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14743454 No.14743454 [Reply] [Original]

How important is knowledge of mathematics?

>> No.14743515

Unless you're a physicist/mathematician/engineer anything above introductory college level (calculus series, linear algebra, diffEQ etc.) is pretty much useless

>> No.14743525

>>14743454
Logical mathematics is very interesting. Except for arithmetic, nothing else.

>> No.14743644

>>14743454
Absolutely critical if you want to study philosophy.

>>14743515
Nonsense.

>> No.14743653

pure mathematics is one of the most interesting subjects in the world and should be pursued for its own sake

>> No.14743681

knowledge of mathematics and the sciences is just as important to becoming a complete human as is knowledge of history, philosophy, and the arts

>> No.14743694

>>14743454
It is the metaphysics of STEM

>> No.14743705

>>14743653
>>14743681
>>14743644
>>14743525
>>14743454
nerds pls go

>> No.14743718

>>14743705
pseuds pls go

>> No.14743745

>>14743644
Can you please explain how it is critical to philosophy?

>> No.14743857

Basic knowledge of geometry is enough to prove the existence of souls. See Plato's Meno.

>> No.14744562

>>14743745
All of mathematics rests on a limited set of axioms. Every brick perched atop this towering edifice of human creation owes its stability to the irrefutable reasoning that preceded it.
At its base is only logic. No ill-defined terms and obscure arguments, but clearly defined objects and rigor have made math

>> No.14744613

>>14744562
Interesting. Would you suggest someone interested in formally studying philosophy to formally study math first/instead?

>> No.14744621

>>14743454
"Knowing mathematics" doesn't mean anything. You mean reading through that chart carefully? Not so important, if you're not a mathematician

>> No.14744640
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14744640

>>14744613
>Let no one ignorant of geometry enter here

>> No.14744675

>>14744562
Then you only need formal logic for philosophy, and most of math is useless for it

>> No.14744738

>>14744640
I know geometry though. I’m talking about studying mathematics as opposed to philosophy at an undergraduate level.

>> No.14744778

>>14743454
What a fucking shit list. Seriously. It STARTS at fucking ALGERBRA. Fucking idiots, you start at arithmetic. Read Quick Arithmetic by Carman and Introduction To Mathematics by Whitehead.

>> No.14744787

>>14744738
Well he said maths is built upon logic, which is the domain of philosophy...

>> No.14744791

>>14743454
Specifically what mathematical concepts?
At the very least I’d recommend that you pay close attention in mandatory mathematics courses relevant to your major, because most students that fail to follow along with earlier maths courses get utterly assfucked in the later ones. This is because many (if not all) mathematical subjects are closely related to one another. Kids who were let off easy in high school usually get off the worst.

>> No.14744792

>>14743454
>>14744778
Check out the book Men Of Mathematics by Bell, too. Also, yes, math is a versatile and useful tool. If you have any interest in
>Music
>Any science
>Any engineering
>Certain trades like Electioneering
>Business and Finance
>Or just want the greatest most efficient way to help train and grow your brain

>> No.14744794

Lol. Whoever made that chart is a fucking faggot. There's a reason this shit takes a degree, you need to study it extensively and complete problems to understand it. You can't just read a succession of books. Fucking retarded shit

>> No.14744804

>>14744792
>Electioneering
Meant Electricians. Also, check out the book Mathematics For The Non Mathematition and look at the Former Maths (not just Mathmatics) list on /sci/

>> No.14744806

>>14744794
That succession of books has exercises to study, moron.

>> No.14744810

>>14744794
I agree it's a shit list.
But tell me, where do you find a detailed explanation of how to solve these things offline without a teacher? You realize that most books have practice tests and questions, yes?

>> No.14744820

>>14744794
The same applies to philosophy, dumbshit.

>> No.14744826

>>14744738
Unless you are very interested in math, then I would say no. You don't need to understand upper level mathematics to be able to interpret important philosophical texts/thought. Although personally I would definitely recommend a double major in another subject (and math is a great supplement) if you plan to study philosophy at an undergraduate level, because the degree itself lacks recruitability potential (assuming you want a non-philosophy job).

>> No.14744833

>>14744810
Here is a complete mathematics education from Cambridge:

http://dec41.user.srcf.net/notes/

>> No.14744840

>>14744738
If you double major in mathematics and philosophy or linguistics and philosophy you can LARP as a neoanalytic reincarnation of Bertwig Russenstein

>> No.14744842

>>14744833
high quality post. any more links like this? I'm trying to teach myself maths since universities don't want me.

>> No.14744875

>>14744842
Edx
coursera
MIT ocw
khan academy

>> No.14744885

>>14744842
Here are some more from for Part II and Part III: https://tartarus.org/gareth/maths/notes/

>> No.14744909

>>14743454
>How important is knowledge of mathematics?
mathematics is 100% required in order to be able to think well and clearly

>> No.14744973

>>14743515
fpbp

>>14743644
this isn't true. certain analytic autists want to LARP as STEMfags but for the most part it's really not necessary.

>> No.14745020

>>14744875
>>14744885
thank you anon! you're a hero

>> No.14745036

>>14744909
mathematical thinking yes
mathematics and all it's autism not really

>> No.14745055

>>14744973
>>14745036
Brainlet cope.

>> No.14745069

>>14745036
if you don't actually study advanced mathematical concepts then you're not really getting much out of your mathematical thinking

>> No.14745098

>>14743454
That's entirely down to the analogical applications you find for it [topology, out of that list, in particular]

>> No.14745155

If you want to study Philosophy at the graduate level, the best possible undergraduate degree to get is either Mathematics or Physics.

https://www.philosophersmag.com/essays/131-want-to-be-good-at-philosophy-study-maths-and-science

>> No.14745292

>>14745036
>it’s
Never gonna make it

>> No.14745787

>>14743454
Maths is an extremely fun and satisfying subject, and I would advise anyone to give it a proper shot.

