can you guess the tricks?

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[@rubenverg]

as usual, my guess is "adding zero" and "multiplying by one"

[@talastra]

Heeh ...

[@sleepycritical6950]

My guess would have been to divide by one though sooo

[@talastra]

I like to watch your videos, although they're often so far beyond my knowledge that it's like watching a professional athlete do things I can't grasp how they're done. I appreciate all you do, and I wish I could see more number theory. (I know about alll the videos on the o ther channel).

[@gavasiarobinssson5108]

Yeah. Too difficult

[@johnchessant3012]

wow, the 24 was carefully chosen so that we get a perfect square in the denominator at 14:04, neat! is there any connection to the Ramanujan tau function?

[@bobsmith-ug6zo]

Does this integral have something to do with conformal field theory on a torus? I swear I’ve seen it somewhere before

[@talastra]

No, I cannot!

[@yoav613]

You are not the only one

[@MartinPerez-oz1nk]

THANKS PROFESOR !!!, VERY, VERY INTERESTING !!!!!

[@michaelslack8900]

Is there a way of motivating the use of the triple identity here? Or is just one of those out-of-a-hat things?

[@DeanCalhoun]

I think the point of the video is to introduce the triple identity, and the problem is given as an example of its use

[@rafaelfreitas6159]

This is such a serious business that I'm positive the pentagon could be involved! ;)

[@F-S.]

Question from a non-mathematician: If you put y=1 in die final sum do you get a geometric series with the squares as exponents (1+x+x^4+x^9+ ...)?

[@Noam_.Menashe]

No, you get Jacobi's function.

[@garrettthompson3286]

1+x+x^4+x^9+... is not geometric because the common ratio is not the same (it goes from multiplying by x to x^3 to x^5)

[@F-S.]

@@garrettthompson3286 Is there a name for a series which exponents follow a rule and which are not geometric?

[@violintegral]

Why is this video unlisted?

[@itzerr5547]

Plz try this one : find all natural number n such that, 2019+n! is a perfect square.

[@Alan-zf2tt]

Brilliant!

[@rainerzufall42]

13:26 (-1)^n, not m

[@rainerzufall42]

... all m are n

[@minwithoutintroduction]

رائع جدا كالعادة 🎉

[@gavasiarobinssson5108]

Eulers formula?

[@sukendebnath162]

Cooool

[@rainerzufall42]

18:20 cos 30° = 1/2 sqrt(3), sin 30° = 1/2 => 2/9 \pi² sqrt(3). There's also a \pi missing in the expression before: \pi², not \pi!

[@leroyzack265]

It is one of the gorgeous integration result I've ever seen 😮

[@rainerzufall42]

dq = - e^-x ??? I have my doubts... nice typo!

[@assassin01620]

What typo?

[@rainerzufall42]

@@assassin01620 If dq eqals - e^-x, then e^-x is infinitesimal small! Correct is: dq = - e^-x dx (meaning q'(x) = dq/dx = - e^-x).

[@assassin01620]

​@rainerzufall42 That's fair

[@assassin01620]

​@@rainerzufall42it's funny, before I posted my first comment, I thought to myself "surely they don't mean the dx, right?"