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you are so wonderful

Theres some mistakes here

Can this problem be solved ONLY with the math known to Fermat?

Soooo... this is simple !?

hmmmmm... i always put my shoes on before i put my watch on, but i also always put my watch on before i put my shoes on, i guess phi and lambda simply wont cut it for me.

Crystal clear! Thanks again!

Is Z[\zeta] not equal to n_0 + n_1\zeta + ...+ n_{p-2}\zeta^{p-2} since the degree of the minimal polynomial is phi(p)=p-1?

Galois was one of the very rare minds (Gauss level) that died too soon.

Many things in this video are WRONG! Duplicating @sbares 's comment: Gal(x^7-2, Q) is not C7 as you claim, it is a group of order 42, as is seen by the tower of extensions Split(x^7-2,Q) = Q(2^(1/7), exp(i2pi/7)) > Q(2^(1/7)) > Q where here ">" means "extension of" (sorry, can't type TeX in youtube comments lol). The minimal polynomial of 2^(1/7) over Q is x^7 - 2, so this extension is of order 7, and the minimal polynomial of exp(i2pi/7) over Q(2^(1/7)) is the seventh cyclotomic polynomial, so the order here is phi(7) = 6. Thus |Gal(x^7, Q)| = [Split(x^7-2,Q) : Q] = 7*6 = 42. There's a similar problem with (x^7 - 1)(x^5 - 1). The minimal polynomial of a seventh (or fifth) root of unity over Q is not x^7 - 1 (or x^5 - 1), it is the seventh (or fifth) cyclotomic polynomial. It is not too hard to see that the splitting field here is the 35'th cyclotomic field, so the Galois group is in fact (Z/35Z)*, which is isomorphic to C12 x C2 Finally, the example x^5 - 2x + 1 factors as (x-1)(x^4 + x^3 + x^2 + x - 1) so the Galois group is not S5, it has to be a subgroup of S4 (In fact, Sage tells me it should be the whole S4).

wtf am i watching

Great explanation.

Please come back!

This video blows my mind. Good job.

The rocket doesn't need to reach the escape velocity to "get out" of the gravitational field because during the launch it's almost always accelerating and, depending on the fuel usage, the acceleration towards outer space can become greater than g. The escape velocity is only needed by relativity-wise inertial bodies (which relativistically don't accelerate because they follow inertial world-lines). By the way, since gravity has a really weak field, even though every body and energy source generates a gravitational field, the farther away those other bodies are, the more negligible their gravity becomes when calculating escape velocity. It's also not considered that the escaping body could at any moment have its velocity vector diverted by an extraneous cause (maybe an electromagnetic interaction, maybe another gravitational field, maybe something else) or even totally nullified by a transfer of momentum (a sudden hit against another body). So the escape velocity would be totally valid if not exact in a universe with the earth, the tennis ball and no other mass/energy. However, in the practical case, at the point when the actual velocity could become less than the escape velocity the body would already be too far from the first gravitational field and would get a stronger attraction to a second one.

I dont understand any of this shit, cant it be explained simpler? I don't know how geniuses brains work, but most of these stuff seems like they came out of ass

Thank you A LOT for that video. Finding that formula with simple math is so satisfying when youn understand, it's really fun and yet extremely comprehensive.

Amazing vid, one of the best here in YT

What software do you use for making the animation and for editing?

9:46 missed the opportunity to say "It gives us superman"

Proof of Fermat's Last Theorem for Village Idiots (works for the case of n=2 as well) To show: c^n <> a^n + b^n for all natural numbers, a,b,c,n, n >1 c = a + b c^n = (a + b)^n = [a^n + b^n] + f(a,b,n) Binomial Expansion c^n = [a^n + b^n] iff f(a,b,n) = 0 f(a,b,n) <> 0 c^n <> [a^n + b^n] QED (Wiles' proof) used modular functions defined on the upper half of the complex plane. c = a + ib c* - a - ib cc* = a^2 + b^2 <> #^2 But #^2 = [cc*] +[2ab] = [a^2 + b^2] + [2ab] so complex numbers are irrelevant. Note: there are no positive numbers: - c = a-b, b>a iff b-c = a, a + 0 = a, a-a=0, a+a =2a Every number is prime relative to its own base: n = n(n/n), n + n = 2n (Goldbach) 1^2 <> 1 (Russell's Paradox) In particular the group operation of multiplication requires the existence of both elements as a precondition, meaning there is no such multiplication as a group operation) (Clifford Algebras are much ado about nothing) Remember, you read it here first)

At 2:11 you say "any legit algebraic operations". I think, this statement is misleading. You clearly meant addition and multiplication, but you need to already have some knowledge about field extensions to understand that you didn't mean taking roots here, since for a layperson taking a root is just as good an "algebraic operation" as addition and multiplication.

So basically you need to factor out groups of roots, if each group forms an abelian group then you solve.

Composition of functions is the written the wrong way round here!! Great video otherwise though

🎉 excellent explanation

That was awesome

Where did this guy go ? This is one of the best channels in yt

😮😮🎉🎉

why can't we extend to 5+? I feel like I was given a bunch of random information and then told "yeah well you can prove it's not solvable with all that but we're not gonna actually tell you that" never really explained why you can't extend the galois group? why can't we have a wheel of 2, 3, 4, and 5? simplicity doesn't help if I can't understand anything with the concept, it's just random information

BRO HOW DOES HE NOT HAVE MILLIONS OF SUBS BRO THIS GUYS FREAKING AMAZING

Will you be making more videos? Hope all is well. Like your content

why are equations that involve flipping in their Galois group not solvable by radicals? where is the proof that it is never the case for equations of degree 4-1?

Fine. But what about the *PROOF* of this theory? That would be real *explanation* of Galois' Theory, not just a short preview of what it implies. To name a theory again and again and again and again isn't knowing it.

Can someone explain how once you cross the event horizon there is no path out? Is it just because there is no force or material strong enough to get out? What about hawking radiation or even the plasma jets erupting out of supermassive black holes? It seems like the plasma jets found a way out to me

Thank you I'm now interested in math too, but come from physics. Need those intuitive explainations. 🎉

I didn't realize the BGM at frist but soon I found what made me feel thrilled...

👋👋👋👋👋 Excellent!

9:57 Abel (/ˈɑːbəl/ AH-bəl). Even though I don't expect any American guy can pronounce the foreign guy's name properly. 😮‍💨

we are back baby

I shall return when I understand sets :>

Man what a great video

Wait, what makes "h" tend to infinity? And what does that have to do with escape velocity? Does h mean a height that keeps on growing or what?

I got lost when calculus started😂😂, still love the video

I love the background music, it is so soothing that I felt like I was peacefully dying in sleep.

I found this confounding. And I feel sad belonging to the confused group.

The explanation was beautiful. The background music almost ruined my focus.

I think this video has some great potential, but about one third of the way, it starts to blast through the contents... I know some basics of group and field theory, so I was able to get to the half of the video, but suddenly it just stops explorative tone and starts speeding up. I think Galois theory is after group and field theory in university level math, so no wonder there, but, the phase shift is unfortunate. "Explained simply" stopped being explained simply about halfway the video.

This is a great video!

Huh? 🤷‍♂

Excellent video

14/8/2023. Consulter d'autres sites où je développe la solution ""FACILE"" du dernier théorème de FERMAT, ne voulant pas me répéter sans cesse de sites en sites.