>> No.14746529

>>14745155
This makes sense to me because Math and Physics use a lot of logic and require a fairly high level of intelligence to comprehend but don’t you think what goes on in Mathematics and Physics departments either misses the point or goes way beyond it? I took a lot of Math in undergraduate and I don’t think it really helped with anything. Most of it was just rote memorization and systemized regurgitation of formulas. We didn’t really learn about the logic underlying the principles that we were using, but I didn’t focus on Math so I don’t know if that happens.

>> No.14746878

>>14744613
It'd be stupid not to. The laziness of post WW2 philosophers has made them incapable of recognizing obvious fallacies and the gave birth to post-modernism.
At least study a fundamental science.

>> No.14746883

>>14746529
You had shit teachers, you're not supposed to have to regurgitate or memorize formulas. You're supposed to use them as tools.

>> No.14746895

>>14746878
I agree and I kind of feel like what passes for philosophy in the academy today is kind of a joke. The only reason I’m interested in philosophy is because I have such a diverse range of interests and philosophy seems like the only field that allows you to take courses in mathematics and logic as well as Latin and Greek.

>> No.14746906

>>14746883
I went to one of those big state schools. It’s considered a high end institution but the curriculum is pretty much designed with corporate job training in mind across the board and I think that may have been the case in mathematics as well.

>> No.14746910

>>14745787
I flunked highschool maths and I've been out of school for ages, so I feel brain has atrophied to a certain extent. Do you think doing a university undergraduate course from scatch would be copable?

>> No.14747020

>>14746910
It depends on the course. I’m not sure you could start with undergraduate level Calculus if you flunked high school math, but most undergraduate Universities offer courses that basically start at high school level math so you could start there.

>> No.14747035

>>14744820
How many problem sets do I need to work out before I understand Hegel

>> No.14747108

>>14745155
Would you limit that statement to just Math and Physics as majors or do think programs like Engineering and Economics could also provide an adequate foundation of math and logic to approach graduate level philosophy?

>> No.14747292

>>14744613
I'd suggest at least knowing logic and proofs. I know many STEM students who can do 'advanced' math but couldn't prove the basic theorems that support it all

>> No.14747305

>>14743454
If this chart a good start if my knowledge of mathematics is at a high school level?

>> No.14747328

>>14743454
>How important is knowledge of mathematics?
It's crucial. Knowing the four basic operations has helped me a lot.

>> No.14747340

Post-structuralists dont need math

>> No.14747366

>>14747340
behold the eternal pomo homo

>> No.14747375

>>14747292
The reason I ask is because I’ve already graduated with an economics degree that I steered towards math and stats but I’ve discovered my single largest interest is greek philosophy and just greek and latin general to be honest. The problem is I don’t have the prerequisites to pursue this directly through the classics without starting over with a new degree so I was looking at philosophy and I don’t know if that even makes sense or if I’d be prepared.

>> No.14747624

>>14743454

I mean define important I guess
I'd say don't study mathematics unless you like it or need it for something specific it probably won't be helpful to you otherwise
I suppose it can help train you to think in a more logical way if you do it enough but you don't specifically need math for that and it's a whole lotta work just for that

>> No.14747986
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14747986

>>14743454

>> No.14748042

>>14747986
Today; some Ted respect was lost; on account of idiosyncratic style.

>> No.14748044

To the people saying to study Mathematics instead of Philosophy in undergraduate to study Philosophy in graduate, would you not be better off just studying Philosophy but loading up on Mathematics and Science electives?

>> No.14748292

>>14746910
I definitely doable if you put in the work. I'd suggest looking at some first year books, like real analysis and vectors or whatever. It'll give you a taste of what your getting into.

>> No.14748309

>>14748042
Ted came of age in a time of futurist triumphalism, and dropped out of society long before he'd ever have to wrap his head around "vaporware"

>> No.14748441

>>14743454
maths is important and fun af but this chart was made for pseuds. For anyone who wants to seriously/even recreationally get into maths I'd suggest at least getting some footing of introductory calculus and spending a few weeks playing with sequences and epsilons and deltas. From there, if questions of "space" interest you it could be worth to pick up a topology book, you can go deeper into analysis, or you can try out some algebra if you're more of a 'structural' thinker. Do this for a while and only then try to get your feet wet with some set theory/first order logic (just because these concepts are incredibly dry if you don't have at least one system tucked away in your head for which they correspond to).

>> No.14748450

Both are built on top of objective and absolue logic. While an incel philosopher might sperg out how logic is a subfield of philosophy or something of that sort, it's obvious that logic applies to everything no matter who/what/when or where. The only difference between the two is that mathematics has to be studied while philosophy doesn't. That is because maths has lots of concepts and conceptualisations of aspects of concepts which all have to be defined, explained and proved logically. This is not the case with philosophy due to the fact that, excluding religion, there are no unknown/abstract concepts to be defined, let alone proven. All the consequences of philosophical view stem from the core main concept, just as in mathematics everything is a consequence of axioms.

>> No.14748461

>>14748441
the chart literally puts an intro calculus book before anything more advanced and says the set theory book is optional so it literally says exactly what you just said

>> No.14748471

>>14748450
you are brain-damaged

>> No.14748511

>>14748461
eh ish,


learning 'basic mathematics' from Lang is kind of a meme more than anything else. I don't think anyone actually learns from Lang so much as they use him and other Bourbaki books as reference. "Basic Maths" I'm pretty sure Lang wrote for lols.

