Redpill me on number theory, /sci/. Is there any mathematical

>What exactly is "beautiful" about the proof that the primes are infinite?
assuming you mean euclid's proof, it's 'beautiful' because it's old, simple, and short, and can be adapted to other arguments of infinitude

the integers are 'boring' because they're just... basic numbers, but you can come up with questions of seemingly arbitrary difficulty about them

zeta functions are among the most interesting number theoretic objects (two millennium prize problems about them)

>>8637572
it's only "boring" because it doesn't have much of those flashy results that brainlet non-experts quote to appear knowledgeable, such as: muh [math]e^{ipi} + 1= 0 [/math]
>b-b-but it contains all the most important mathematical constants!

also the only reason why people view irrational numbers as less "boring" anyway is that we can see many ways to express them using natural numbers, such as:

[math]\frac{\pi^2}{6} = \sum \frac{1}{n^2} [/math]

and

[math]e = \sum \frac{1}{n!} [/math]

though the irony is that the first of those results is also in a way related to number theory via the riemann zeta function, and the relation the zeroes of that function have to the primes

>>8637655
Here we're talking analytical number theory, then. Because the infinite sum requires some more axioms, usually the limit and this requires the norm on the reals.
The zeta function is a tool in a framework that includes the laws of arithmetic, but there are of course no infinite sums in arithmetic itself.

>>8637572
Can I have his channel name or a link?

>>8637572

/sci/mon pill INBOUND!

(0)!>0

>>8638698
huh

How can you not find primes interesting
They are seemingly the only random thing in the universe, the only thing for which we cannot find a generating formula (for all)
Also they are the building blocks of all composite numbers

>>8638724
I like the magical prime number 7

>>8637976
https://www.youtube.com/user/njwildberger/featured

>>8638764
xd lol

>>8637572
The idea that Euclid's proof is "beautiful" is a meme. Like Euler's formula.

What's immediately interesting is that your "boring and tedious" integers actually turn out to be extremely finicky objects when you start trying to answer questions about them. The disparity of something that looks like it ought to be simple actually being complicated makes people curious.

One thing I really like about it is how many different fields it connects. You can apply virtually any mathematical tool you can imagine to number theory in some method or another, even tools that seem totally irrelevant. Complex analysis turns out to be very closely related to where the primes are. Stuff about what happens in arithmetic progressions needs combinatorics. Asking questions about remainders will lead you into modern algebra. You can end up anywhere.