/sci/ - Science & Math

>>14571839
Group theory then Tensor calculus.

>>14571839
Whatever most applies to the latest thing in computing/physics.

Top tier: calculus
Good tier: solving for x
Mediocre tier: square roots
Shit tier: logarithms
Retard kill yourself tier: trigonometry

>>14571864
That's a good one. I wish you a pleasant day

>>14571839
literally anything except category theory

>>14571873
Thank you for your reply. What do you think of algebraic geometry? What do you think of arithmetic geometry?

>>14571873
>t. filtered by category theory

>>14571878
Hi. What do you think about algebraic geometry?

>>14571839
I would agree with this. Although, funnily, the less prestigious correlates with more $$$.

I like math, but I also like $$$ so I study less prestigious math.

>>14571839
"prestige" lmao. Not to mention every branch of math is interwoven with one another. Plus your fields are much too broad, for example most of the work in DG now has huge overlap with PDEs in global analysis and algebraic geometry in complex geometry. Speaking of AG, thats way too broad in itself because people who work in arithmetic geometry see themselves as more number theorists.
But of course there are many ways about number theory, its not really its own field because it touches avery other branch of mathematics.
"Probability" in the general sense is not something anyone works in, people care about the behavior of SPDEs, high-dimensional problems in statistics and data, complexity and combinatorial problems.
NC/quantum geometry is not "dead", but i wouldnt call it "hot" atm either. its also too new to have real "prestige" if thats even a thing.

If want a list of my personal favorite fields of math, very broadly speaking, i would say as an unordered top 5

>diophantine geometry
>kahler manifolds
>Hodge theory
>automorphic forms
>homotopy groups of spheres

I suppose, really taking into consideration what is possibly meant by "prestige", an unorderd top 10 would be, without personal bias:

>synthetic geometry
>differential geometry
>calculus
>diophantine geometry
>diophantine approximation
>mathematical physics
>dynamical systems
>statistics
>algebraic geometry
>differential equations

these are all too broad to even properly discuss wht makes them prestigous, and there are several other areas deserving of being called prestigous, but there you go.

>German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."[1][note 1]

>>14571839
>Comparatively not prestigious ...
this is a very weird listing that seems like undergrads not knowing what they're talking about.

Alg geo is currently definitely on top of the prestige list in pure math, but it stops being simple when you start looking at potential applications to other parts of math or science. For example, mathematical physics has its own prestige as it ranges from everything from functional analysis to lie theory, etc etc.. and algebra in general is quite prestigious. Theoretical CS is similar as it involves quite prestigious fields like analytic number theory, algebraic geometry (the current approaches to P vs. NP are all algebraic geometric), solved longstanding open conjectures in pure math, etc..

So prestige only makes sense for relatively newer fields of mathematics that mathematicians are flocking to, but to more classic fields of math and fields where math is even a little applied, prestige is less clear.

Analysis not being prestigious is also a weird take. It's more than analytic arguments are EVERYWHERE, and so you expect it in most areas of math.

Also prestige among pure mathematicians is completely different than prestige among applied mathematicians is different from prestige in STEM in general. Algebraic geometry holds no prestige among the public while holding a great deal in math. Even among pure mathematicians, some view other topics as prestigious. Among scientists, probability theory, analysis, and ring theory are king.

Finally, all of what I said is relative bullshit that changes depending on what exciting results come out in a given field. Alg geo is currently prestigious given how it glues different ideas together. Combinatorics grew a huge amount in prestige when people realized counting and counting arguments are fundamental even in infinite structures. This shit doesn't really matter as much as being autistic enough about what you like to convince others that it's cool

>>14571876
I think that the prestige of a field is a fucking meme and there's no way I'm jacking off your dick about your field being good.
>>14571878
category theorists are the literal janitors of the mathematical community. All they're doing is trying to organize math, IE cleaning. They don't make anything on their own.

>>14571864
>Retard kill yourself tier: trigonometry
Fuck you

>>14571839
S tier: Probability
A tier: PDEs and Dynamical Systems
B tier: Differential Geometry and Analysis
C tier: Everything Algeblabbery

>>14571839
I don't know, but make sure Graph Theory's on the fucking bottom

>>14571997
Based Gauss, literally nothing tops number theory

>>14573034
>All they're doing is trying to organize math, IE cleaning. They don't make anything on their own.
not the other anon, but I agree as far as pure category theorists go. But I think ACT guys (applied category theorists in CS, physics, etc) have some interesting results

im pretty sure bakers calculate stuff sometimes, and they have more baking shows than math shows

>>14571864
>Retard kill yourself tier: trigonometry

Any field that can leverage category theory to do new things is now prestigious. This includes algebraic geometry since Grothendieck, homotopy theory especially after Lurie, arithmetic geometry especially in the Langlands program, and parts of mathematical physics.

Any field which didn't adopt category theory is usually seen as stagnant.

>>14574047
>>14573852
>>14573034
>>14571878
>>14571873
Post graduate level alg geo is just schemes, which is just category theory.

>>14574062
Try talking to some Italian geometers, they are still doing Castelnuovo/Enriques style algebraic geometry in current year.

>>14573688
lmao someone's salty over their homework.

