/lit/ - Literature

[Anonymous No.10796651]

tired of being a math brainlet so im reading euclid's elements. where do i go from here?

[Anonymous No.10796655]

that's now how u learn math u useless neet

[Anonymous No.10796657]

[Anonymous No.10796660]

>>10796651
Are you trying to learn math the same way you learn about humanities?

This is really funny.

[Anonymous No.10796678]

>>10796651
who's Euclid?

[Anonymous No.10796680]

>>10796660
>>10796651
yeah cmon OP, you gotta take courses

[Anonymous No.10796686]

>>10796660
i know this is 4chan so you're dying to be a smug cunt without reason, but have you considered that i wanted to start with Euclid because reading him offers me the ability to hone my basic geometry skills while also giving me insight into his influence on western culture? it's almost like this course offers several dimensions of enjoyment for me and i'm not trying to learn math the fastest and most efficient way possible. did you consider any of this? no, of course not, you were just eager to post a reaction image.

[Anonymous No.10796687]

>>10796655
>>10796660
Don't bully OP. Euclid is fun and holds up well, it's a good way to get into math. Even though his system differs in its axioms from modern mathematics, all his theorems are still true in analytic plane geometry.

[Anonymous No.10796713]

>>10796686
you still need to follow an online course and do exercises or you won't get it mate. Maths is different from lit, you need to engage with it much like engineering or science or you'll be incompetent

[Anonymous No.10796725]

>>10796713
i intend to do exercises alongside whatever i'm reading, but I wanted to keep this thread /lit/ and strictly about books. i find the history of math interesting as well as math itself.

[Anonymous No.10796921]

>>10796713
>online course
That is useless. You can't learn proper math on your own because there will be no one to push you to do what needs to be done. When I started I too had this conception that studying math was this difficult process to enlightenment, but actually it's more dull than that. Even if you understand something, you still have to memorize things and review them and do the exercises on your own. In my first year Real Analysis course I had to learn the proofs for about 50 theorems for the exam and I'd find out over and over again how there was something that I really didn't understand and I had to return to the chapter and start over again. You can read something like Rudin on your own but you'll never find the motivation to study it as a math major does.

OP, I say stick to historical books and maybe some high-school calculus and algebra if you don't know that. Try out 'What is Mathematics' by Courant and Robbins. If you really want to know some actual math, focus on just one subject and study it for a few years. I recommend Logic/ Set Theory.

[Anonymous No.10797620]

>>10796651
Don't expect to learn too much math. All you'll get from it in terms of knowledge is some theorems, but you will be exposed to lots of logical reasoning, which will thereby enhance your reasoning skills (and your ability to do math as a result).

Pick up a high school textbook or something after that

[Anonymous No.10797638]

The other posters are right that you're not going to learn much modern mathematics from Euclid, it's still a fun read though and does get you into the mathematical way of thinking. What you should do OP is get a discrete mathematics book, something that covers basic set theory, some number theory, proof techniques, etc. Once you have that down you really branch out into analysis, algebra, etc.

>>10796687
This.

[Anonymous No.10797651]

>>10797620
This is true
>>10796921
This is ultimately the case
>>10796660
>hasn't read Nicomachus, Euclid, or any noteworthy mathematician

Lel. The moral of the story is, plebes, that not only should OP learn Euclid, he could go many places from there. OP if you like Books V or VII, then I recommend Nicomachus. If you liked Books I and II, Apollonius is your guy. If you liked the last books dealing with three-dimensional objects the best (Bks. 11 - 13), then go with Archimedes.

Nothing like testing your wits against the best mathematicians in the game. Many modern mathematicians could not read Euclid's entire book well. In fact, I do not even believe I, myself, have grasped the entire book the way it was supposed to be grasped, but I do understand the fundamental importance of the entire thing, and then centrality of it all (how it comes together at the end).

[Anonymous No.10797666]

>>10797651
>>10797651
>In fact, I do not even believe I, myself, have grasped the entire book the way it was supposed to be grasped, but I do understand the fundamental importance of the entire thing, and then centrality of it all (how it comes together at the end).
Same here. The only Books I truly grasped were Books I-VI. I couldn't follow it after that

[Anonymous No.10797687]

>>10796651
Euclid -> Apollonius -> Archimedes

[Anonymous No.10799003]

>>10796651
>math brainlet
>starts with the Greeks who didnt believe in zero
LMAO

[Anonymous No.10799802]

>>10797666
Book V was literally just arithmetic.

[Anonymous No.10799843]

>>10799003
this
initiate with the indians

[Anonymous No.10801263]

>>10796651

[Anonymous No.10801272]

>>10801263

[Anonymous No.10801359]

>>10799802
I know mate. I read it. You must've thought VI meant 4

[Anonymous No.10801373]

>>10801359
holy shit there are pseuds on /lit/ don't know how roman numerals work? sad!

[Anonymous No.10801387]

post me a chart for probability bros, some shit that will start me off basic bayes shitand take up to and beyond some markov shit

[Anonymous No.10801405]

>>10801359
>>10801373
Yes, I misread his post.

But still, Book VII is just arithmetic also...

[Anonymous No.10801414]

>>10797687
Archimedes is obviously the most complex of the three.

However Apollonius gets up there. Meh. I've read all three. They are all radically different and focus on extremely different areas of mathematics, as different minds are wont to do.

