic geometry), which may inspire them.

>Grothendieck used to draw shit on his notes
just like me!

he drew that because he thought the theorem was satanic

I'm interested in algebra, geometry, and rigour. Which is why I'm not enjoying so much algebraic topology, and I am quite enjoying the small amount of plane algebraic geometry I've done (and algebraic number theory and Riemannian geometry for that matter). Also, how can I explain to a prof that I want to do a PhD in this subject without sounding (a) like a retard, and (b) like I am talking out of my league, given that I don't have that much experience in the subject

>try to write out a theorem in algebraic geometry
>accidentally create a primordial summoning symbol and your stationery becomes infested with demons

How important are anime girls to learning Math?

memes

You will never be able to convince a prof working in the area that you aren't talking out of your league (because you are), but unless that prof is a huge jackass, it shouldn't be a problem.
The question is, how do you really know that you want to do a PhD in it ?

I've never seen a polynomial in my life

how can i get over my hatred for all things set-theoretical or topological
i enjoy algebra but i am at the point where i need a good background in topology to continue and i just don't think i can push forward

...

not at all, they lead you into falling for meme lists

>interested in rigor

They aren't important but they can increase your enjoyment of doing math. It's always nice to have company when you're engaged with something that pleases you, and anime girls are the most pleasant companions in the world.

Just get an algebraic geometry book and work through it.

Since you have done Riemannian Geometry, start with a book on complex algebraic geometry. That way you can lean back on differential geometric techniques if you aren't comfortable with heavy algebra.

so people can pretend to know category theory

Some people find it easier to problem solve in that mode of thinking. I personally prefer it.

can you teach me the art of mathematical anime grills?

there is something relaxing in the algebraic approach(in contrast to complex analytical one), just take a commutative algebra book such as eisenbud, a theoretical algebraic geometry book such as shafarevich 1 and an enjoy a book such as harris

You should start with classical complex algebraic geometry.

Eisenbud is really long and may get boring if you want to do geometry.

A-M is much shorter, the exercises are nice, and you can probably move through it quickly if you are comfortable with standard algebra.

best tip for doing algebraic geometry is too read a classic or undergraduate level text where the geometry is more obvious. Post Grothendieck Algebraic geometry is awesome and patrician as you can get but without a solid understanding of the actual geometry its is abstract autism.

Shalom Veeky Forums
I was stuck on this problem for an embarassingly long time for some pretty stupid reasons.
The problem is to find the surface area of the cone z^2 = 4(x^2+y^2) the answer is (sqrt5)*4pi
Some guy here mathhelpboards.com/calculus-10/surface-integral-2568.html got the right answer. Is this the right way to do it or just a fluke? If it's the right way, why is it R dr dtheta?

this is how you calculate the area of a surface of revolution
just take a differential surfaces book

i want to find square numbers of the form [math] n! + 1 = k^2 [/math] for integers k
there are only three known solutions for n: 4,5, and 7
i would like to know exactly how many there are
i have tried some simple number theory and analysis approaches, but nothing
i found an interesting approach which treats the factorial as the order of a symmetric group, and then used some other basic group theory stuff, and it felt like i was getting close to something, but i am inexperienced and was unable to prove anything significant related to the original problem
ideas?

en.wikipedia.org/wiki/Brocard's_problem

Give up

>Overholt (1993) showed that there are only finitely many solutions provided that the abc conjecture is true.
finitely many then

god damnit every time i think i've found something cool ramanujan or terry tao have already published 9 papers and a movie about it

>abc conjecture implies finitely many solutions
so what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?
i suspected that there were only finitely many solutions after bruteforce searching for n up to about 10,000
i also can't seem to find any bounds on the number of solutions, only that there's finitely many
i must know the number

I'm currently interested in quasi-perfect numbers.
Wanna join an effort?

en.wikipedia.org/wiki/Quasiperfect_number

if they like it
if they want to look cool and impress professors/grad students

The axiom of foundation is essentially unnecessary in the definition of Set ... it should remain a well-pointed topos with NNO even without foundation. So it's unlikely to make a difference. The real obstacle in the proof is "size", it's concretizable in proper classes / large sets IIRC.

It's way easier to reason about and prove things about programs that don't have side effects or an environment to worry about. If you can prove things about a program you can optimize it better and make sure it doesn't break stuff - typed functional programming (especially dependent types) allows you to specify the behavior of a program much better than the bolted-on type systems like Java and C++ have.

>so what's the consensus on abc conjecture?
It's now Mochizuki's theorem

>has anyone been able to learn IUTT and confirm mochizuki's stuff yet?
Yes but not peer reviewed

>so what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?