Stewart for calc may be the university standard but if you have a serious interest in math you'd be so much better off chewing on spivak for a year

Again, the set theory books won't be any fun till way after this, and too many people trying to get into maths have this mindset of "oh if I learn all the axioms then all of maths will grow from the seeds of this in my head quite naturally" when this is just not the case. Wait for at least a year or two before dipping into the Halmos

Axler for linear algebra is a good recc though

Dumit and Foote is the standard for algebra even if its a bit terse to self teach from

lol the Tao analysis books are ....cute, but they hold your hand a bit too much, I would honestly just use them in supplement with baby rudin (which is 100% what they're designed for anyway). Tao's later books are a bit more fun in my opinion (epsilon of room etc)

Munkres is another book that's more a reference than something you actively learn from. If you're interested in topology, work through the first few chapters of Rudin so you at least know how open sets behave and then play around with some of the earlier bits of Hatcher

don't know shit about number theory myself so can't comment on those

the differential geometry books look right enough but I'd add Spivak's calculus on smooth manifolds in there as well even if its typsetting is straight from the 70s

algebraic geometry looks good in that it has Hatcher

and if you can work your way to actually understanding algebraic geometry you don't need this list at all and can probably select the material that would be best for you on your own

>> No.14748533

important for a well-rounded education but you don't need to get much beyond undergrad level courses if you aren't a mathematician. Logic is way more important for a general scholar than pure math

>> No.14748599

What else should I major in? My school offers joint degrees and I'm torn between physics and biology. I want to write a scifi novel and I think a background in STEM would make it more convincing.

>> No.14748616

What do y'all think of biochem/physics with a minor in math for a well-rounded education in stem?

>> No.14748629
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14748629

>>14748599
>physics and biology
>scifi
>STEM
>>14748616
>biochem/physics
>stem
OH NO NO NO

>> No.14748661

>>14748629
I read on my own. I'm not going to pay a school a massive tuition to read through a syllabus that I'd do for free anyway.

>> No.14748684
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14748684

>>14748661
>studying retroactively refuted fields for free
OH NO NO NO NO

>> No.14748695

>>14748684
>retroactively refuted fields
You know this is too reductive. Newton's laws and evolutionary theory are going to be refuted?

>> No.14748702
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14748702

>>14748695
>are going to be
They already were, brother...

>> No.14748708

>>14748695
Newton's laws have already been refuted.

>> No.14748722

>>14748695
Newton refuted the great Copernicus. Einstein refuted Newton.

>> No.14748723

>>14748708
>>14748702
But they're still contextually applicable, you know what I mean. We still learn calculus in schools because it's applicable. I still don't understand your argument against stem.

>> No.14748726

>>14748661
Philosophy isn't any more reading-based than physics is.

>> No.14748732

>>14748726
that's not true

>> No.14748743

>>14748723
I'm not arguing against STEM. You just said something plainly false about Newtonian mechanics.

>>14748732
It is true. You would know that if you had studied either, as I have.

>> No.14748758

>>14748743
You've studied physics and philosophy? There's thousands of pages of philosophical thought and that's just the greeks. You can learn physics by skimming textbooks and practicing problem sets.

I was talking about this anon's problem with stem.>>14748684

>> No.14748771

>>14748758
>You've studied physics and philosophy?
Yes.

>There's thousands of pages of philosophical thought and that's just the greeks.
There are even more pages of scientific thought and that's just the Greeks. This may shock you, but you don't need to read the Greeks or indeed any dead historical figure in order to study philosophy. Philosophy is an activity, not a body of doctrine.

>> No.14748777

>>14748771
>>14748758
>I was talking about this anon's problem with stem.>>14748684
Oh, and ignore the guenonfag - he's a troll.

>> No.14748795

>>14748771
I'll take your word for it if you've actually studied both of them. What did you think of your education anon, was it worth it, do you think math would've been a better secondary subject? I'm considering what area of study I'd like to go into.

>>14748777
Why do guenonfags hate stem?

>> No.14748802
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14748802

>>14748795
>Why do guenonfags hate stem?
Because he retroactively refuted it. Just read any of his books.

>> No.14748805

>>14743694
Nice dude, I'm gonna steal that phrase for my physics students

>> No.14748813
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14748813

>>14748629
>>14748684
>>14748702
>>14748802
Holy based....

>> No.14748817

>>14748795
I'm happy with my undergrad education. I also took a lot of math classes. Math has greater overlap with Philosophy because they have a lot of courses in common. So Math+Philosophy is an easier double-major. It's down to personal taste.

>> No.14748824

>>14743694
>>14748805
Except metaphysics is actual the metaphysics of STEM.

>> No.14748835

>>14748802
How does this quote pertain to people that are isolated in labs pursuing knowledge that genuinely interests them? It seems like a criticism of intellectual defensiveness and posturing rather than experimentation.

>> No.14748840
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14748840

>>14748835
>pursuing knowledge that ""genuinely interests"" them

>> No.14748845

>>14748802
>Just read any of his books.
Based. Crisis of the modern world unironically made me get out of pursuing stem furhter. I just cannot support a machine so obviously destructive to everything that is good in this world.

>> No.14748847

>>14748840
This has always been the case, Guenon was led into his area of study in some way. Does this illusion make the interest feel less genuine? And does it matter at all if it's always been the case, this seems like an impossible ideal.

>> No.14748849
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14748849

>>14748835
>Just leave them alone! They are not hurting anyone! As long as there is consent its fine!

>> No.14748852

>>14748845
I study it out of a wish to understand a sliver of the natural world around me. Fuck working in the industry.