Reading their influential, fundamental primary texts is absolutely fascinating. The principle of exhaustion, how Pi was derived, was a very entertaining thing to see demonstrated.

[Anonymous No.10801581]

this is a good thread

[Anonymous No.10801636]

>>10801581
Mods, sticky this thread

[Anonymous No.10801676]

>>10801263
>>10801272

I have been looking for something like these for a while, I dont know why no one would ever post them. Thanks, if you have any others it would be appreciated

[Anonymous No.10801736]

for geometry, Hilbert and Efimov
for Calculus:
if you're a brainlet, Stewart
less brainlet, Spivak
less brainlet, Terry Tao
even less brainlet, Rudin

then Papa Rudin

for Algebra, Artin (after Rudin), although I don't know a lot of Algebra, go ask /sci/


then the Odyssey

[Anonymous No.10801739]

Start with the Greeks

[Anonymous No.10801757]

>>10801739
Absolutely HOWLING at humanities students learning mathematics in chronological order.

It's kinda cute, but it also shows why STEMfags think you can just learn the latest philosophy since anything earlier would obviously be incorrect and not worth learning.

[Anonymous No.10801968]

>>10801676
those are /sci/ meme bait lists don't bother

[Anonymous No.10802017]

>>10801968
Are you fucking kidding me. Well, how are they a meme?

[Anonymous No.10802037]

Get this book. It's the only one you'll need for awhile.

[Anonymous No.10802059]

>>10802017
dont listen to him lol, only the first one is a meme, second one is legit

[Anonymous No.10802746]

>>10801263
>>10801272
Needs more mathematical logic

[Anonymous No.10803298]

>>10801757
>the latest philosophy since anything earlier would obviously be incorrect

don't you think this just show that philosophy simply reflects and justifies the tastes of the current épistémè and is therefore mostly useless? i do

[Anonymous No.10803453]

>>10803298
I think it shows that a discipline that is essentially a millennia long dialectic is useless without hearing the other half of the conversation. But let's confirm our biases instead. Philosophy is dumb!

[Anonymous No.10803463]

>>10803453
that's why brainlets are attracted to philosophy, you can never be wrong, its all just your opinion man

[Anonymous No.10803479]

>>10803463
yeah you don't really know what you're talking about and this post really clarifies that.

[Anonymous No.10803507]

Does this really have any place here? STEM fags are generally the most boring and uncultured dullards on the planet and this hardly counts as literature.

[Anonymous No.10803640]

>>10803507
>STEM fags are generally the most boring and uncultured dullards on the planet and this hardly counts as literature.
Then why don't you just leave the thread, faggot?

[Anonymous No.10803671]

>>10803507
>Reading one of the most important and influential benchmarks of human thought ever put on paper hardly counts as literature.

Masturbate harder.

[Anonymous No.10804806]

>>10803507
Maths is patrician as fuck

[Anonymous No.10805150]

>>10803507
Wait, which type of math? Fun, greek math, like Euclid or Apollonius, or set theory?

[Anonymous No.10805390]

Don’t listen to the haters OP.

Currently reading Galois’ Theory of Algebraic Equations by Jean-Pierre Tignol. It’s a good development of Algebra from the Greeks (really the Arabs) to Galois, and written as more of a historical overview of mathematics than hard computation, although it doesn’t glaze over equations like so many soft mathematics books. I’d recommend giving it a read when you’re done with Euclid.

Rudin’s intro to real analysis is a good introduction to more modern mathematics. It’s very rigorous and pedantic however, so I’d recommend you pair it with Francis Su’s Lecture dearies for Harvey Mudd college (just look it up on YouTube).

Speaking of YouTube, if you want to have some basic idea of concepts in mathematics, look up 3Blue1Brown’s YouTube channel, as well as Bill Shillito’s “Intro to higher mathematics” series. Institute Henri Poincaré is another great YouTube channel, although more directed towards graduate students.

If you’ve finished with this, you probably have the gumption to get through Benoit Mandelbrot’s Fractal Geometry of Nature, which is a revolutionary text pertaining to higher maths. I recently got ‘Chaos in Wonderland’ which is more of a fantasy about Fractals, it looks interesting and you can find PDFs online, but I haven’t yet read it so I can’t comment

For general problem solving skills, Miklos Bona’s “walk through combinatorics” is fantastic and lots of fun. Read it and struggle through as many problems as you can, it will change your life.

Hoffatader’s books are all excellent. As is Asimov’s “1, 2, 3 infinity”. Flatland is a mathematical fiction, as are several of Borges short stories. All can be read comfortably by the layman.

If you really want to seem patrician, brush up on some sacred geometry (it’s all over YouTube, secrets in plain sight is a good series although it tends towards the conspiritorial). There exists a Spanish book, who’s name escapes me, that analysed Pi and use its relation to various arts and cultures. I mention it because, aside from being a good book, it’s the only piece of literature I’ve ever read that treated Pacific Northwest Salish/Haida carvings as mathematical objects, and although I was forced to pan my edition for pocket money I’ve been fostering the vain hope of someday hunting down another copy for years now. If anyone here recognizes The description I’d be very greatfull.

[Anonymous No.10805505]

>>10796651
i read the elements of euclid, then realized the rest of math wasn't worth learning at all.

