Doing the World's Hardest Integral (joke video)

[@eigenchris]

It is my belief that math and video game speed running have a lot in common. Both are studied by people who have a strange absurd level of dedication, and both have experts who manage to discover incredibly complex tricks, which are then relayed to the community, refined by others, and then used to pull off even more complex tricks. In this way, doing integrals reminds me a lot of doing glitches in video game speed runs.

[@dantereinhardt6911]

That is a fair comparison, and I really liked your video.

[@jefferybenzos5879]

Does this integral have an actual solution? I couldn't find anything online so I was starting to suspect that it's nonelementary but I'm not sure, also amazing video

[@eigenchris]

I didn't see a solution after a quick google, so if the solution is elementary it's probably pretty hard. I'm not sure if it is or not though.

[@Daniel_VolumeDown]

@@jefferybenzos5879 so I typed this integral in wolfram alpha and it shows solution in form.of series

[@JosephStalin-yk2hd]

Is there a rigorous proof of this specific integral?

[@tiltltt]

With one video you managed to recreate exactly how it feels to study math, congratulations.

[@markojojic6223]

I honestly feel like only he has the sheer prowess to focus on this exactly like a radom bro gamer looking at 20-year old Futurama jokes.

[@phitsf5475]

All the Calculus fundamentals in 5 minutes or less. Amazing work.

[@cykkm]

Alas, that's too optimistic. Matrix glitches for some integral forms have not been discovered yet...

[@signorellil]

Wow. It began as a standard April's Fools joke and ended up as my own take of what could be the Calculus Version of the Legend of Zelda!

[@mastershooter64]

zelda calculus :)

[@cykkm]

@@mastershooter64 Yay!!! Kudos to Zelda Calculus!!! Love it!

[@Aequorin628]

4:36 This would have been the PERFECT place to have said "and this was, of course, discovered by Ramanujan." It feels like he's always popping up in the most random places.

[@nicholasleclerc1583]

Euler : Finally, a worthy opponent; our battle will be imaginary !

[@johnchessant3012]

as an integral connoisseur, I learned some new techniques in this video which I will be adding to my toolbox for when I engage in my hobby of creating horrific integrals for math stackexchange people to solve

[@somebodyhere3160]

wait..... those integrals were created by you???????

[@Wabbelpaddel]

Wow, Satan must be a huge fan of you

[@jackmccarthy7644]

I love that at 1:46 the fake wikipedia article describes the whole rest of the video. Hilarious video.

[@eigenchris]

Thanks. I feel like a lot of my prep for this video was typing out fake text.

[@jameeztherandomguy5418]

@@eigenchris "Redirected from 'Calculus-Induced Depression'" LMAO

[@martiddy]

I didn't even know it was a fake article until I read your comment.

[@RMGamer31O]

I also like the page at 3:09 about time paradoxes

[@Ganerrr]

there's no way i actually looked up desmarais thinking that was a about to be a real trick 💀

[@bantix9902]

same, he got me good

[@rickmcn1986]

I spent so long trying to google Desmarais's theorem before the penny dropped.

[@stevenglowacki8576]

I knew about the squaring of the Gaussian, and it made sense that you started with something that was real. You really got me with the next few steps; I was a bit confused about how the Desmarnes or whatever theorem could possibly work, especially with the list of the adjoints, but I somewhat accepted that it was real along with the next step or two, because I thought you were intentionally using real, obscure, but ultimately unhelpful things to continually transform the integral into something more complex before going "I'll cover the rest in the next video". I was not expecting the turn that you went down. I also follow speedrunning a little bit, and I agree that there are many aspects of it that are very similar to advanced math and physics. I particularly like when people do deep dives into the video game physics in a way that treats it just like a math and physics problem in an alternate universe with different rules. Bismuth even gave a talk somewhere about how the problems solved in speedrunning were in some ways similar to problems in real physics, and they provided useful toy models for people to practice their analytical skills. I'm guessing you saw it, though that was after this video was published.

[@eigenchris]

Yeah, that squaring-gaussian bit is basically the only non-lie in this video. I don't actually follow speed-running that closely, or know who Bismuth is, but I've watch a couple breakdowns of how certain glitches work, and many of them seem like things you'd need a PhD to come up with.

[@stevenglowacki8576]

@@eigenchris Bismuth's talk was at "Big Techday 22" so searching for that with his name on youtube should lead you there quickly.

[@poutineausyropderable7108]

When Chat GPT generates a solution.

[@zestyorangez]

lmao

[@VegaAltair-wj5tr]

lmao, true

[@yudanoh6822]

Even though it's writen joke video in the title, had me in the first half not gonna lie. Great video love all the Easter eggs (I could find), my favourite is the amount of equal signs in the code.