>> No.14748860

>>14748847
>Guenon was led into his area of study in some way
Guenon was not part of the masses though.
> Does this illusion make the interest feel less genuine?
You are just confirming his deep insights by putting your "feeling" above absolute metaphysical truth.
> this seems like an impossible ideal
Guenon is just pointing out your delusional nature. If you are capable of grasping his thought, you will just deny STEM willingly in the future. He is not promoting some "ideal" one needs to "strive" towards, he is just stating the truth.

>> No.14748868

>>14748860
I'm just confused as to how this criticism only applies to stem and not every academic path.

>> No.14748869

>>14748852
>understand a sliver of the natural world
Then consider reading >>14748702 where he refutes the very notion that current profane science can give you any real knowledge of the world.

>> No.14748872

>>14748868
>not every academic pat
It does, actually, but some paths are still reconcilable to tradition and one does not forfeit his soul by pursuing them (unlike with STEM).

>> No.14748874

>>14748869
I study it because the systems are beautiful. If you pursue any subject for "real" knowledge then you're misunderstanding the nature of knowledge.

>> No.14748881

>>14748872
The greeks studied physics and math. How's that not an ancient tradition?

>> No.14748907

>>14748874
>If you pursue any subject for "real" knowledge
Guenon retroactively refutes your profane misunderstanding of the true nature of knowledge.

>>14748881
Guenon retroactively refutes the notion that ancient sacred/traditional mathematics and physics are the same as the ones studied today by the moderns. In fact, what is today called "physics" is a deep and childish misunderstanding of what the Greeks actually studied. Read any of the following - "Introduction to the Study of Hindu Doctrines", "The Crisis of the Modern World", "East & West", "The Reign of Quantity and the Signs of the Times".

>> No.14748916

>>14748907
mathēmatikoi>akousmatikoi(Guenon)

What's real knowledge then?

>> No.14748918
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14748918

>>14748874
>I study it because the systems are beautiful.
There is no beauty to be find in something that actively denies the very basis for and the existence of beauty. If you want beauty, study theology.

>> No.14748925

>>14748918
But God created the heavens and the earth. You're telling me God's creations aren't beautiful?

>> No.14748927
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14748927

>>14748916
>What's real knowledge then?
Read "The Multiple States of the Being" to find out. Just follow this chart, brother.

>> No.14748935

>>14748927
who should I read before guenon?

>> No.14748940
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14748940

>>14748925
The heavens and the earth have inherent sacred qualities which modern 'systems' outright ignore by reducing them to mere 'pure quantity'. If that's not a perversion of beauty, I don't know what is...

>> No.14748957

>>14748935
Nobody. His first book is perfectly sufficient to understand his thought on its own and it's very clearly written. If you know something about the Greeks and Western Medieval Philosophy (early Scholasticism), he is going to be easier to follow, because he makes references to them to make his work easier to understand for the Westerner.

>> No.14748958

>>14748940
>modern 'systems' outright ignore by reducing them to mere 'pure quantity'
Do they ignore these qualities? Do you have any argument to prove that something's intrinsic parts aren't beautiful? Are the petals of lily not also beautiful?

>> No.14748964

>>14748958
>petals of lily
There is actually no such thing, there's not even such a thing as a lily. You're not thinking scientifically enough, we need to go further and consider 'quarks' and 'dark-matter' and other made-up buzzwords.

>> No.14748969

>>14748958
>Do they ignore these qualities?
Yes, brother. Read Guenon (pbuh) where he refutes them for ignoring quality.

>> No.14748970

>>14748964
That's like arguing that a microscopic angel isn't beautiful because we can't see it. You're catering to sense perception.

>> No.14748981

>>14743644
checked but you have to back in the locker

>> No.14748989

>>14748970
The argument is that that lilies have a deeper sacred meaning embedded into them by God, which STEM denies by reducing lilies to a collection of made-up garbage like 'quarks'. True beauty is then only 'study-able' insofar as one recognizes this and tries to uncover these sacred mysteries. If you think reductionist 'quarks' themselves are beautiful, you have been damaged by modernity into believing in an inversion of beauty.

>> No.14748997

>>14746878
this is too wrong and retarded. math people don’t have any advantages when they enter philosophy. they aren’t even comparable. i haven’t even heard your philosophy but i already know it’s going to be retarded based off what you said so far.

>> No.14749013

>>14748989
Beauty is also conceptional, we wouldn't have literature otherwise. To expand, or reduce to a micro/macro scale is a mysterious conception, a beauty beyond the simple kind of intuitive materialism.

>> No.14749018

>>14748997
Nonsense.

>> No.14749020

>>14749013
>Beauty is also conceptional
>To expand, or reduce to a micro/macro scale is a mysterious conception
I don't know what makes you think I deny this. I just recognize that this specific kind of materialistic reduction into meaningless made-up pure quantity is inherently ugly and not deserving of worship.

>> No.14749033

>>14748042
How is he wrong?

>> No.14749036

>>14749020
But this pure-quantity is the only way we can observe this micro-scale. That's why I don't think you believe this, you're hung up on the trees while missing the forest.

>> No.14749042

>>14749036
>micro-scale
This is a meaningless and retroactively refuted notion. If you think reducing everything to 'quarks' isn't ugly and punishable by death, then you have been deluded.

>> No.14749049
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14749049

>>14748802
>>14748813
>>14748840
>>14748927
>Guenon
Based.