[Anonymous No.10805528]

>>10805505
When you realize that you could literally spend all day contemplating one proposition, that you could literally just sit there, flipping through the pages, understanding the fundamental theorems of the different propositions/definitions/common notions necessary to come to that conclusion, then you've fully understood what is meant by 'logic'.

It's a fucking masterpiece. You could spend an eternity studying it, and while there ARE some logical fallacies, they are few and far between. I believe there is some proposition in book VI which is single-handedly responsible for most constructions in geometry after Euclid. So responsible, in fact, it is barely mentioned, just assumed, like II. 4 - 7 (Apollonius loved these)

[Anonymous No.10805598]

>>10805528
yes it's a nice book. but math in general is disgusting and dull, don't bother with the rest. it gets difficult after book X though..

[Anonymous No.10806463]

>>10805598
Ah yes.

Math is not 'disgusting', it is beautiful. You could study many different kinds of math, and Geometry is probably the best kind there is. I'm reading Ibn Al-Haytham right now and holy fuck is he hard.

[Anonymous No.10806485]

>>10805598
And what the fuck do you mean AFTER book X??

Book X is by far the most severely ridiculous book in the whole Elements. It is the one with the least applicability to modern mathematics, but I actually went through the rigmarole of understanding it, just to fully grasp what Euclid did with Book XIII.

The Books after X were hard, but because books XI and XII didn't directly reference X, I would say the hardest books were X and XIII in that order, because of just the sheer complexities of X.

[Anonymous No.10806541]

>>10805598
>but math in general is disgusting and dull

[Anonymous No.10806546]

>>10796651
Foundations of Geometry by David Hilbert. Euclid actually had a lot of flaws in his proofs that involved relying on spatial intuition instead of his stated axioms. The first construction, that of an equilateral triangle, is in fact flawed, for example. He stated without reliance on his axioms that the two circles intersect. Hilbert recognized this flaw and created a system of 20 or so axioms from which all the results of geometry can be derived and for which all axioms cannot be proved from the others.

[Anonymous No.10806770]

>>10801263
>>10802059
why is the first one a meme?

[Anonymous No.10806773]

>>10801272
>>10801263
ANYONE have more charts like this?

[Anonymous No.10806822]

>>10805150
both.

[Anonymous No.10806839]

>>10796651
That's not how you learn Math. Fucking hell.

[Anonymous No.10807089]

>>10806839
how do you learn math?

[Anonymous No.10807111]

>>10807089
by not reading the interesting works some of the finest minds we've seen, that still influences great thinkers 2400 years later

[Anonymous No.10807322]

>>10807089
Depends on your goals. If you pick up "Geometry for Dummies," and do all the problems, you'll come away with more practical problem solving skills than reading Euclid's Elements. However, you probably won't know shit about why anything you're being told is true or how it relates to fundamental axioms. Generally in modern education settings we see the former level of understanding as "learning math," and ITT, we see some people dismiss the latter. Sad state as Euclid used to be the standard geometry text, and yet nothing we shove at kids today is more rigorous than it despite the fact we COULD improve on it.

[Anonymous No.10807354]

>>10807111
>>10807322
t. non-mathematicians
Kiselev is a finer, actually rigorous intro to geometry.

[Anonymous No.10807362]

>>10796651
>euclid
Yet another mathless pleb falls for the biggest meme.
At least you didn't do Kahnacademy, I suppose.

[Anonymous No.10807363]

Euclid's Elements, Euler's Elements of Algebra.
Learn basic arithmetic skills.
Anything more than this is autism. Mathematics is overrated.

[Anonymous No.10807368]

>>10807363
>Elements of Algebra
>recommending a book filled to the brim with errors and poor motivation/ flimsy proofs
Why does /lit/ have the absolute worst taste in Math books?

OP, read G Chrystal's algebra books.

[Anonymous No.10807375]

>>10807362
Because Euclid and Euler were geniuses who had a better intuitive understanding of mathematics than any modern mathematician with their autistic analysis.

[Anonymous No.10807390]

>>10796651
i'm laughing at how retarded this is
you could have gotten through geometry revisited by coexter and gotten more out of 100 pages of difficult, rigorous proofs than with the entirety of the elements

[Anonymous No.10807395]

>>10807375
kek, i bet you're a literature undergrad or something who doesn't know jack shit about mathematics other than the few euclidean\calculus bullshits he learned in high school

[Anonymous No.10807399]

>>10807375
/lit/ in a nutshell. kys brainlet

[Anonymous No.10807420]

>>10807390
>preferring "difficult, rigorous proofs" rather than seeing a system of geometry developed holistically from basic, intuitive axioms
This is autism.

>>10807395
I'm a NEET and I understand that mathematics is just the science of quantity and is therefore a slave to higher sciences like metaphysics.

[Anonymous No.10807426]

>>10796651
Sure, if you want spotty intuition. Maths education has moved on.
https://math.stackexchange.com/questions/328028/what-are-the-differences-between-hilberts-axioms-and-euclids-axioms/328102#328102

I'd still say Books 1, 2, and 5 are worth reading. Anything else is, quite frankly, better spent learning from a proper geometry text.

