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

>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.

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

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.

This.

This is true
This is ultimately the case
>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).

>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

Euclid -> Apollonius -> Archimedes

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

Book V was literally just arithmetic.

this
initiate with the indians

...

...

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

holy shit there are pseuds on Veeky Forums don't know how roman numerals work? sad!

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

Yes, I misread his post.

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

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.

this is a good thread

Mods, sticky this thread

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

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 Veeky Forums

then the Odyssey

Start with the Greeks

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.

those are Veeky Forums meme bait lists don't bother

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

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

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

Needs more mathematical logic

>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

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!

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

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

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.

>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?

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

Masturbate harder.

Maths is patrician as fuck

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

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.

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

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)

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..

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.

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.

>but math in general is disgusting and dull

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.

why is the first one a meme?

ANYONE have more charts like this?

both.

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

how do you learn math?

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

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.

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

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

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

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

OP, read G Chrystal's algebra books.

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

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

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

Veeky Forums in a nutshell. kys brainlet

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

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.

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

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.

>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

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.

You reek of NEET "autodidact."

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

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

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.

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

> 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?

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.

>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.

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

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

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.

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

>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."

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.

non-Euclid

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.

You're an absolute sycophant towards dead men.

Exactly, user.

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.

not all dead men

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

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

#this

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

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

>parroting academia
Morons.

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

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.