>>14749036
>pure-quantity
OH NO NO NO NO

>> No.14749052

>>14749042
>>To expand, or reduce to a micro/macro scale is a mysterious conception
>I don't know what makes you think I deny this.
Yet you agreed with me here

>> No.14749061

>>14749036
>observe this micro-scale
why would one ever want to? every good ancient philosophy admired beauty and denied modern physics.
>>14749052
>not denying studying a thing's parts means not denying my specific modernistic reductionist notion of parts
brainlet detected.

>> No.14749070

>>14749052
You need to reread that post if you think anything in it support the need to affirm even the existence of 'quarks', let alone the supposed 'value' in studying lilies by employing them.

>> No.14749079

>>14749061
>>14749070
We don't have the tools to study the micro-universe, we can only observe what we observe. You're asking people to study math without numbers.

>> No.14749081
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14749081

>>14743454
>How important is knowledge of mathematics?
Very important.

>> No.14749086
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14749086

>>14749079
>We don't have the tools to study the micro-universe, we can only observe what we observe. You're asking people to study math without numbers.

>> No.14749094
File: 89 KB, 805x851, 15713074256040.png [View same] [iqdb] [saucenao] [google] [report]
14749094

>modern physics

>> No.14749096

>>14749086
when you don't have an argument empty your pockets of memes.

>> No.14749097

>>14744613
Plato in the Republic states that one who wishes to be a philosopher must first be trained as a mathematician.

>> No.14749107

>>14749097
Based. Most of modern philosophy would not exist if this was a hard requirement for being considered a philosopher.

>> No.14749123

>>14748599
Unless you are absolutely wedded to going to medical school, pa school, graduate school of some sort then I physics would be at least marginally better than biology. The plus is that you have a lot of graduate options open to you but the downside is that biology is almost completely useless at just an undergraduate level.

>> No.14749139

>>14748845
So what did you do instead?

>> No.14749149

>>14749107
Most real philosophers alive today have a mathematics background.

>> No.14749165

>>14749149
>philosopher"s"
There is at most one real philosopher alive at any given time in modernity. Guenon's successor should make himself known anytime now.

>> No.14749197

>>14748835
somebody pays for the labs and cuts their paycheck and they have an agenda. these people don't exist in some sacred vacuum.

>> No.14749212

>>14749097
>>14749107

A valid point, the principles in mathematical logic embody the same rationality needed for an endeavour like philosophy, except I presume the mathematics of the Greeks would be lower in complexity than modern high school mathematics.

So I cannot even begin to understand why the consensus of this thread has been to suggest to those who wish to study philosophy that they need to bore through (if they don't find mathematics intuitively enjoyable that is) the complexity of university level mathematics which I assume embodies the same unchanging principles as any other level of complexity beneath it but its realistic application in every-day problem solving and rationality likely grows more and more tenuous

>> No.14749236

>>14749097
What does that mean though? I’m suspicious that what Plato meant by Mathematics and what is being taught in undergraduate Mathematics departments aren’t the same thing.

>> No.14749245

>>14749149
Like who?

>> No.14749259

>>14749212
Exactly. I fail to see how what you would study in your senior year as an undergraduate in Mathematics has anything to do with what Plato was talking about.

>> No.14749323

>>14749212
>realistic application
>every-day problem solving
>rationality
Not maths.
>>>/g/
>>>/sci/

>> No.14749340

>>14743454
Mathematics beyond an elementary level is only really useful for teaching/learning problem solving skills.

>> No.14749551

>>14749323
So does university level maths go so far from its original aims and established foundations that it becomes some sort of abstract intellectual masturbation almost entirely divorced from reality?

Also how can maths become non-rational at any point when surely that is its central essence,the equivalent to what your essaying is like claiming that black can lose its darkness

>> No.14749585
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14749585

>>14749551
>original aims and established foundations
Those would be sacred and metaphysical in nature, nothing like the modernist Anglo-bugman notion of maths which you seem to take.
>almost entirely divorced from reality
Only if you take the "only the material world is real" Anglo hylic bugman materialist viewpoint as a doctrine.
>Also how can maths become non-rational at any point
Only if you take the rational-irrational Anglo hylic bugman materialist dichotomy as a doctrine.
Maths is supra-rational in its nature, with rationality constituting a part of how the argumentation is laid out.

>> No.14749593

>>14749551
>becomes some sort of abstract intellectual masturbation almost entirely divorced from reality
And philosophy doesn't do this?

>> No.14749605

>>14749585
You're conflating applied mathematics with modern math. There's plenty of blue sky study still done in the subject, albeit mostly computationally.

>> No.14749621

>>14749593
Of course, but not to the degree of mathematics, which seems to entirely lose itself in its fiction

Philosophy at least retains some connection and significance to its principle subject - be it the nature of knowledge, reality etc - no matter how convoluted it becomes

>> No.14749634

>>14749605
>applied mathematics
That is not maths though, any "application" of maths would properly place the activity into the field of application itself.

>> No.14749639

>>14749605
>You're conflating applied mathematics with modern math.
No, I am actually refuting ''applied mathematics'' and denying their often-implied equivalence to sacred maths by moderns such as yourself.

>> No.14749647

>>14749621
>at least retains some connection and significance to its principle subject
Tell me what the "principle subject" of mathematics is?

>> No.14749656

>>14749585
You claim maths is supra-rational, does that phrase actually mean anything? What exactly do you claim can exist above rationality?

Likewise what reality do you say exists above the material world? Or is this just the typical indefinable mysticist jargon used to express that something exists beyond our minds (although what that is is neither defined or its nature alluded to )


Also by original aims I was more referring to measurement of geometry, logistics, area, the likes used by the contemporaries of Plato in architecture and measurement

>> No.14749663

>>14749656
>measurement of geometry, logistics, area
Those are Anglo bugman misunderstandings of the true sacred nature of Platoistic/Plotinistic mathematics.