It's still in limbo basically. Not much news since Conrad's summary. A few people are convinced but they're in the minority.

>Not much news since Conrad's summary.
kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Nov20.pdf

what kind of background do i need to try to work on stuff like this

i feel like this is one of those things where a proof is going to come from magical arithmetic geometry lala land and it's going to be way too complicated for me to understand

>nationalist jap supports his fellow nationalist jap
Heh

check this out youtube.com/watch?v=_X1p7HhCzmA and tell me it isn't useless shit

Functional programming is a lot more mathematically natural I think. Also code is usually very short in length.

why don't you see for yourself :)

kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Oct.pdf

You do realize thats not IUT Mochizuki right?

what made you think I thought it has anything to do with inter-universal Tiechmemer theory?

Please help

why are there four roots to z conjugate = z^2, z is a complex number? I only got two.

i unironically went through the same part of the book 2 months ago and couldnt figure out why either

But that's a good path to learn stuff, I'd argue. I don't know too much about number theory either.

Kek. Pic related is one more I took a while to understand but it wasn't as bad as that one.

I mean news for us non-experts. Consensus last I heard is that this guy is just as incomprehensible as Mochi.

Fuck off to another thread with this garbage.

>Fuck off to another thread with this garbage.
But this is /mg/

Which means programmer garbage is not welcome here.

en.wikipedia.org/wiki/Curry–Howard_correspondence

>Which means programmer garbage is not welcome here.
math is a subset of computer science

subcategory*

>why are there four roots to z conjugate = z^2, z is a complex number? I only got two.
wolframalpha.com/input/?i=conjugate(z)=z^2

Why did you feel the need to post this? Type theory is quite different from "programmer garbage".
>subset

>en.wikipedia.org/wiki/Curry–Howard_correspondence
en.wikipedia.org/wiki/Brouwer–Heyting–Kolmogorov_interpretation

>posting this instead of
Pr*grammer spotted.

>>en.wikipedia.org/wiki/Curry–Howard_correspondence
>en.wikipedia.org/wiki/Brouwer–Heyting–Kolmogorov_interpretation
ncatlab.org/nlab/show/computational trinitarianism

Exactly backwards.

Thinking in terms of sets is pretty backwards indeed.

So called "functional programming" is in no way related to this. Types in those languages usually fail to even form a category. Discuss "programming" in

can't define logic without computation user

>logic is all of math
Pr*grammer spotted.

Who did you hear that from? A brainlet?

I love when brainlet westerns don't give the credit Mochizuki deserves because they all see it as incomprehensible alien bullshit when in reality it's just on a way higher level than anything weak brain westerns have come across. The best facepalm moments is westerns who dive into IUT proof without reading the 10+ prerequisite papers required to even begin it and get shook like "woah this is impossible to understand". It's like bunch of highschoolers diving into Perelman proof for Poincaré-Conjecture expecting to understand it because numberphile talked about it. I look down on people with this ignorant-thickheaded behaviour because it contributes nothing to the community and just honestly makes them look retarded. By the way over 30+ European mathematicians and some more from North America have confirmed the proof

>non-experts
Non-experts discussing this should kill themselves.

>Non-experts discussing this should kill themselves.
Why?

>t. chink with an inferiority complex

You're fine with buzzfeed journalists who's never taken a course in physics and not beyond highschool math should write articles on black holes and string theory? It's kind of like that.

Not him, but I'm not fine with anyone writing articles on black holes and string theory because black holes don't exist and string theory is a bunch of unphysical bullshit mathematics.

(you)

The fact that you buy that shit is one more reason to distrust Mochizuki actually achieved anything.
(Go back to China.)

So they don't have to embarrass themselves by making retarded posts.

How does one obtain the physical intuitions needed for doing math?

by doing math in the "right" order. real analysis gives you intuition for topology. linear algebra gives you intuition for algebra. complex geometry gives you intuition for algebraic geometry. none of those are actual prerequisites.

>real analysis
Stopped reading right there, what a stupid suggestion.

NEW 3BLUE1BROWN VIDEO

youtube.com/watch?v=OkmNXy7er84

That's pretty good for wasting your time.

>hurr hurrrrr
if you have anything to say, go ahead

it's faster than the other way around, so where do you waste time?

>hurr hurrrrr

I shaved my head today but it's snowing outside and I own no caps. What do?

>it's faster than the other way around
How much does it take?

Die

can someone explain the determinate to me at three different levels?

>fresh out of intro linear algebra level
>graduate level
>wizard level

I still don't really know what "it" is.