[@Avighna]

I recognised the inverse square root algorithm haha

[@bend.n]

never trust javascript

[@tomkerruish2982]

It's good to be cautious of Ketter polynomials, considering that they are Keter-class SCPs.

[@Saturos02]

So I've been struggling with Gilgamesh all this time and you're telling me there's a skip?!

[@quantumhorizon7514]

Can't you just Dumbledor transform the integral into a second order ODE involving hte Gandalf operator?

[@eigenchris]

The Dumbledore transform only works for harmonic functions, though.

[@BS-bd4xo]

Bro, the first half was so believable 😭

[@artey6671]

Well, that was cruel. You made me wish that Desmarais's theorem, adjoint functions and Baker-Nachbaur type are a thing. I guess even in mathematics, if things seem too good to be true, they probably are. I appreciate your creativity, though. You might need a few more = signs at 4:01, though. Six signs only check for equality, identity, memory address, system time and RNG seed, so someone with a different IP address might encounter a bug which you didn't catch.

[@karolakkolo123]

Damn it, I really believed the Desmarais's theorem is a thing

[@commentingchannel9776]

At 4:01 too, lovely reference to the Fast Inverse Square Root algorithm (first two lines)

[@artey6671]

@@commentingchannel9776 We probably all watched Nemean's video, right?

[@narfwhals7843]

I'm sorry if I'm missing something but why don't we just do a wrongwarp to page 251 and then load the corrupted save to put the solution into our inventory? Is the setup TAS only?

[@eigenchris]

That's a better approach in theory, but it's pretty precise. Only 4 people have managed to execute it without a TAS, and they each have at least 1000 hours of integration under their belts.

[@eigenchris]

@@nicholasleclerc1583 Yeah, that was a big shame. I'd like to state that the eigenchris channel stands against cheating in all its forms. I hope Two learns from this and grows as a person.

[@mariofeds1101]

Im going into your joke videos as a highschool physics class and i gotta say you say some real funny words, i hope i understand them some day

[@pdsm1552]

After a degree in physics and some self study in maths, nope still don’t understand most of it 🤷🏾‍♂️

[@shufflecat3334]

I'm working on a particularly difficult math problem which has to be solved to get at an even more hard to acquire solution for a project I'm working on. This video pretty much sums up how I feel right about now.

[@Caspar__]

I was looking for the Desmarais theorem but I only found one about rings. Now I realized that the theorem doesn't even exist.

[@aidangarvey7049]

Damn even as someone who cleansed my mind of integration as soon as I finished the calc courses I needed, I got like 4 programming jokes out of this.

[@idaho_girl]

I'll have to check but this just might br the integral I've been needing for some of my physics research calculations!!! Thanks!

[@dor00012]

That escalated quickly

[@dancoroian1]

"...okay, and the ziggurat has appeared," so nonchalantly and almost *immediately* after beginning to focus on Aya, just killed me 🤣

[@mitchellschoenbrun]

I did see the text "(joke video)" but even so you had me going for a while. I thought you were serious about solving the integral. It all seemed serious until 1:39 where the Desmarais's theorem is introduced. I have no doubt that it is a real thereom. I was taken aback by the statement that the theorem was part of a Calculus 2 class if you just go back a couple of decades. Since I've been familar with Calc 2 for more than 50 years and have never run into to, I'm wondering if that is just part of the joke or I just somehow missed it.

[@eigenchris]

Everything in this video is made up, except the Gaussian integral at the start. I guess my monotone delivery lends credibility to what I'm saying even though it's all fake.

[@mitchellschoenbrun]

@@eigenchris You are quite right. You must wield this super power judiciously.

[@tariq3erwa]

And I thought I 've overcome my Integral anxiety, turns out there's more

[@Tekkerue]

This is the best calculus speed run tutorial I've ever seen. Thank you!

[@NoNameAtAll2]

I was waiting for sudden warped spacetime glitches with a slight mix of quantum gravity, but simple buffer overflow might be okay too

[@FranciT98]

I expected a shitpost, instead I got art. And developed a mild phobia of double integrals.

[@DeathGeco1000]

Seeing the source code for the physics engine made me laugh.

[@DeathGeco1000]

...and we never saw the solution to the primary question...

[@bantix9902]

The tutor in my physics exercise actually recommended your channel to me :)

[@user-yk7mp8yp8x]

i have actually waited months for this video... literally every day for the past 2 weeks awaiting eigenchris april fools vid.