>> No.14749664

>>14749639
Most "moderns" that actually study math realize that there is a vast difference between the two and don't overgeneralize the entire subject.

>>14749634
Obviously, that's my point.

>>14749621
Math is all derivation, there's a literal connection to a principle.

>> No.14749665

>>14749647
reality

>> No.14749671

>>14749656
>does that phrase actually mean anything
Yes, read Guenon (pbuh) where he retroactively destroys your modernist delusions.

>> No.14749672

>>14743454
thats such a fucking bad list jesus. it's like the famous "start with the greeks" one. it's so needlessly long and redundant just for the sake of sounding smart. just start with morris kline's
>mathematics for the non-mathematician
before reading his
>Calculus: An Intuitive Approach

That's all you need before you are better than 99% of the first world population at maths. Don't fucking fall for that meme list

>> No.14749680
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14749680

>>14749656
>What exactly do you claim can exist above rationality?
>Likewise what reality do you say exists above the material world?

>> No.14749685
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14749685

>>14749656
>You claim maths is supra-rational, does that phrase actually mean anything? What exactly do you claim can exist above rationality?
>Likewise what reality do you say exists above the material world? Or is this just the typical indefinable mysticist jargon used to express that something exists beyond our minds (although what that is is neither defined or its nature alluded to )

>> No.14749706
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14749706

>>14749685
>>14749680
wow sure showed me,

I'm having an intellectual crisis mortyyy, my very believe in the fundamental characteristics of reality is forever altered by your sagacious reasoning

>> No.14749709
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14749709

>>14749656
>What exactly do you claim can exist above rationality?
>Likewise what reality do you say exists above the material world?
God.

>> No.14749716
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14749716

>>14749706
>wow sure showed me,
>I'm having an intellectual crisis mortyyy, my very believe in the fundamental characteristics of reality is forever altered by your sagacious reasoning

>> No.14749724

>>14749664
Of course, I'm not saying that maths every fully severs itself from reality, although as I was saying with the french fag doesn't the connection become so tenuous at some point of academic complexity that any remaining connection to the principle subject (reality) is negligible?

>> No.14749725

>>14749709
>>14749685
>>14749680
>>14749706
Jesus, you'd think people that at least pretend to read philosophy would be able to argue.

>> No.14749727

That’s it lads, despite being incredibly slow (overanalyzing) at it, I’m going to get into maths once and for all

>> No.14749737

>>14749724
>principle subject (reality)
It never had a connection to the purely materialistic notion of reality the bugmen here try to impose on it, so your understanding of the issue is flawed from the get-go.

>> No.14749750

>>14749727
>slow
True math is not "temporal", so you cannot be "slow" at it. Also, I can guarantee you have not done true math yet, so you cannot know if you are any good at it.

>> No.14749753

>>14749725
Yeah sadly the primary rebuttal of any atheism or anything resembling an emphasis on rationality or materialism is often some obnoxious straw man centred around some kind of modern hedonist degeneracy or some veiled criticism or caricature without any real significance or value to any kind of debate

>> No.14749758
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14749758

>>14749725
>Jesus

>> No.14749764
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14749764

>>14749753
>he expects to "debate" on 4channel instead of picking up a book by an author like Guenon who completely demolishes his materialist world view

>> No.14749769

>>14749737
But how could it not have a connection to materialist reality? The birth of mathematics came out of necessity, out of the need for geometric measurement in architecture or of logistical management for city states or royal households

>> No.14749770

>>14749725
>Jesus, you'd think people that at least pretend to read philosophy would be able to argue.
That is so epic and edgy, anon. Show these retarded Christcucks by using God's name in vain!

>> No.14749777

>>14749769
>The birth of mathematics came out of necessity
>out of the need for geometric measurement in architecture or of logistical management for city states or royal households
This is merely a retarded reductionist modern materialistic account of it. It's fine if you want to hold that as a personal doctrine though, I live in an accepting Anglo country.

>> No.14749788
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14749788

>>14749139
Became a carpenter who studies theology and philosophy in his spare time.

>> No.14749794

>>14749777
Okay frog man, why don't you offer up your alternative to the "retarded reductionist modern materialistic account" of mathematics

And please for the love of god write it in a precise way that actually makes sense instead of hiding behind obscurity and ambiguity

>> No.14749808
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14749808

>>14749794
>why don't you offer up your alternative to the "retarded reductionist modern materialistic account" of mathematics
Simply read René Guénon .

>> No.14749820

>>14749750
STANDARDIZED TESTS THOUGH

>> No.14749821

>>14749808
I'd rather piss in my own mouth you fucking cowardly contemptible French frog-eating cannibal

>> No.14749827
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14749827

>>14749821
>I'd rather piss in my own mouth
Oh, that I do not doubt, my hylic Anglo friend...

>> No.14750326

>>14749788
I sort of wish I could do something like that. I wouldn’t be able to afford my student loans though and apprenticeships are hard to come by where I live.

>> No.14751652

What degree is the most intellectually liberating?

>> No.14752295

>>14751652
Aside from the craft your own degree programs that are available at some Universities and which are of no practical use to anyone besides military and business executives, I think it’s probably Philosophy. At my University, it’s the only degree program that lets you incorporate courses from any variety of disciplines as part of your degree focus and the only humanities discipline which you could predictably claim that your peers and lecturers will meet at least a minimum intelligence threshold. That is, unless you have a particular proclivity for another field that would really compel you to plunge yourself into the material.

