Unsolved Problems in Calculus

[@rtg_onefourtwoeightfiveseven]

The fact that you put the most important open problem in mathematics second in the video (as opposed to first or last) just tickles me for some reason.

[@caspermadlener4191]

The first and fourth problems are generally understood as problems in algebra, not analysis. The derivative is here just the linear operator sending xⁿ to nxⁿ⁻¹, for n non-negative integers. Someone under this comment made the valid point that these problems are still very likely to be solved using analysis. Most algebraic problems have the nice property of being true in "general" (char 0) if and only if they are true over the complex numbers.

[@mm18382]

Was just about to say that. As much as I enjoy the author's videos, confusing calculus with algebra reveals a poor understanding of maths Especially given that the author mentions himself the generalization of Casas-Alvero to fields of char 0. Which is clearly not calculus-related

[@jamesphillipturpin1452]

​@mm18382 From what I gather (I could be misinformed) even generalizing to complex numbers makes it unsolved. So there is an unsolved complex analysis problem, even if that is not the most general case of the unsolved conjecture.

[@tepsoram]

It seems that the conjecture is false in fields of prime characteristic and moreover, if it is true over the field of complex numbers, then it is true for all fields of characteristic zero. (See EMS Newsletter of June, 2011, available online). These are apparently the main reasons for regarding it as a problem most likely to be resolved by analytic rather than algebraic methods.

[@caspermadlener4191]

@@tepsoram Completely valid point, I had to change my comment.

[@caspermadlener4191]

@@mm18382 Actually, the case over the complex numbers turn out to be equivalent to the general case, so analysis can still be used!

[@dewaard3301]

I love how your videos jump right into the topic. No 'skip the first 1/3rd of any video' or any such nonsense.

[@blakegundry]

You used a picture of Fourier instead of Navier, just wanted to let you know

[@XoPlanetI]

Apply Fourier Transform to get Navier's pic

[@jsalsman]

Is "ODE" really pronounced ode? I've only heard O-D-E (like P-D-E).

[@ThoughtThrill365]

haha, no.

[@breadmemes9502]

how are you verified at 130 subscribes

[@empmachine]

Yea.. Initialism, not acronym.. IMHO

[@paravalent7974]

youtube employee​@@breadmemes9502

[@ugniusmonkevicius9544]

6:33 That's J. Fourier not Navier

[@Kero-zc5tc]

Only 3 comments I see mentioning vid did something wrong 💀

[@stevenfallinge7149]

Seems like everyone's wanting to flex or something.

[@umbraemilitos]

O.D.E. it is an initialism.

[@AKA-f7p]

Navier is Fourier?! Why did you just paste Fourier's portrait when representing navier? Why????

[@FullPwned]

Who the fuck says ODE like that? Every single person I have met says O, D, E.

[@AngryArmadillo]

Small correction for the Jacobian Conjecture: The function f must itself be a polynomial.

[@Daniel-gx4zx]

There are more unsolved problems than the ones presented here, the is one sitting on my desk and you didnt talk about it.

[@RigoVids]

love the video, minor note on the animations, the text sliding up from a white mask effect seems to clip off the bottom of some hanging letters, in particular it's noticeable with the many y's in equations. See the Navier Stokes portion of the video for reference. Otherwise loved the video!

[@dex2234]

Ive never heard ODE pronounced like that lmao

[@sinx2247]

Why is no one mentioning that literally none of these problems are in Calculus

[@glebdrozdov3204]

The first one is

[@lepidoptera9337]

@@glebdrozdov3204 No, it isn't. Calculus allows for smooth deformations of functions. A deformation of a polynomial is not a polynomial. The first problem is more likely an algebra or number theory problem. It is definitely not something one can solve with methods from calculus.

[@richardtrager7125]

The Navior-Stokes Equations are literally differential equations

[@lepidoptera9337]

@@richardtrager7125 Yes, and you need methods from functional analysis to get anywhere close to the solution of Navier-Stokes related problems. At least historically calculus and functional analysis are NOT the same field. The AI (or the stupid kid who wrote this video) doesn't know the first thing about mathematics.

[@projectseven2727]

​@richardtrager7125 it's a fluid mechanics/ transport phenomena issue, not a math one

[@TheDavidlloydjones]

Louis: lou-ee; not lou-eeze. The latter is Louise, a women's name.

[@marcelob.5300]

Perhaps Louis was having seconds thoughts about his gender? Great catch, but I'd accept him pronouncing it as "Jeronimo" or even "María Antonieta", lol.

[@jocabulous]

Pretty sure the script and audio is ai generated anyway

[@dyip-vb1wl]

Shut up no one cares

[@isavenewspapers8890]

@@jocabulous We can come up with more original insults, now can't we?

