How Was Fermat's Last Theorem Proved for Regular Primes?

[eliyasne]

That was an amazing video! :D
I'm so happy to have subscribed to you, i don't know how can one live their lives oblivious to such an elegant piece of math visualisation!

[maxsch.]

Your subscriber count will grow exponentially with this kind of quality. Keep it up! :)

[gamabuga]

man your videos are amazing... you bet soon enough your channel will explode with views

[strangledpuppy]

This video is great, I sincerely hope you will never feel like all that work you put in such videos was wasted

[Koospa]

Incredible video, super interesting and well explained, can't wait for more!

[dcterr]

Very good video! I learned all this stuff in math grad school, but I really enjoyed your explanation, which was very clear as well as historically interesting. Good job!

[NonTwinBrothers]

This is legit such a good explanation, how is there only 8, 000 views?

[eguineldo]

Absolutely amazing explanation, thank you so much for creating this!!

[willnewman]

The definition of regular prime given in this video is very wrong. All p have Z[zeta p] with unique factorization of ideals. This is true in any ring of integers like Z[zeta p]. A prime is regular when p does not divide the order of the class group.

[mattkerle]

Awesome video! I'll need to watch it through a few times to really understand it!

[theultimatereductionist]

0:45 For all INTEGER n, of course. I believe (am very certain, but have not yet proved it) that
for any positive real numbers x, y, z with x<= y < z that there exists a positive real n such that
f(n)=0 where f(n)=x^n + y^n - z^n. I believe the -z^n term will always dominate.
Am writing this out right now, expanding y^n and z^n with y=x+b and z=x+c with 0<b<c using the binomial theorem.

[riadsouissi]

Excellent video, please continue these series and if possible delve deeper into ideals and number theory

[liubin]

2:04, "Holds for n => holds for multiples of n"? This looks wrong. It should be the other way around, as shown on the following screen.

[BuleriaChk]

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)

[mahmoudalbahar]

Many thanks to you, for making such great video.

[tauceti]

This made me get stoked to hit up my abstract algebra books again

[TheJara]

Top notch presentation..both videos...please post more videos like these on abstract algebra and other pure math...and I will make a video about your channel...

[NicolasMiari]

I believe the cyclotomic polynomial is (in the case of p prime exponent) only what you get after dividing by (t-1); i.e. the polynomial whose roots are the PRIMITIVE roots of unity of order p (1 excluded).

[theultimatereductionist]

In 1986 I took Harold M Edwards' book "Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory".
I practiced and practiced, tried and tried, to read and do the homework exercises in it. Just couldn't.
I needed a guide. I still do. When I applied to graduate school in math, I gave "hoping to solve FLT" as my goal/motivation.
How naive and ignorant I was of higher math, especially since I was not an undergraduate math major,
but an undergraduate chemical engineering major.
But, I soon changed my focus/interests in graduate school away from FLT to differential algebra and the study of finding exact solutions to nonlinear DEs, which I believed, and still do, is an infinitely more practical & important problem.

[leothorp]

Awesome video- one of the most accessible explanations I've seen. Love the music in it as well, where is it from?