>> No.14752362

>>14751652
>>14752295
I feel compelled to add to this that, as an insider, I still retain a generally pessimistic view of the trends occurring within graduate departments and academia. I don’t see any interesting research being done in my department, which known for being continental and is a fairly prestigious research University. In fact, there’s been a significant push towards the “intersectional” topics in the milieu of gender and race theory to a significant degree precisely because that’s where the money is made today. I’ve gotten push back from anons for saying that before, but it is true. So, I think undergraduate and even graduate level education in philosophy is probably intellectually liberating more so than other fields (I didn’t study philosophy), but I’m still suspicious. I think undergraduate is less subject to it.

>> No.14752668

>>14747986
based

>> No.14752679

>>14748935
what's great about Guenon is you can start with Guenon. if you're coming from /pol/ then maybe Evola is a better starting point

>> No.14753440

I’m an Economics refugee and I’m considering Mathematics and Philosophy. Convince me which one I should go with.

>> No.14753445

>>14753440
By refugee I mean I already have a degree in Economics with little to no formal coursework in Mathematics or Philosophy, just self study.

>> No.14753544

>>14744810
why is it a shit list?

>> No.14754037

>>14752362
What program did you take?

>> No.14754067

>>14744562
>All of mathematics rests on a limited set of axioms.
Not quite, most of the mathematics most contemporary mathematicians can be encapsulated in a theory that rests on a limited number of axioms + one axiom scheme (that is technically an infinity of axioms but can be written rather concisely in a single principle).

However almost none of them uses that theory, and the theory itself is not quite fully understood (we don't even have a model for this theory, we cannot prove it is not self-contradictory).

Then you have the minority of mathematicians who work on a astonishing variety of alternative logical systems. They're rather overshadowed by the majority, but some of them do profound work, and they're growing more relevan year after year. It's not only alternative axioms, but even alternative systems of reasoning, with different deduction laws.

Then you have the bedazzlingly wide space of possible axioms systems that haven't been explored yet. All of them are also part of mathematics. The mathematical meta-universe is vast beyond description.

>> No.14754077

>>14744675
If you want to be able to talk about intuition (which is essential for practical knowledge) you'll make use of mathematics beyond formal logic. There's a reason Kant so crucially rested on geometry in his Critique of Pure Reason.

>> No.14754175

>>14747340
There has been some measure of mathematical LARPing among post-stucturalists, see Lacan, Deleuze and especially Badiou.

>> No.14754191

>>14744778
I didn’t learn Arithmetic until Calc 2. This isn’t the 19th century, bud.

>> No.14754237

>>14747986
>>14748042
>>14749033
Ask anyone who's ever worked with proof-assisting software or anyone who works in an algorithmic-dependent fields that also relies on advanced mathematics (like operational research), and they'll tell you how hard it is to actually computerize maths.
I don't know when Ted wrote this letter, but this was probably already decades ago, and we've already automated many things without significantly making mathematicians less relevant. If anything that's the opposite.

>>14748511
I second this. Lang is not for beginners, his books are more for reference, like dictionaries.
I especially agree with the argument against the "foundationalist" approach to math. Actual mathematicians start from intuitions and simple theories that evolve into more complex theories. All-encompassing logical systems are interesting but besides a few basic operations they should be learned late and almost as a additional field.

>> No.14754299 [DELETED] 

>>14743454
https://discord.gg/KVJuYcv

>> No.14754463

i studied mathematics and philosophy in college, and my very trite advice is to pursue mathematics if the subject fascinates you. i don’t think that there is much benefit to learning commutative algebra or whatever if math makes you want to die. that said, reading up on basic math is in general beneficial just because it gives your brain a good workout if nothing else. imo math and humanities are complementary – without philosophy it is easy to fall into “ontology where? there is no ontology to analysis, this is true because it is true because it is true because it—” and so now i approach research with a flexibility/open-mindedness wrt methodology that i doubt i would have been able to cultivate studying math alone. disclaimer out of the way, my background is in differential geometry and probability. i am primarily interested in geometric flow in riemannian manifolds, and “stochastic processes general.” i’ve taken a decent amount of analytic number theory and algebraic topology, though, and also covered the requisite analysis bases. provided you want to move forward studying mathematics, i have a lot of suggestions about this chart, which i'm putting in a separate post because there's too much fucking autism in it for the character limit.

>> No.14754477

autistic follow up to >>14754463

my first suggestion is to include mathematical histories and philosophies in your reading list, with a general history of mathematics as a primer. context and concepts are really important, if your intent is to use mathematical knowledge to grapple with more philosophical questions. boyer’s history of mathematics is a classic. as you are introduced to more mathematical concepts, read their histories too. i won’t recommend one for every single topic you may encounter, but you can check stackexchange/mathoverflow etc for reviews on the content. knowing the why behind all of these different fields helps reinforce your footing.

second, in analysis there are no rudin books. there is a family of books, lovingly termed “baby rudin” “papa rudin” and “grandpa rudin” and baby rudin is the standard for analysis intro. please, read/work through baby rudin or none of this other shit will make any sense to you. you’re going to need some background on measures and sets and the like if you want to get into all of the other books on this list. you’ll get a much better learning experience from those than the other books suggested for analysis.

third, for number theory i’d recommend you read stein’s elementary number theory for the basics and then dig into hardy and wright because hardy and wright move pretty quickly and go quite far. if you need a different pace, stein first, then hardy. (h&w are excellent, by the way, just a little quick for self-studying)

fourth, for differential geometry, you go straight from carmo to riemannian topics…i think including spivak’s 5 book comprehensive introduction to differential geometry would be a good choice here. i’d also suggest an introduction to manifolds and differential geometry by loring tu after carmo because those are pretty approachable. guillemin and pollack’s differential topology is also approachable.

sixth, if you’re going to get into commutative algebra and algebraic geometry, hartshorne is great but i’m going to go ahead and echo >>14748511 here and say that if you’re a commutative algebraist or an algebraic geometer you probably do not need a chart.

this last thing is going to be controversial but i found that studying probability really helped me develop my mathematical thought or whatever, and for probability i recommend ross’ first course in probability, tijms’ understanding probability, kolmogorov’s probability theory, jaynes’ logic of science, and finally durrett’s probability, and if you can finish durrett you can go wherever you want. probability theory is a lot like analysis but with new and fun terminology and a bit of a spin on how things are done. also, the whole like epistemology behind bayesian vs frequentist methodology is really cool and i recommend digging into reading on that but won’t put a bunch of suggestions in here because my post has enough autism in it.