[Anonymous No.10807427]

>>10807399
But in our time, education is overwhelmed by mathematics and on more than one score. For, while a contemplative interest in the properties of shapes and numbers is almost completely extinct, an illiberal and utterly inhuman form of mathematics dominates the years of learning of our boys and girls, almost completely from the very first year of the primary school to the very last year of college. In place of arithmetic and geometry, whose relation to reality is definite and understandable, there is now an indefinite confusion of branches which go by the name of mathematics, the nature of whose objects nobody understands! Such topics as topology, non-Eudidean geometry, Boolean algebra, transfinite numbers, projective geometry; not to speak of other more recognizable subjects like algebra, trigonometry, integral calculus, vector analysis and the theory of equations. These new subjects are not only more confusing but much more difficult to acquire, and therefore much less likely to leave the mind at leisure for other liberal studies. But the predominance of mathematics today is not restricted to those courses which go by its name, because mathematics, in some form or other, in matter or in method, has crept into every other corner of the curriculum. According to the modern positivistic conception, mathematics and not wisdom is considered as the prototype of science. In subjects ranging from physics to education, covering every field of human learning, there is an evident tendency to assimilate all knowledge to mathematical knowledge and to resolve all realities into mathematical formulas. This trend reaches its apex in the development of symbolic logic, in which guise mathematics invades even the field of philosophy, to distort all the basic conceptions of the mind, and to deflect all the activities of thought from attaining their fulfillment in true wisdom which consists in knowledge about God, by keeping them whirling endlessly around the nihilistic circle of sheer mathematical emptiness.

[Anonymous No.10807436]

>>10807426
>Sure, if you want spotty intuition. Maths education has moved on.

No, mathematics has been hijacked by false philosophy. As Aristotle said, the first principles / fundamental axioms are known INTUITIVELY, not by analysis.

>Around 1900, Hilbert did a thoroughgoing axiomatization, with all details filled in. The result is vastly more complicated than the partial axiomatization by Euclid.

This is the autism of the modern mathematician. He is never satisfied with intuition and must constantly expand his analysis to autistically make his system "complete". But as Godel showed, this is impossible anyway lmao.

>Hilbert did a thoroughgoing axiomatization, with all details filled in.
>with all details filled in.
kek

[Anonymous No.10807444]

Aristotle:

Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premisses. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand-they say-the series terminates and there are primary premisses, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premisses, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premisses are true. The other party agree with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal.

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premisses is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its originative source which enables us to recognize the definitions.

Now demonstration must be based on premisses prior to and better known than the conclusion; and the same things cannot simultaneously be both prior and posterior to one another: so circular demonstration is clearly not possible in the unqualified sense of 'demonstration', but only possible if 'demonstration' be extended to include that other method of argument which rests on a distinction between truths prior to us and truths without qualification prior, i.e. the method by which induction produces knowledge.

[Anonymous No.10807445]

>>10807436
You reek of NEET "autodidact."

[Anonymous No.10807449]

>>10807445
Jokes on you, I've barely taught myself anything about mathematics.

[Anonymous No.10807453]

>>10807449
Excellent. Your post is even more worthless. Stop leading some retard who's barely learning math in his late teens/ early 20s astray.

[Anonymous No.10807462]

>>10807453
You're the one leading him astray by trying to get him to learn more mathematics than he needs. Ask yourself how much of the mathematics you've learned has improved your mind and happiness, and how much of it has been puzzling over minute problems and abstract definitions.

[Anonymous No.10807496]

>>10807427
tl;dr: booh ooh group theory is too difficult, let's stick to the pythagorean theorem

[Anonymous No.10807507]

>>10807462
> not being able to appreciate the abstract beauty of mathematics and its practical consequences as a descriptive model of the physical world
then why do you talk about a topic on which you have no expertise whatsoever, you absolute fucktard?

[Anonymous No.10807511]

>>10807462
are you serious? i mean when i was 15 i also didn't understand the through-line principles underlying mathematics and claimed it was useless, but then i grew up.

[Anonymous No.10807512]

>>10807507
>not being able to appreciate the abstract beauty of mathematics
If you actually cared about this, you would be wholeheartedly recommending Euclid.

>its practical consequences as a descriptive model of the physical world
Overrated. It's more like we get the physical world to conform to our narrow-minded mathematical models.

[Anonymous No.10807517]

it truly amazes me how many gaps in maths knowledge americans and british have
in france, you're considered a dullard if don't know multivariable calculus, linear algebra, and ordinary differential equations by 15 or so

apparently it's commonplace to take these classes in post secondary education. absolutely absurd

[Anonymous No.10807519]

>>10796651
Terence Tao thinks the Elements are a waste of time for learning.
Next.

[Anonymous No.10807521]

>>10807511
Childhood is thinking mathematics is a useless waste of time. Adolescence is thinking mathematics is the purest fountain of knowledge. Maturity is understanding that mathematics is a mere tool with some fairly beautiful aspects.

The modern mathematical autism I am talking about is when mathematicians think that mathematics is a kind of philosopher's stone capable of uncovering all the secrets of the universe and solving all of life's problems, or thinking of it as the highest and purest branch of knowledge with the most perfect form of abstract beauty. Actually, ancients like Pythagoras and Plato kind of thought this way as well, but the moderns go further in their autism.

[Anonymous No.10807527]

>>10807517
Is your precocity in mathematics the reason that the French are hyper-critical bastards?

[Anonymous No.10807599]

>ITT declared 'superior math students' with formal education get butthurt because they apparently can't understand the curiosity to read such a brilliant, original and beautiful work such as The Elements, even if one read it more like a Literature book as opposed to studying textbooks
>"you are wasting your time reading Euclid, just read some dull math textbook"

>they don't see Euclid or Archimedes or Apollonius or Nicomachus just as they see Plato and Aristotle, and their fields as an extension of one another in Ancient Greece

"The laws of nature are but the mathematical thoughts of God."