[@snah70]

Haha, that was actually quite a good impression of Michael Penn's style. 🙂

[@siquod]

I think there is a theorem stating an integral has an analytic solution if and only if it is wolfram integrable. But the free version is in permanent alpha, and paying for your integrals is poor sportsmanship.

[@homerthompson416]

I used Feynman's Leibniz rule to differentiate under the integral sign, and strangely enough the answer was one over the fine structure constant to first order.

[@alankuo5579]

Evaluating one hard integral is better than evaluating many simple integrals.

[@ritemolawbks8012]

Calc IV? That's violates the Geneva Convention.

[@albertoreyabuelo2504]

Incredible applicatoon of Desmarais Theorem, but you forgot the +c in the integral to enter the temple. Eveyone shall pay for their sins in the afterlife...

[@rubixtheslime]

Decided to try out the game, only problem is I don't have a computer, only a deck of Magic: the Gathering cards. Which we all know is identical to a Ryzen 3990X in computational abilities, but I forgot how to do it. So I just set up my deck to evaluate lambda calculus expressions, then made a lambda calculus expression to simulate a Turing machine. Though I'm not very good at Turing machines either so I then set up the Turing machine to simulate the game of life. From there I was able to make a redstone engine in life, which I am much more familiar with, so I was able to finally create a quad core CPU and an RTX graphics card, and the game's running very smoothly! I Was especially surprised at how much content there is, I'm hundreds of hours in and I just got to the "o" level on the loading screen!

[@hitoshiyamauchi]

Wow. When I was a university student. I had a PC-88MA2. The memory map is a bit different from PC-88MA2, but I see one of the PC-88 machines. I still recall when I wanted to access the VRAM I use out c. First I need to change the stack pointer since when you change the memory bank you lose the stack pointer after xc000. (Probably no one knows what I am talking about.)

[@estebantapia1225]

I had to look if Desmarais Theorem was an actual thing haha

[@steffenbendel6031]

Alternatively you could try to resurrect Feynman and integrate under his grave.

[@MochiClips]

Ah that was really good I'm glad that integral was integraled 💪💪 thank you gilgamesh

[@signorellil]

I'm so stupid I've checked the Wikipedia for Desmarais Theorem!

[@oskarjung6738]

You are not stupid. You have just been used to some of the most use less theorems and identities that is there in existence, that you don't even question it anymore. Which means you are a battlehardened mathematician. And thus very smart.

[@tomkerruish2982]

If you freeze frame the video, you'll see that the theorem is a redirect from "Calculus-Induced Depression." ngl, I wondered about it myself.

[@chattava]

Cheers Chris, awesome work as usual.

[@QuantenMagier]

This reminds me of how I helped a friend with her Analysis homework and I did a whole 2h detour with her to Pascal's triangle to find the 8th roots of unity before I found an easier 5min solution where you just had to calculate the absolute value.. xD

[@QuantenMagier]

@@Batwam0 Well she thought she understood it and took some notes, but when she was home again to write down her homework she didn't understand her notes anymore.. xD

[@xiaohuwang4173]

Now I know how it feels to be an ordinary person sitting in a math class

[@sphakamisozondi]

Bruh, where's the solution? WHERE'S THE SOLUTIOOOOONNNN?!

[@theoriginal639]

1:45 "The integral can be computed using the method described in the Gilgamesh Codex." Rofl

[@timeodaneosetdona]

Solving an equation to gain access to a dungeon is giving me flashbacks to a dream I had the night before a Linear Algebra exam. In my dream, the only way I could go anywhere was to find the correct linear transformation of my personal position vector. I woke up exhausted but I did do well in the exam....

[@alejrandom6592]

Not me thinking "oh I wanna learn more about these ketter polynomials" 💀

[@parthdeshpande2966]

Lmao you had us in the first half ngl till the squaring of the integral. Then you lost us.

[@ToriKo_]

Wow I love how far this video went off the deep end, after it already went off the deep end

[@teqnify63]

“lawn”

[@voltmatrix1250]

I like your funny words, magic man

[@angeld23]

4:02 the 2 lines of fisqrt at the top for no reason is sending me

[@notsojharedtroll23]

Did not expect the Fast Inverse Square root on that JavaScript code

[@manuc.260]

"there's actually another way to gain access" made me literally spit out my drink, thanks 🤣

[@jackkalver4644]

The gamma function in the derivative of an elementary function

[@eklhaft4531]

Just like a normal lesson in college I have absolutely no idea what's going on xDxD

[@crowbar_the_rogue]

"Some of you have probably spotted this is a perfect opportunity to use the Desmarais's theorem ..." Yeah ... sure ....

[@sardarsaad4018]

i am in middle school. you have shown me a truly haunting world.

