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At first I was amazed that he can do backwards writing so neatly. Then realised he just flipped the video

Mathematicians: Look at my integral of my dreams.
Physicists: Cool. But does that serve any purpose?
Mathematicians: NO, but look at it. It's so magical. ;p

Holy cow that’s the prettiest integral I have ever seen

Wow, this guy is both left handed and can write backwards! How rare!

Never have I understood "Sufficiently advanced math is indistinguishable from magic" more than this very moment.

2:40 dude nice thank you for being aware that you can’t just interchange infinite sums and integrals willy nilly.

The screen inversion to get his writing right totally blown my mind to the point that I’m unable to focus on what he says.

As an engineering student my first instinct was to use a euler's method of approximation cause "fuck that work" LOL

That was NOT the result I was expecting form this. Absolutely beautiful

Damn i got stuck watching this video and the integral of e^-x^2 in loop because at the end of each video the guy says “click on the video on the screen” and its an infinite loop :D

What's most fascinating is the way he looks to be writing from right to left for us. It's surely inverted but stil.. Thanks for the vid

Nice result, but now you should explain what is the value of the infinite sum 🛡️

the pause at 5:50 was so relatable haha struggling to do simple differentiation after doing many things that are a lot more complicated

Wolphram Alpha says the final sum is approximately:
1.2912859970626635404072825905956005414986193682745223173100024451369445387652344555588170411294297089849950709248154305484104874192848641975791635559479136964969741568780207997291779482730090256492305507209666381284670120536857459787030012778941292882535517702223833753193457492599677796483008495491110669649755010519757429116210970215616695328976892427890058093908147880940367993055895352006337161104650946386068088649986065310218534124791597373052710686824652246770336860469870234201965831431339687388172956893553685179852142066626416543806122456994096635604388523996938130448401015323385569895478992261465970681807533429122890910049951364103584723741679660994037428872280908239472403012423375069665874314768350298347009659693019807122059415474239188849548892043147840373896935928327449373018601817579524681909135596506205768427008907326547137233834847185623248044173423385652705113744822086069838116970644789631554803110868684680780701057034230000954776628299270222642661822130291609344850492556799951212817650810621807347685511270748919272166418829000073661836619726956875357964537813752368262924072016883803114377731170

uniform convergence is not sufficient to invert limit and integral, because the integration interval is not a segment (ln is not defined as 0)

we need more integrals like this, this is amazing

"He will never cancel the n!"
spits out cereal

I was thinking you must have practiced writing backwards, but you could also have reversed the video right-to-left.  Very sneaky!  Love your work.

Something that surprised me more than the continuous sum being equal to the discrete sum is the bounds of those sums.
The continuous sum of x^(-x) from 0 to 1 equals the discrete sum of n^(-n) from 1 to infinity... SAY WHAT?!?!?