@Daminark if catagory theory is useful for number theory I'll give it more points couse I kinda respect number theory

My point is that your continual glorifying of analysis (which already gets quite a lot of attention) to the sharp expense of everything else is assuming a value system you haven't proven, so until you prove that all intellectual endeavor is toward those ends such that analysis would be so far ahead of anything else, your claims have not one iota of validity over my reduction of everything as tools of NT

@Daminark well since science is just analysis in disguise so idk what else you want

You hate science bro?

I don't hate science

I just don't give science brownie points over algebra and the like

When you wanna nuke the moon or cure cancer you won't care much about schemes...

And if you're studying schemes you won't care about nuking the moon

What if the moon is about to nuke us?

Then I can't do schemes?

Well the moon would be scheming against us

So we need to learn about schemes to fight back!

that's a nice scheme you got there

we got a stack of them too

And if we are able to put ourselves in a situation such that the moon is screwed if it tries anything, we can stack it all up

Dammit

Sniped

Hahahahah

@aminliverpool Right, that's kind of what I was getting at with my last few comments

@Daminark bro analysis is infinity, how badass is that??

All first order logic is kind of finitary. So, ZFC, even with its plethora of infinite cardinalities, is still kind of finitary

Cantor set is awesome

But yeah you see my point, like until you prove that a given value system is objective, there's no validity to prioritizing any of them

Nothing is objective...

So just let people find intellectual fulfillment however they wish

Well in that case nothing is over or underrated

Nihilist...

Cantor set saddens me, so many things you want to be true just go merp thanks to its ilk

Analysis gives you counter intuitive results

algebra just tells you things you have no intuition about

I find that there's intuition there for algebra, much as it may not be pictorial

Different kinds of intuition, algebra's is more structural

Topology is the subject I find where the results are black magic

structural is a euphemism for symbolic

False

You can think about interactions between abstract objects

Without reducing them to symbols

That's what algebra is, it abstract the notion of symbolic manipulations in analysis and NT

The fact that, say, every group is a permutation group, that's a statement with content

You don't draw the group and tilt your head 90 degrees until it makes sense

But you have the notion that if we objects with sufficient... I dunno, operational symmetry, you could call it?

They can all act via permutations

Yes but what is a group but a certain kinda of symbolic manipulation?

@aminliverpool While you can recover some math for sure from infinity, the fact that you lose the existence of "the set of real numbers" seems like a legitimate problem to me

It's an abstract entity, it's a set with an operator that can be expressed symbolically but whose ontology isn't strictly confined to that of symbol calculation

In some sense, it's a model

The point of it, and a lot of constructions, is that you have objects that you construct out of a set and some rules, either some n-nary operation or a preferred subset of its power set and associated functions, or whatever

And the idea is that you're trying to find out what parts of things can be abstracted to other types of objects that share only a subset of characteristics

There's an element of the 'unreasonable effectiveness of math' here, though.

For instance, the SU(3) group might seem pretty esoteric and arbitrary.

And yet, our understanding of QCD is directly predicated on the relation between quarks and SU(3).

So SU(3) seems to be part of nature, so to speak, in a very operational way.

@Daminark seems reasonable...

$x^2-5y^2=44$

Anyone familiar with pell's equation

This forms the inspiration at least, and then later you realize that those objects of study become have content to look for

@Semi Is it quantum mechanics?

@aminliverpool not every Lebesgue measurable set is Borel

yeah.

Though QCD is a good deal harder and more recent than standard QM.

The proof I know of it is a cardinality argument, Borel sets have cardinality $\aleph_1$ (which you know because the hierarchy terminates in $\omega_1$ steps exactly), Lebesgue measurable sets have cardinality $\aleph_2$ since every subset of the Cantor set is measurable

(I should admit, though, that I'm stretching the evidence a bit. The flavor symmetry that the connection to SU(3) reflects is only an approximate symmetry.)

Wow such lies @Semi >:(

I'd say more but uh

I don't know QCD

I mean of course every mathematician can study only finite math

The point isn't whether it is necessary, but whether it is interesting

But, in favor of SU(3) being essential: The essence of what defines QCD is the QCD Lagrangian

I mean for sure there's some metaphysical sketchiness with infinite sets

and that's defined precisely with reference to the fundamental and adjoint representations of the SU(3) group.

So in that sense SU(3) really is built into QCD in a very strict way.

but, uh

But really, it's hard to talk about mathematical objects "existing" in the same sense, as say, you or I existing. Mathematical objects have sort of their own category in terms of existence

QCD is freaking weird.

They model physically existing things, sure, but still

@Daminark that's what I find fascinating about analysis, you got things that metaphysically don't make sense yet you can build some intuition about them

Lol @Semi I know one of my friends is taking a class called QFTCS, and I keep forgetting what the last two letters stand for (I'd guess curved spacetime?)

Said it's pretty witchcrafty

@Zee No I mean analysis is a beautiful subject, I have great respect for people who do that, as I do scientists, social scientists, philosophers, etc

My point was just that I see no good reason to elevate any of them over the others yet

@Daminark don't lump them with those people

It's really just a matter of personal taste. If half of all people want to learn spectral algebraic geometry, go ahead

Well I don't think anybody should stop anyone from studying anything

@aminliverpool one goal, sure, but to many, the subject is an end in itself

But don't mean they got my blessings

@aminliverpool math an illusion? You gotta stop smoking crack

No one is asking for anyone's blessings, we're just saying your claims of x being overrated are baseless and not taken seriously. Thus, the continued bashing is not really getting you any blessings either

You use some results and not others

There are mathematicians out there who very much want to be grounded in nature somehow

@Daminark well I do think it's overrated, at least in terms of output that benefits humanity or even math itself

There are other mathematicians who don't care

All mathematicians care about nature those who don't are acting, it's a defense mechanism

I don't believe that claim in the least

@Daminark let me ask you a question and you gotta answer honestly

I kinda went the opposite way, I was into physics and then switched to math because most of what I found cool about physics was the math side, and other elements in the subject didn't resonate well enough with me such that I felt I could pursue it well

@Daminark if you are the last human in humanity, and in 10 years the world will cease to exist, will you do math?