>>14573155
Based

>>14572576
thank you for your answer! what areas of algebra would you call prestigious? group theory? ring theory?

>>14571878
the axewound in your pants will never be a vagina

>>14574106
based. I need to learn 'talian

>>14574498
why do you think this is a good thing. what do you think about probability?

>>14577577
love it

>>14577674
I'd like you to elaborate on probability theory.

>>14577698
What do you mean? Do you want to know more about it?

Dont you need to go through all of them for most math majors anyway? When i studied applied mathematics in university even in the first year we got a touch on most of these topics

>>14577717
I apologize that I may not sound specific. There are reasons why people choose certain areas of mathematics. These may be applications, for example people may choose to study Calabi-Yau manifolds because of mirror symmetry and field theory. Some people choose because of their own thoughts of importance in mathematics. I myself personally find algebra and group theory of extreme interest. They are fundamental structures that can allow us to study things that cannot be understood geometrically. This makes the field profound. And I ask you. Why does probability theory pique your interest?

[math]p[/math]-adic analysis.

>>14577763
Group theory itself is best understood geometrically.

What an unintelligent question. No such thing exists. And if someone tells you it does - they are egotistical. We know exactly jack shit about the universe and what actually matters. A breakthrough in topology could be a breakthrough in physics and etc. The most prestigious field is one that has the most potential for a scientific breakthrough, and you have no way of knowing which one that is unless you are spearheading the change yourself.

>>14577839
I like your answer. but I disagree. what about mathematics itself? do you think that the study of algorithms or some smooth manifolds can be more fundamental and important than research in algebra?
is not an arbitrary thing.

>>14577839
>The most prestigious field is one that has the most potential for a scientific breakthrough

>>14577839
Prestige is a social thing. Of course some fields are more prestigious than others. It's got nothing to do with your philosophical wankery but with the sociological dynamics of science and research.

>>14577866
Possibly. It could very well be there is a breakthrough in algebra waiting for us. In fact if faster than speed of light travel becomes possible with Erik Lance’s design then it will most certainly mean that our algebra will need new operators. I mean, the whole existing model would have to get rebuilt to suit the new model of the universe, meaning new operators, new laws and etc. We just don’t know.

>>14577968
That’s exactly what I meant by people being egotistical. I disagree with the notion that those at the top of the social hierarchy in science are moving humanity in the right direction.

>>14571839
>[math]∞^∞[/math] category theory

>>14578028
That's a stupid answer. I'm disappointed.

>>14578036
you are a hypocrite or a very naive ignorant person. why do you care what happens to humanity? there is analytic philosophy that can solve many social problems, but none of the analytic philosophers or those who know these things (including me) do anything. i will live a limited amount of time and want to spend that time on something that is interesting and can impress me. i really hope that you are a hypocrite and are not that naive

>>14577777
please elaborate?

>>14578051
Can you elaborate more on how I’m a hypocrite and what exactly I am naive about? You could be right, but I struggle to understand how.

>>14578063
you are naive and ignorant if you don't understand what analytic philosophy is. if you don't understand that most social problems can be solved by methods and concepts from analytic philosophy. you want a fun fact? analytic philosophers study realism, anti-realism, epistemology, ethics and social facts, but won't lift a finger to solve problems in the real world themselves

the problem with people like you (if you are naive and ignorant) is that you spend your limited time and limited resources on things that indirectly or absolutely do not solve the problem globally. you do not know how to solve the problem and often such people do not understand what the problem is

if you understand that all problems can be solved well and efficiently, but you don't do it anyway, and then say you're sorry that the top of the social hierarchy is moving humanity in a certain direction, then you're a hypocrite

There is no problem with either option. in the first case, you have no moral responsibility. in the second case, no one would think to point a finger at you, because they don't understand anything.

>>14578088
You are using insults to establish some kind of superiority which just doesn’t work . You are basically ego tripping without even realizing it, and that’s fine, I do that too, but that’s not an argument.

You are implying that I’m not doing anything to solve the problem. I’m not sure how you came to that conclusion. I don’t think all problems can be solved, or that I know every problem and how to solve each one. I know of a few problems and I have ideas on how to solve them. It may or may not work. It’s something I’m passionate about and willing to make huge sacrifices for. I don’t see how that’s a waste of time even thought my time on Earth is limited. I think what decides if you are wasting your time or not is if you are enjoying what you are doing.

>>14578120
I think we should end our conversation here

>>14578088
>>14578120
nice reddit spacing tourists

>>14578133
lol irl it would have been over a long time ago as I don’t deal with people who don’t have basic manners

S: dynamical systems and PDE
A: Probability theory
B: number theory and logic
F: everything else

>>14573155
Based

>>14574047

math is pretty stagnant if new things is just rephrasing existing theorems in the language of category theory

>>14571878
>category theory
what is it used for?

>>14579030
classify trannies as women

>>14579035
lol. let's not talk about trannies though

>>14579119
trannies are the single most useful invention known to personkind

>>14579121
True but this is a thread about math. Stay on topic!

>>14579035
Tranny's Conjecture: Prove that the category of genders exist.

Tranny's Corollary: There exists a morphism from man to woman.

>>14579565

Tranny's lemma: morphism from man to woman is not invertible

>>14578171
elaborate on the theory of probability