/sci/ - Science & Math

>>11265378
counting

triple integrals
quotient rule

>>11265378
Unemployment

>>11265385
This. Counting is some serious bullshit.

>>11265378
Dense Isomorphic Complex K-perfectoids

>>11265388
Lol

>>11265378
hardest what you moron? most difficult to learn?

>>11265378
Physics.

>>11265378
>What is the hardest math field?
IUT

Fractional distance might be the easiest, and I pride myself on that.

PDE

>>11265378
programming

Barnett Integration/Barnett Spaces

>>11265839
This is correct, to the extent that I am not familiar with anything harder.

>>11265385
Yep, fpbp, you need to have literally genius-level IQ in order to understand some modern combinatorics.

Someone post the iceberg graphic, I've lost it

>>11266020

>>11265378
Unironically Inter Universal Teichmuller Theory

>>11266055
Thats the one! Thank you very much anon.

>>11265378
Op, you have your answer:
>Random Sequence Extrapolation

>>11265622
no

>>11266055
Funny how the hardest ones are from physics.

>>11266229
?

The hardest ones I see are from CS, which is even funnier

>>11265378
Macroeconomics has these bullshit convoluted equations that could fucking trick the Dalai Lama into making a small mistake somewhere and fucking the entire thing up.
It's fundamentally the surreal fact that multiplying one million digits by hand can be harder than proving the Riemann hypothesis.
>>11265622
>computations in local coordinates in general relativity
Please kill me. End my suffering.

>>11265378
Topology.

>>11266055
P=NP because any hyperoperation can be expressed by an infinite polynomial equation, retard

>>11266792
>infinite
>polynomial

Square roots by hand

>>11266869
Mclaurin expansions are the hardest math?

>>11266575
Read Nakahara.

>>11266229
all of them are physics, just because basic math isnt BRANDED physics it still is bound to physics you brainlet, i thought you guys were smart?

>>11265880
Eh, it all has to do with where your talents lie. I'm sure there's plenty of people doing stuff with combinatorics who wouldn't dare stray into real analysis. Obviously not that they couldn't do it, but they'd be much slower at it than people who are inclined towards that school of mathematics.

>>11266869
Too hard to fold the paper for you?

>>11266055
Why aren't prime numbers on the bottom? Shit list.

>>11266055
Where is model theory

>>11266792
Here is some thing I don't understand about Clay's Millennium Prizes. For RH, they have a nice paper by Bombieri
>https://www.claymath.org/sites/default/files/official_problem_description.pdf
that clearly states in mathematical terms exactly what the problem is. However, they do not have such descriptions of the other five unsolved problems. I would like to work on P=NP but I am not sure what P or NP are, and Clay doesn't have any source material, and don't think I have ever come across the exact technical specifications. Same thing for Yang--Mills and Navier--Stokes which I think I've solved. I can't make a formal proof because I don't have a formal definition of the problem. For YM, it's pic related. For NS, I think it can't blow up in finite time because "finite time" means a natural number of time steps, and the time would have to enter the neighborhood of infinity before the solution could explode.

Pic from here:
The Golden Ratio in the Modified Cosmological Model
http://www.vixra.org/abs/1807.0136

>>11266055
I feel like anyone completing undegrad in math should be able reach the bottoms of "serious math"

>>11265378
Inter-Universal Teichmüller Theory

https://www.unz.com/akarlin/intro-apollos-ascent/

>>11268217
Dear Arcón. Recommend me a complex analysis book!

>>11268243
My CA skills are pretty much barely par for an undergrad tier. When I need to remember something, I use these Orloff notes.
>https://math.mit.edu/~jorloff/18.04/notes/topic0.pdf
Just change the topic number to go forward.

>>11265378
Nothing that I work on, I'll assure you of that.

>>11265378
In terms of what? Hardest to learn? Hardest to publish in? You could give a lot of different answers, and it's hard to give one that isn't entirely subjective. At the research level, most math is more or less the same, and what you find difficult usually boils down to personal tastes.

If I had to pick something, I'd say topos theory, at least in terms of how much you need to learn in order to actually solve problems and how much context from other subjects you need in order to fully appreciate it.

>>11267619
>all of them are physics
>I'm not the brainlet, you are
kek

>>11265839
dis the rite answer

probably high level arithmetic/algebraic geometry or theoretical PDE

>>11267237
neck yourself.. , anime-watching subhuman.....

>>11266055
>mfw am engineer and know everything above "serious math"

>>11265385
Great. I'm taking combinatorics along with real analysis 1 next semester. How screwed am I?

>>11265839
you do those in high school analysis class

>>11265432
Hey Peter Scholze, sup?

>>11270539
Nothing much man, just fapping to some anime girls. You want some IQ points buddy?

>>11270522
real pde, not "solve le heat equation with fourier transforms"
real pde is functional analysis + dynamics + geometry
read evans

>>11265378
Algebra.

>>11265432
Math isnt actually that hard

>>11268217
>I want to work on P=NP
>I am not sure what P or NP are

Wat. This is readily available information online. P is the set of computable problems solvable in polynomial time, NP is the set of computable problems that are (as of yet) not solvable in polynomial time. Mathematically,

[eqn]P=\{O(n) \mid \exists m \in \mathbb{Z} \text{ s.t } O(n)=c_0+c_1n+c_2n^2 + ... + c_mn^m\}[/eqn]
[eqn]NP=U-P[/eqn]
Where U is all computable problems. The goal is to show that [math]NP=\emptyset[/math]

Basically, prove every function can be expressed as a finite polynomial that's equivalent and you've got yourself a Fields medal.
Best of luck finding a polynomial function to model the TSP though

Arithmetic is unironically the hardest field of maths.

>>11270879
>np equals the set of non-polytime, computable problems
Keep pluggin away there champ, you're gonna solve this millennium problem in no time.

>>11270879
>NP is the set of computable problems that are (as of yet) not solvable in polynomial time.
No it isn't.
Even I know this much.

>>11271097
this image can't be real

>>11270539
Props for noticing, Anon.

>>11270879
that's not what NP is idiot
NP is nondeterministic polynomial time, which essentially says "polynomial with an oracle." an easier characterization is that a search problem (i.e, one which searches for a solution to a given input problem) is NP if you can verify whether or not some possible output is actually a solution in polynomial time. so if you give me a traveling salesman graph and a budget, i can give you a traversal of your graph, and you are able to check whether or not my traversal is within the budget you set and whether it's a traversal at all (very easy in polynomial time)
there are plenty of non-polynomial problems that are also probably not NP, though there's a whole complexity hierarchy which hasn't been resolved yet. for example, satisfiability of quantifier boolean languages is probably not NP. if i give you a set of variable assignments for a quantifier boolean expression, it isn't easy to tell whether or not it's true.

>>11266055
lol @ cohomology is genius level gap
undergrad category theorist gang

>>11266055
>""""strokes""""
>>11268208
a model of a logical statement is a set with corresponding functions that satisfy the logical statement.

for example, R=the real numbers equipped with its standard addition is a model of the abelian group statement("every number has additive inverse and commutative and blah blah")

when you take a logical statement, it's very illuminating to look at the class of models that satisfies the statement.

>>11272852
this.

>>11272852
Oh yeah? How about you compute the de-Rham cohomology of the real plane minus two distinct points with your category theory, you little bitch? Haha, it's always the mediocre undergrads that study category theory. Get real, faggot.

>>11273710
literally trivial you fucking pathetic moron