>> No.14754866

>>14749097
Math in Plato's time consisted of basic arithmetic, geometry and logic.

>> No.14755311

>>14754866
Exactly what I was thinking. Sure, I can see some argument for pure Math, but you’d probably get even closer to the Mathematics that Plato was talking about in Engineering or something than you would in pure Math and even you’d being going way beyond the thing.

>> No.14755431

>>14754463
>>14754477
Thanks, a shekel has been deposited for your effortposting.

Am I naive if I want to approach mathematics (for the most part) strictly historically? My plan was to grind basic bitch high school / pre-college math on my own, get up to first-year college level so I'm at least familiar with the terrain and my mind can think mathematically, but then read through stuff like Morris Kline's 700pg history of mathematics, in particular to understand the emergence of modern mathematics from the early modern period. Once I hit the Enlightenment, from what I can tell, it's going to get a lot more difficult, but I figure I can tough it out. I doubt I'll ever be an expert on fluxons or quaternions, but I really want to understand the emergence of major mathematical concepts like the number line, the different classes of numbers, differential and integral calculus etc., as they emerged concretely as real answers to real problems. Luckily I already have an OK backing in early modern metaphysics so I am hoping this will scaffold me.

My ultimate goal is to be able to study the developments in the epistemology of logic and mathematics (tacit or explicit) in the 19th century, leading up to the crisis of mathematical foundations. But I'm somewhat doubtful that I'll be able to do any of this, since frankly I just don't like math. I gave up on math in the first place in my teens because everything seemed arbitrary and I could not fucking handle being told "THE NUMBER LINE IS WHAT IT IS, NOW DO WHAT THE THING DOES WHAT IT IS WHEN YOU SEE WHAT IT DO" without having it explained whether the number line is some kind of ontological axiom of numbers or a heuristic or what. My slippery method of getting around this problem is to learn it historically, more as metaphysics than as an arbitrary language full of unreconciled and unexplained conventions, but I wonder if that will even be enough.

Also, the idea of learning probability and related things makes me want to kill myself. I know people who "think quantitatively" and they disgust me. Some primal part of me fears becoming them if I start giving a fuck about graphs and distributions.

I think I may just be fucked for learning math. I hate practical applications, I hate puzzles for puzzles' sake, I hate arbitrary rules, I can't visualize worth shit so not only is geometry difficult for me, I also have trouble picturing and manipulating whole equations while manipulating their variables and I suck balls at mental arithmetic.

>> No.14755442

>>14755431
fluxions* my bad

>> No.14755546

>>14755431
thanks for the shekel anon, i cannot wait to spend it. to your question: no, that's not naive. approach math metaphysically all you'd like. i do recommend walking through basic bitch math but it's extremely goofy to go ass deep into differential geometry and algebraic geometry etc etc if you 1.) do not like math and 2.) only want to understand it historically, philosophically, and conceptually. asking "okay but why?" and trying to squeeze out some kind of fundamental ontology from a mathematician most often leads to a brick wall because there's no acknowledgement of the why behind the what is - a little recognition wouldn't kill anybody. no argument regarding people who "think quantitatively" and pride themselves on that because they are usually terribly rigid and unfun, though you don't seem like you'd be particularly susceptible to their flavor of nonsense because it rests so heavily on being "non-normative." (ha ha ha ha ha) it sounds like you'd be able to stomach mathematical histories just fine but i'd advise staying away from springer GTM texts considering your math allergy. your perspective is valuable so do keep questioning why the number line is what it is now do what the thing does when it is when you see what it do

i'm going to dig around for a couple of books that i can suggest to approximate math-as-metaphysics via mathematical histories

>> No.14755578

>>14754477
also i just realized i skipped from fourth to sixth so here's some great evidence that doing too much masturbatory idiot math is detrimental to useful skills, like counting

>> No.14755634

>>14755578

Oh man, I noticed that but thought you were making an ontological joke...

My Autism Rules!

>> No.14755641

>>14755634
i'm going to need you to unread my correction so i can take credit still, thanks

>> No.14755676
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14755676

>>14755431
>Once I hit the Enlightenment, from what I can tell, it's going to get a lot more difficult
Everything is pretty straightforward until around the early 1800s, with the emergence of abstract algebra. Thus begins a transitional period of abstraction without rigor, until the 1880s with the emergence of analytic philosophy and mathematical maturity.

>> No.14755886
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14755886

>>14743454
I remember Kaczynski writing in a letter that certain courses in Mathematics are useful for thinking clearly. He recommended a number of subjects worth studying. Other than that, mathematics is just a game or else a way to make a career or to advance technology.

>> No.14755893

>>14743454
As a mathlet I must sadly state that it is extremity important

>> No.14756038

>>14755311
I think it's better to keep in mind his intent with math, which was for better understanding. Those schools just so happened to be the first steps to be taken.

>> No.14756661

>>14755886
>I remember Kaczynski writing in a letter
In other words: you're a moron.

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