[Anonymous No.10807602]

>>10807519
And they aren't, if you have any interest in mathematical primary texts from before Zermelo.

I'm reading Completion of the Conics, for example, and Ibn Al-Haytham uses Euclidean properties frequently, but the very translator, Hogendijk, references Euclid's Elements and Data.

[Anonymous No.10807604]

>>10796651
non-Euclid

[Anonymous No.10807607]

>>10796660

I know that feel. Seeing these humanitards struggle with lowly STEM and trying to learn it through pretentious and ineffective methods really exposes them. It's not even the right way to learn Humanities.

[Anonymous No.10807613]

>>10807599
You're an absolute sycophant towards dead men.

[Anonymous No.10807621]

>>10807599
Exactly, anon.

If I had a nickel for every time I've seen some retard storm into a Euclid thread going 'I THUNK THAT ITS NOT APPLICABLE' I'd be rich.

And they're wrong too, that's the funny thing. Every single aspect of Euclid is applicable. There are only two real objections to be made with The Elements, one with the first Proposition. One with the twenty seventh.

That's it.

[Anonymous No.10807624]

>>10807613
not all dead men

[Anonymous No.10807627]

>>10807599
You can enjoy the work. You simply won't have the insight I have. I'm satisfied with that. Have fun.

[Anonymous No.10807645]

If you care about mathematics you should not bother with the elements, it's long, translated, and filled with errors, not to mention it has nothing to say about non-euclidean geometry.
REad the elements if you're fascinated by the origins of axiomatic thought in mathematics, and like the idea of readding the granddaddy of logical proof
Modern textbooks do everything euclid did better, with more clarity, more generalized, and probably in your native toungue, pic very related

>>10807519
#this

[Anonymous No.10807650]

>>10796660
pretty much confirms that this board consists of aimless pseuds, honestly. hell, I even read the elements. this insistent tribalism surrounding it is really silly. it reminds me of some dumb, wide-eyed american, eager to bark at his first taste of knowledge

it's cute, i guess

[Anonymous No.10807768]

>>10807645
Very very dumb. Where are the mods to ban these pseuds?

[Anonymous No.10807772]

>>10807650
>>10807645
>parroting academia
Morons.

[Anonymous No.10807821]

>>10807772
>>10807768
you'll never catch up to me even if you gave it your all tomorrow, and you'll eventually learn maths the proper way, amerifat. everyone sees right through you

[Anonymous No.10807826]

>>10807772
Maybe you should actually read it. If you're still vehement about defending it afterwards, you're not very bright, and you'd be betraying a severe lack of mathematical maturity.

[Anonymous No.10807849]

the /math/ general on /sci/ is laughing at us

[Anonymous No.10807957]

>>10807420
>mathematics
>metaphysics
>science
>not adhering to the formalist school of thought
>thinking math could give more than a fuck about reality, concrete or otherwise
>2018

[Anonymous No.10808053]

>>10807821
>>10807826
The problem is that people will see these posts and actually think it’s legitimate. I can guarantee most of the ducking retards talking about math over in /sci/ would be utterly unable to read most complex geometrical proofs mathematicians have written, because they are unaqcuainted with the logic and foundation of geometry as a whole.

From certain arithmetical properties, musical harmonies are derived. This is still true. This has applicability for the soul, but you wouldn’t care about that. You’re interested in practical applications. In so doing, you’ve turned mathematics into something it was never intended to be.

This is the best thread we’ve had of these in a while because you can look through and see the amount of anons reading Euclid. It’s an important book to read, but if I told you that you don’t just read it for the mathematics you probably wouldn’t understand.

I mentioned earlier I’m reading Hogendijk, he references Euclid’s Elements and Data constantly. Old mathematical texts are discussed all the time in academia. In reality FOR WHATEVER REASON you seem pretty delusional and butthirt yourselves. I win in this debate, and this thread is evidence

[Anonymous No.10808074]

>>10808053
/math/, and a resident literal genius tripfag alone would BTFO you, you complete sophist

[Anonymous No.10808085]

>>10808074
He's smarter than all of /sci/. Kill yourself.

[Anonymous No.10808094]

>>10808074
And you've lost, little brain-damaged STEMlord.

[Help me No.10808151]

>>10801263
Just dive into Spivak. Fortune favors the brave.

[Anonymous No.10808685]

>>10808053
>This has applicability for the soul, but you wouldn’t care about that. You’re interested in practical applications. In so doing, you’ve turned mathematics into something it was never intended to be.
What the fuck are you talking about? Modern mathematics solves both practical and highly-theoretical problems. It doesn't differentiate from but contains everything that has been done before and is still valid. If you want to know math you don't have any choice to make, there is only one way: you learn it all and you start with the modern part because, as I said, it contains everything it needs.
Yeah some people never understand the foundations, but there are also some people like the ones I'm seeing in this thread who don't get their hands dirty and just read some old books and stop there, ignoring all subsequent development. Can you even tell me what an affine Euclidean space is? Or what a scalar product is and why it's important? Any mathematician will tell you that you don't know shit about geometry without those, no matter how many works by Euclid or Nicomachus you've read.