Sure, why not?

I would not

And I suppose that the crux of it all

Again, our ends are different

You just wanna play a game...

I respect that

Who said it's a game? You're learning true things

yo chat

Well in chess you learn true things as well...

@Daminark u can learn true things in a game

The context here is such that "game" is rather trivializing

No, that's your own bias

Well, what's your operating definition of "game" then?

Games can be very important to the player

Well if philosophers can't define game then I won't

Well in that case your claim that number theory is a game ceases to be even well-defined

Lol all language is ill defined

that's such a vague claim that it barely even makes sense

Now you gonna ask me to define language?

I mean, ill-defined in the sense of, it's not even clear to what your conversation partner what you even mean

@EricSilva that language is ill defined?

yes

@EricSilva define any word completely logically and I will kneel down and kiss your feet

there are like a million different ways you can mean that, some basically true and some basically false

wut

some ppl study math for $$$$

Rip mathjax @Eric

Like when many people say "X is just a game", they mean it in a rather trivializing sense

@Daminark you don't know what's a game? You used the word many times am sure

lol

@Daminark banach-mazur is just a game

totally worthless tbh

I tend to call a game a tree

trashhhhh

@Daminark Example?

Also what sort of things do you want to be true that are squashed by the Cantor set

@Akiva Poincare-Hopf is a theorem that felt a lot like black magic

that theorem is still black magic when you understand it tbh

not cause it's like esoteric but because it's just cool

The proof makes total sense when you see it, but like, when I take a step back and realize that you can draw triangles on something and then get a number which is associated with any vector field with isolated zeroes

That's just, for lack of a better term, trippy

@Daminark welcome 2 my life

@Daminark Oh yeah that one's cool

Even Hopf Degree theorem is pretty whoa

Like, compute numbers for two functions and boom, you can homotope them

For some reason I had thought you were talking about like point-set

Yeah, topology has a lot of really cool results

Just like, being able to make that kind of a conceptual jump is really nice

@Daminark I suppose you can replace game with entertainment in your case, you do math couse its fun

Oh, I mean I know little point-set topology

@Zee I mean, would you say enjoyment and entertainment are synonymous?

I had a professor who once said that if you're enjoying yourself doing math, the math you're doing isn't very interesting

Well nah scratch that

I was going down a sketchy direction

@Daminark anything done just for enjoyment is entertainment, I would say

@Eric Interesting to whom? Also who said that?

keerthi

@EricSilva very smart, who is it if you don't mind me asking?

Sniped

keerthi might've been quoting some bigshot

@Daminark i think here "interesting" meant "publishable"

I mean, I guess it depends on how you're deriving the enjoyment

@Zee idt it was particularly wise, just meant as a joke

@Daminark an important point is that enjoyment and fulfillment arent the same

I mean, I peg the latter as a subset of the former

nah

it like definitely isnt

No it makes sense, you can't really enjoy something too difficult, at least not direct type of enjoyment

you can be fulfilled by things that aren't enjoyable

And to publish something it has to be hard

@Zee not necessarily

I mean, the act itself might not be enjoyable, but the fulfillment will bring enjoyment

not necessarily

@EricSilva says you

i mean, lots of stuff gets published that isnt hard

Well ok, but we mean by good publications

And plus, many problems that are hard for being clever/tricky, like you're solving a puzzle, they can be very enjoyable, and then you have something publishable

@Daminark you can definitely have a fulfilling job that you dont derive enjoyment from

I don't quite buy that

@Daminark these tend to be rare in math from what I seen, puzzle things are popular so they get closed quickly

Again, maybe the actions you're taking aren't enjoyable in themselves

But I cannot think of something where you don't enjoy the fulfillment

@Daminark my dad says this of farm work

he hates doing it but he thinks it's his calling

@Zee There are always puzzle problems remaining out there, though many are gonna be rather tough to solve if they haven't been solved already

Almost any work that supports a family is gonna be fulfilling

@Daminark I actually like those problems but they seem to be rare...

Once you get kids, you stop being the main character of your life

Which sucks...

if you get kids

Ya but people without kids tend to be unhappy

In which case I dunno if it really sucks that you cease to be the main character :P

[citation needed]

@Zee that is like pure nonsense

And I'm not sure that's a uniform experience

i can find just as many studies supporting that as i can refuting it

it's like a claim that just can't be supported

@EricSilva it's the conventional wisdom, which is to say BS

ya

I agree, there isn't a scientific agreement on it

They don't enjoy... What?

Having kids

I was responding to Eric

their jobs?

Well that's not my point

My point is that the fulfillment is the generator of the enjoyment

So they might be all "UGH" during the job

ok this is a nonsense semantic game

But afterwards, when they see that they've done something right, THAT'S the enjoyment

seems reasonable

im skeptical

Like washing the dishes

satisfaction and enjoyment are also different things @Daminark

Ok what? Are you thinking of enjoyment in a hedonistic sense?

im using enjoyment to use what it usually means

i.e. to derive pleasure from something

I don't really think enjoyment and satisfaction are different

Different use but they seem to imply each other

ok it's a semantic game, you can disagree, language is flexible

The definition of pleasure, from Google just now, literally includes the word satisfaction

i strongly believe that there are no true synonyms