[@devoidsloth]

The scary part Is I have so little idea what’s going on I’m just like, “mhm, looks good to me”

[@reformierteapologetik5166]

This reminds me of some of my math lectures..

[@orktv4673]

This is the type of content I am subscribed for. I mean, besides the usual good math/physics content.

[@dino2808]

this video is amazing but what i like most about it is looking up "desmarais theorem" gives you suggestions like "desmarais theorem integral monotonic function" and in duckduckgo leads to the wiki article of monotonic functions. am i missing a bigger joke or did this video solely trick so many people that search engines are now fucked too?

[@eigenchris]

That's funny. There's no bigger joke. It's just something I made up.

[@dino2808]

congratulations then for manipulating the algorithm lmao @@eigenchris

[@duck5332]

this channel is a gem stone

[@longsarith8106]

Hello teacher, when you start your cosmology?

[@eigenchris]

Hopefully the first one will be posted by Monday. Just need to make a couple more edits to the 110a video.

[@anibalismaelfermandois6943]

Love the evil bit hack reference

[@SNTz55]

Bro introduced doom to calculus 💀

[@royalredbird9717]

I'm an 11th grade, and understood nothing

[@windigo1592]

Every math tutorial ever

[@pra.]

I checked the internet for 5 minues for Desmarais despite reading the title

[@MynameisS_A]

4:01 As a programmer, the comments in the code had me dying. 😂😂

[@mp3lwgm]

WolframAlpha evaluated this integral as a series in less that 1/10 th of a second.

[@venkadesansumathi4373]

That escalated too quickly...

[@MGoebel-c8e]

Lol, the one thing that is missing is giving Math505 the credit he clearly deserves.

[@leyasep5919]

4:01 oh, you made me lol even more with the inverse FP square root trick...

[@dyachenkotimofey6682]

WHEN IS HE GONNA CONTINUE GENERAL RELATIVITY???

[@rubixtheslime]

_yesterday_

[@dyachenkotimofey6682]

@@rubixtheslime I really miss it

[@rubixtheslime]

@@dyachenkotimofey6682 it was a joke

[@justmath331]

Wow can we actually square integrals?

[@eigenchris]

The trick for squaring the gaussian integral does actually work. It's basically the only thing in this video that isn't nonsense.

[@justmath331]

@@eigenchris thanks

[@lucianchauvin8587]

lmao the quake code

[@matkosmat8890]

Dang! I hadn't spotted the monotonic function!

[@natepolidoro4565]

I'm actually curious about who that old guy in the picture actually is

[@eigenchris]

Not sure. I think I just searched for an old stock photo from the 1800s. A photo with him and a woman (probably his wife) is on a number of websites, including this one: imagerestorationcenter.com/why-didnt-people-smile-in-old-photos/

[@albertdotd]

But actually, this integral is unsolvable in elementary functions, right?

[@eigenchris]

As far as I'm aware, that's correct. I didn't look particularly hard for the real answer, though.

[@epikherolol8189]

Me 17: Yes i totally understood everything 😢

[@Gaaaaaaabrrrrrrriel]

As a new engineering student, I have no idea where the joke is, because I can't understand fuck all just like in a real class

[@__hannibaal__]

Why I never heard about G.Desmarais

[@LukeAps]

I dont know math, and this was helarious.

[@77thTrombone]

ROTFL, eigenDude. I would not have known about the G-skip, since (as memory serves,) my engineering-oriented curriculum went from Calc III to Differential Equations, and thence into Advanced Calc. I expect that R-ballery can accomplish the same topological shunt, as long as we can identify the necessary n-space to transform. This would more reliable, as your solution is dependent on game version. Stories of integrators finding themselves in various places _other than_ the textbook room are amply documented in Usenet. (Although the bidet incident remains controversial.)

[@Charlieee1]

(Redirected from Calculus-Induced Depression) on the wikipedia (1:45) article. :)

[@Charlieee1]

and the code at 4:05 :)

[@Charlieee1]

============

[@vivada2667]

wtf did you make a fake textbook too in addition to the seven theorems and the wikipedia article

[@jensphiliphohmann1876]

The last sentence is pretty hilarious. 😂

[@justroomdecor9498]

Damn from calculus to cs..

[@bautibunge737]

Men, I haven't noticed it was april fool until now

[@alejrandom6592]

This is art Mr. Autochris

[@André-b3w]

I love it because Mesopothamia is kinda the Math's birthplace

[@oakleypankratz8547]

I don’t know where the math ended and the nonsense started and that’s scary

[@theonlinezone6904]

next video : collapsing the wave function with the Gilgamesh skip

[@kingplunger1]

you had me for like the first minute or so ^^