[Anonymous No.10808709]

>>10796651
Imho, one gets more out of Euclid after having a degree of mathematical skill. It's not an elementary textbook in the vulgar sense of the word, that is, being for beginners. Just go with Birkhoff's or Moise's textbook instead and *maybe* later go read Euclid. There's a reason why major universities have their courses on Classical, i.e. Euclidean, Geometry restricted to upper-level undergraduates.

But really, I'm just some anon so take my advice with a grain of salt.

[Anonymous No.10808781]

>>10796651
Start with your high school math books.

[Anonymous No.10808801]

>>10808685
then where would you instruct one to start?

[Anonymous No.10808817]

>>10808685
Can you tell me what the Synthetical approach to mathematics is?
>>10808801
He doesn’t know what he’s talking about, just more bullshit.

[Anonymous No.10808827]

>>10808801
Not him but I would recommend to start with "Basic Mathematics" by Serge Lang to get a solid understanding of high school mathematics. After that work through a Linear Algebra and a Real Analysis book.

[Anonymous No.10808865]

OP here. Thanks to everyone who offered their opinions on how I should approach math, I have no interest in pursuing it at a career but I can't stand have such a glaring gap in my knowledge. I'm ignorant on the subject and now have a better idea on how to approach it, thanks.

[Anonymous No.10808884]

>>10796651
>reading an outdated mathematician
Seriously, this is the most ass backwards thing I've seen on here in years.

Wtf are you doing retard, literally just learn highschool math. I swear you faggots just want to brag about reading >muh classics

[Anonymous No.10808892]

>>10808884
>hasnt read Elements
Enjoy being part of a growing minority

[Anonymous No.10808947]

>>10808801
I answered that before >>10796921

>>10808817
Something that doesn't come near the scope and problem solving (both theoretical and practical) capabilities of true mathematics.

[Anonymous No.10809120]

>>10808947
>>10808947
Exactly my point. It’s not always about practicability. Sometimes you read simply because it’s an interesting approach to mathematics. No sense being dogmatic about mathematics. The analytical-Synthetical-diorismotic approach to mathematics is just plain rigorous.

[Anonymous No.10809155]

>>10808685
>but there are also some people like the ones I'm seeing in this thread who don't get their hands dirty and just read some old books and stop there, ignoring all subsequent development.

see >>10807599
you need to understand not everyone is trying to get to graduate level math, calculus, etc. There are people simply curious, that see the greek mathemathicians just like they see plato, and because of that curiosity, they read the elements, for instance, as I said, more like a literature book than a math 'textbook'.

You are right, those ancient works aren't the best to actually study and learn math, but you are assuming everyone is trying to get to advanced math subjects, thats why you think its wrong to just read euclid, but try and see things the other way around.

[Anonymous No.10809654]

>>10809120
>>10809155
The anon I was replying to claimed that we've "turned mathematics into something it was never intended to be", which is a bullshit statement. I have no problem with people leaning some maths without trying to get too advanced with it (in fact I even encourage this approach). But the thing is that mathematics is, ultimately, about solving problems and describing things and the more you progress with it the more of that you'll accomplish. You can stop wherever you want but you can't dismiss the formal approach because it does exactly what it is supposed to do.

[Anonymous No.10809737]

>>10809654
You can definitely criticize the contemporary approach. That’s the idea

[Anonymous No.10809755]

Stop reading this useless bullshit. For fuck's sake. You'd learn more by going to Khan Academy and re-learning high school math. Go fuck yourself.

[Anonymous No.10809900]

from euclid I would go to Apollonius and Achimedes. After that, I would go to Courant/Robbins and read "What is Mathematics?" for an introduction to more modern mathematical theory and notation. Don't listen to all the STEMtards in here going on about how this isn't how you learn math. As long as you have the motivation to get through the difficult proofs and make sure you're grasping every part of the logic as you go along, you'll be fine

[Anonymous No.10810070]

>>10809755
Wrong.
>>10809900
Right

Why are people getting so upset.

Okay so you should modern mathematics. My suggestion is you just read all of Elements and On Conics.

What colleges sometimes do is they will teach On Conics Books I - III, only those books because they are somewhat centrally contained. If I'm going to be honest with you, everyone here should do at least that. On Conics is honestly one of the most rewarding things you can read, and it is very interesting and well thought-out.

[Anonymous No.10810073]

>>10809737
Criticise what? That's it's more abstract meaning that it englobes much more stuff?

[Anonymous No.10810093]

>>10810073
You can just say it's too practical. That modern geometrical approaches focuses less on the theory of developing the proofs that are fundamentally the cornerstones of geometry and more on the system that simply validates said proof.

[Anonymous No.10810131]

>>10803507
you can't be a patrician in 2018 and not into maths

the STEM vs humanities meme is for undergrad retards and salty continentals who want to LARP and write obscurantist drivel for personal benefit, but people who are intellectually honest realize philosophy and maths are inextricable. what is logic. literally the only formidable argument against this is "b-but feminism is rigorous too!" which is obviously bullshit but at least there are still a lot of relatively high IQ if dishonest people involved

[Anonymous No.10810249]

>>10805598
>math in general is disgusting and dull

[Anonymous No.10810254]

>>10796651
Start with Lang's Algebra

[Anonymous No.10811447]

>>10808053
fuck u u dumb sack of shit, why do you think euclid is the end all be all of mathematical logic? what deficiencies do you have that you're unable to understand that people who study modern mathematics both write and understand proofs
what is wrong with the euclid fanatics in this thread that they think you can't have mathematical maturity without euclid?

it would be a shame if you've convinced a single budding mathematician to waste their time with an ancient tome as archaic as the elements. There's a reason it's no longer used as a textbook in geometry courses, but how would you know, you've never taken one

[Anonymous No.10811509]

>>10811447
Then offer an alternative retard, oh wait, you haven't taken a geometry course either.

