a spectacular solution to the Basel problem (sum of 1/n^2 via a complex integral) 

I think he was talking about "i" haha. that play on words is hilarious. btw, thanks for sharing bprp!

THAT'S AN IMAGINARY OBSERVATION.

As soon as I heard it, I knew the top comment was about it

marbanak I think it’s too *complex* of a message for us non-Rick-&-Morty fans to understand

Very sharp thinking!! √-1 love this joke... (i love this joke)

Video was uploaded 5 hours ago...you commented 2 days ago.... Are you from the future

I’m from the future of the future

I was from the past

Also, check out 3blue1brown's video on the same ;)

Existe uma prova muito legal no livro "tópicos de matemática elementar vol. 5" utilizando funções aritméticas.

Hahaha!

Thank you!

i have done similar problem

This isn't a proof, because the manipulations done with the series S aren't necessarily valid.

@@alxjones Thanks. You seem credible in what you said, in spite of the unfortunate man who shares your name. Sorry about that.

@@alxjones well if he proved the the series converges then everything is fine. The thing is that the series does indeed have a finite value so all the manipulations are valid

@@gregorykafanelis5093 the problem is that in the complex case you don't always have ln(xy)=lx(x)+ln(y)... the complex logarithm isn't to be taken carelessly, so maybe already in the third line, there is a mistake.

@@lukaskohldorfer1942 well he then have to say that the ln is restricted for only 2π to 0 angles. But then we get down the rabbit hole. Point being, this proof is a long way from being mathematically strict but it is a nice way to calculate the value of the integral Also let's not forget the famous internet saying for mathematics If the result is correct then the method must be correct. This time we can turn our heads to the other side as you have to admit this proof us truly beautiful not mathematically strict, but certainly has some beauty

xamzx thank you!

blackpenredpen btw can you integrate cosx/x from pi/2 to +inf like you integrated sinx/x from 0 to +inf

Chris Hello : )

I KNOW RIGHT????

Zvi did! : )

What less crazy way of proving the identity do you have in mind? The infinite product for sinc(x) and 3Blue1Brown's lighthouses are both pretty crazy to me.

JohnnyCrash The simplest, should you say, ‘cuz the craziest thing we used was the complex (pun non-intended) definition of cosine in another problem, and everything was pretty straight-forward and self-explanatory....... compared to other proves

​@@nicholasleclerc1583 the problem is that in the complex case you don't always have ln(xy)=lx(x)+ln(y)... the complex logarithm isn't to be taken carelessly, so maybe already in the third line, there is a mistake.

I'm afraid the proof looks wrong to me because the initial integral is not real (negative values inside the ln). But he needs it to be real for his argument.

Forget it, it's all fine, no negative values!

Bernard Doherty I love this phrase!! Thank you. And I think that will be the perfect title of this video too! : )

Bernard Doherty I will change the "skin" to "brush" so that the cat lovers won't go after me. : )

Thanks for that

rino strozzino thank you!

Doug Rosengard I honestly feel that 3Blue1Brown’s logic in that video is kinda dodgy. Don’t get me wrong though, I love his videos. Especially his essence of Calculus Series.

Just curious where you disagreed with his logic in that video. It all seemed pretty well laid out to me. Also he links to a paper in his description "Summing inverse squares by euclidean geometry" which was the basis of the video

No doubt 3brown video on this topic is simply awesome as it triggers the intuition behind the very answer. However, this video is nothing less than amazing for all who loves maths. In other words 3 brown Tries to answer in their every video, "why" certain things are the way it is. This video tells how you get there. I enjoyed both

Obed Garza I was nervous trying to make sure I could fit everything on the board, as always : )

Thank you : )!!!

Unknown Entity : )

YES!!!!

"don't you have to prove its absolutely convergent?" That would be a shame since the series is not absolutely convergent.

@@martinepstein9826 Why? Is absolutely convergent different that just convergent?

@@createyourownfuture3840 They're different. The simplest example of a series that's convergent but not _absolutely_ convergent is 1 - 1/2 + 1/3 - 1/4 + ... This converges to ln(2) but if you take the absolute value of each term you get 1 + 1/2 + 1/3 + 1/4 + ... which diverges.

@@martinepstein9826 Oh...

@@martinepstein9826 Is that what he meant with “absolutely covergent”?