[Anonymous No.10811513]

>>10805598
>math in general is disgusting and dull
Well there's one way to betray your low IQ.

[Anonymous No.10811522]

>>10811513
>MUH IQ

that guy is dumb but you aren't better

[Anonymous No.10811528]

>>10811522
why does iq trigger people so much

[Anonymous No.10811537]

>>10811528
doesn't trigger me as a concept, it triggers me when retards on an imageboard ballpark the iq of everyone around them when they have no idea what the fuck they're talking about. so shove the science denying leftist spiel back up your ass you stupid fucking cunt.

[Anonymous No.10811540]

>>10811537
there's really no need to be this upset

[Anonymous No.10811550]

>>10811447
>There's a reason it's no longer used as a textbook in geometry courses
Only very recently was it taken out of the curriculum.

Many view that as a fundamental mistake as well.

[Anonymous No.10811596]

>>10796651

is it true that in order for someone to be on the cutting edge of pure mathematics, you pretty much have to be born as either a savant or prodigy just because of how far it has come?

[Anonymous No.10811609]

>>10811550
Name 5 mathematicians that think it was a mistake, who have an Erdős number of 3 or higher.

[Anonymous No.10811634]

>>10811609
Euclid has to have a number higher than that. Elements would have to be taken as at least one assertion of inherent value. Take that as one.

Take Gauss as two.

Take Einstein as three.

Face.

[Anonymous No.10811645]

>>10811550
it's still in the curriculum at my college

[Anonymous No.10811762]

>>10811645
I'm sure it is, but I was talking about elementary schools.

Bud, if you're in college, they should be teaching you Apollonius.

[Anonymous No.10811766]

>>10811762
>>10811645
This isn't to say you shouldn't study Elements as an adult, of course. The book has such a vast degree of depth and you can easily find it if you want to look for it.

[Anonymous No.10811784]

>>10811762
we get Apollonius and Archimedes too, once we go through the elements.

[Anonymous No.10811799]

>>10811784
All in one Semester too, huh? Whew.

I guess it might work. You'll find Archimedes to be the hardest, my friend. I've done that. I've read all of the Elements, all of Archimedes' works, save a couple I was not interested in (On Floating Bodies and On the Mechanical Method I skipped), and I also read Books I - VII of Apollonius On Conics. Yes. One through SEVEN. I am actually currently reading Ibn Al-Haytham's Reconstruction of the Eighth Book. Medieval mathematics was actually very confusing. Where they have a clear advantage from using the Analysis-Synthesis-Diorismos approach, they lose in clearness.

But I digress. Most likely you will do just Books I - III of On Conics. And you might read Introduction to Arithmetic by Nicomachus as well? That is going to be one of the most interesting reads you have as well. If the teacher isn't making you do it, I would suggest you read the Timaeus by Plato before beginning Introduction to Arithmetic.

I have a rather old copy of the 'Great Ideas' issues from the Great Books series. It's the mathematics one obviously, but there were so many errors in my edition I had to correct them myself. It was actually fucking embarrassing, Book III is a trainwreck. VERY few people care enough to read this deep into them, unless they are assigned it by their college though. I have an intense interest in mathematical philosophy, which is why you see me taking the On Conics so far.

[Anonymous No.10811819]

>>10811799
It's over 2 semesters. We don't do intro to arithmetic, and only books 1-3 of conics. Read Timaeus in PHL 101 iirc

[Anonymous No.10811823]

>>10811509
>>10807645
already did fuckhead

[Anonymous No.10811828]

>>10811819
Ah well. You should just read that book by Nicomachus anyway. I finished that last weekend. Pythagoreanism is fascinating.

[Anonymous No.10811839]

>>10811828
I'll take a look for sure

[Anonymous No.10811962]

>>10806485
sorry, I meant after and including book X.

[Anonymous No.10811966]

>>10811513
>stop disliking what I pretend to like to appear smart!
bawwww cry me a river faggot.

[Anonymous No.10811992]

>>10803507
pure math and logic, and the (lesser importance) quantum mechanic are quite important,

i mean, they're second to philosophy/lit. that's the hierarchy of knowledge.

though, yeah STEM undergrad are nightmare to get along with, better avoid them if you want to know about these things, but pure math or logic students i think are not that insufferable

[Anonymous No.10812025]

>>10806770
It's a foundational approach, many of the books are on logic. /sci/ doesn't believe in that, they believe in doing, with foundations coming later on and as secondary. The 1st book in the 1st chart is more of a general logic book, in that it will teach you things unnecessary for mathematics and mathematical logic. The author intended a guide contrary to mathematics education, and thus contrary to the mentality of mathfags.

I mostly agree that it's not very good. Truly, the best way to learn mathematics is by exercising your ability (doing problems). This will help with everything, remembering names of logic/proof concepts and how they relate will not. Practice is the only thing that can provide intuition and maturity.

[Anonymous No.10812078]

>>10812025
"Foundational approach" is a meme because even though technically no preliminary knowledge is required for the foundations, practically you need a certain degree of mathematical maturity. Nobody ever learned mathematics---including the wanker who made that meme---did so by a foundational approach.

[Anonymous No.10813001]

>>10796651
Depends on your levels of current brainletism, your language and what you are interested in.
In English, Apostol's books are nice introductions to the analysis/linear algebra that you just can't go without.
After that, what do you want to get into? Geometry, analysis, algebra, probabilities, ...

[Anonymous No.10813293]

As a prelude to Euclid, any good books on Pythagoras or the Pythagoreans?

[Anonymous No.10813335]

>>10812078
It’s not a meme because different individuals across different time periods approach mathematics differently. For instance, I could say that medieval mathematics were more thorough with the construction of the diagram, and the setting up of alternative constructions where the proposition where it’s not possible, than Greek mathematics.

But that Greek mathematicians were more thorough with defining which propositions were important in proving other propositions. Or even defining if it’s a Euclidean property or not.

Meanwhile can you even read propositions with modern geometry? They don’t do Synthetical analysis. They don’t tell you how it’s possible to know what the computer/calculator knows for you. These are the types of limitations people ITT are talking about.

>>10811962
I thought so. There’s no way you wouldn’t have stated Book X was hard. Apotomes are a difficult concept to remember, especially all the different kinds

[Anonymous No.10813346]

still waiting on a probability and stats charts, been two days, step ya pseud game up

[Anonymous No.10813404]

>>10813293
If you’re interested in Pythagorean Arithmetic, look no further than Introduction to Arithmetic by Nicomachus. Rather than being an intro to modern number theory, it teaches you how numbers USED to be taught. And there are some very interesting properties of numbers to contemplate.

[Anonymous No.10813498]

>>10813404
It just sucks that most of the writing of Nicomachus was most likely destroyed in the library of Alexandria fire

[Anonymous No.10813511]

>>10796651
>learning maths with ancient greek texts
Good luck trying to reach a decent amount of knowledge, but hey at least you'll have an excuse to tip your fedora and larp as a polymath because you read le epin euclid.

[Anonymous No.10813522]

>>10813511
it's like if ur such a genius math guy, go blaze through a math degree in 3 years and then do a phd and get a job as a professor instead of being a neet piece of shit, oh, not so smart after all eh

[Anonymous No.10813576]

>>10813511
It’s just a different kind of knowledge. Are you actually fucking retarded?

[Anonymous No.10813762]

Think about math ideas and theorems like a set of tools, and let's say you want to dig a ditch. You have some options. There's an old (but sturdy) wooden contraption some Greek guy made that was pretty darn good for ditch digging back in the day, but it's physically demanding and takes all day. Not to mention the manual is pretty clumsy by today's standards.

Then there's also a sleek, shiny gizmo that's essentially built on the same ideas as the Greek guy's thing and can dig the ditch in a few minutes without breaking a sweat. You're not cutting any corners by using the fancy, new machine. In fact, by using it you start to understand the Greek guy's thing better than he did.

Since this is recreational ditch-digging, you're welcome to use whatever tool you like. But using the old wooden thing is basically like being one of those "living history" people at historical sites who churn butter and badly larp the past.

[Anonymous No.10813836]

>>10813762
What an absolutely horrible analogy.

A better analogy is modern mathematics is just eating food, ancient mathematics is learning to build the spoon to eat the food

[Anonymous No.10813913]

>>10813836
I don't think you have a good grasp of modern mathematics if you think that analogy is sound.

[Anonymous No.10813960]

>>10813913
Actually I don’t think you have a good grasp of ancient mathematics is you don’t. Clearly I am not insulting modern mathematics by that analogy, but by your simplistic linear analogy you are.

They are just different areas of mathematics, pleb. Lrn2learn.

[Anonymous No.10814037]

>>10813960
Your responses are getting flimsier. "Insulting" ancient math is besides the point, and if anything your unwavering reverence for the ancients reflects a flawed bias. I have complete respect for the brilliance of the Greeks, but I also see their limitations and advancements we've made since. Take Proclus's claim that Euclid V was provable from Euclid I-IV, and flawed proof. He sent people on a two-thousand year goose chase on that assumption, and people worshiped the rules of Euclidean geometry as the end-all be-all of geometry because of it. And once we discovered his claim was incorrect, we reached a new level of understanding on the way axioms operate in mathematics, maybe the biggest breakthrough in mathematics. We know more about the spoon now than they did when they made it.

[Anonymous No.10814056]

>>10796651
math was invented by the devil

[Anonymous No.10814061]

>>10814037
A flawed bias? Re-read the post you responded to. I am insulted you insulted modern mathematics with your own logic. Their objectives across time is not always the same, after all.

Synthetical analysis is beautiful, but has very little place in a mathematics degree. But it’s not because it isn’t beautiful.

And also, your post is proof of why you SHOULD care about ancient mathematics. I know I would not understand mathematics the way I do if I didn’t stop in the Islamic Golden age to review some of their mathematicians as well....

Good example though. Proclus was brilliant. I’m thinking about reading Books IV and VII of Pappus’ Collection very soon, and he extant copies of Diophantus’ Arithmetica (whose findings are paralleled in Fermat’s understanding of mathematics)