[@emanuellandeholm5657]

Never heard O.D.E being pronounced as "ode" either. It's always oh dee eeh. Who/whatever narrated this video doesn't really do math. Which is fine

[@linny356]

hey guys does anyone know what the weird * thing is doing between m and n? i heard it stands for multiplication but idk

[@0_Matthiasss_0]

It does indeed stand for multiplication, but it's not usually used when calculating on paper. You can see it more often in programming, or in Excel

[@OtherworldlyYTP]

Love these videos! ❤ Honestly helping me to understand math more

[@ShatteredXeno]

1:04 How can you say all that when you haven't defined _f_ ?

[@mathematicskid]

what?

[@ShatteredXeno]

@@mathematicskid _f_ is a variable, no?

[@mathematicskid]

@@ShatteredXeno no f is a function

[@whatitmeans]

I didn't understand the first one... If I make the following smooth bump function f(x)={0, |x|>=1; e^{x^2/(x^2-1)}, |x|

[@gaetanl5590]

The point is that f is supposed to be a polynomial :)

[@elpman001]

The primitive equations of meteorology which I know are related to Navier Stokes. I think it is still worth mentioning

[@Tuv_Certified_Ehrenmann]

Affine and linear are two different things, all linear functions are affine, but not the other way

[@Ownageffects]

the reimann hypothesis : complex analysis and number theory

[@alacastersoi8265]

I learned a lot in this video

[@ambasing_omaygot]

I don't think Navier is Fourier

[@xovi4902]

casas alvero is solved afaik, recall something in arxiv by one "cesar massri" or something similar

[@sinx2247]

Paper was retraced

[@xovi4902]

@@sinx2247 That's what i get for going off arxiv preprints lol. Shame

[@na1edawg]

It's good to know that there are only 4 unsolved problems in calculus. Also surprised to see how much of calculus doesn't involve any calculus.

[@lepidoptera9337]

Yes, this was the worst math video that I have seen in a long time. It should be deleted.

[@dewah7775]

Yep, I thought he might have confused calculus for mathematical analysis, but the first problem seems more like number theory. Lol it's like one of my English professors who said my math professor "really bragged about me in calculus"(it was a linear algebra class).

[@lepidoptera9337]

I have no idea why the Casas-Alvero conjecture is supposed to be a problem of calculus. Calculus requires that we can modify functions smoothly in a neighborhood of any point. Such a modification leaves the space of polynomial functions and thus invalidates the assumptions of the conjecture that f is a polynomial function. In other words, the polynomial functions are not covering the space of all functions. Not even remotely close.

[@zakialmahin7278]

Do more of these math content. From my viewpoint they are way above your nonmath content.

[@rejectiomundi]

You put fourier as navier

[@septicstache9625]

I don't get how I used to understand each step in these functions and was able to solve them in math class in highschool 😭

[@shubhamkhare7]

This comment section is extremely intellectual and I love it! No shitty BS by random dumb folks...

[@Mathislife-sv2fe]

Why is Fourier, Navier?😂

[@alphazero339]

Why is every single comment saying whats bad about the video are they bots?

[@newwaveinfantry8362]

People are just correcting mistakes.

[@TheTimerOfLife]

0:42 TWO FROM TPOT>!>!>?!?!?

[@TheTimerOfLife]

AND X!?!>!>!

[@marcelob.5300]

Wonderful!

[@lumbersnackenterprises]

Assuming I solved the Riemann Hypothesis (Routine Distribution of Prime Numbers) do you know anywhere I could submit my Paper

[@SanAleksiusII]

Just send it to me and ill take care of it (;

[@lumbersnackenterprises]

@SanAleksiusII I've got my work posted on my channel. It's got something to do with the Square Root of 2 in relation to how Unary works. It's the only possible reason why -1 plugged in for s shows -1/12. The one I definitely solved is Prime Number Distribution which has to do with incremental increases and compounding. Super easy and I've proven it out to 1000 places, it functions because Gauss's Eureka Theorem is proved true.

[@SanAleksiusII]

​@@lumbersnackenterprisesIll check it out, thanks!

[@dewah7775]

Bruh, take your meds. But if you are interested, there are formulas for calculating primes, although very tedious. All that being said you didn't prove anything at all in your videos. You just sort of ramble and look at specific cases, a very tedious and actually impossible process to prove something(literally about something that's infinite lol).

[@Christopher-e7o]

X,2x+5=8')

[@Darkev77]

This video is absolutely brilliant and well put. What are kids in the comments on about?

[@kasufert]

A FINE

[@arnoldtorazzi632]

Funny math its so easy

[@x88.berkay]

cool

[@harkevicsGD]

4h ago das crazy

[@bigbigx2250]

Linear and affine are not equivalent you husk

[@FunctionallyLiteratePerson]

I have never heard anyone say it like ode, just like o-d-e

[@seanstuchbery]

what tf is blud wafflin about😂

[@markshiman5690]

I know you're a new and growing youtuber, but having some personality would help.

[@jacobwilson8275]

Take your own advice. Being a rude comment troll isn't a personality

[@paolarei4418]

​@@jacobwilson8275he wasn't even rude😭

[@jacobwilson8275]

@@paolarei4418 saying "have some personality" is rude.

[@paolarei4418]

@@jacobwilson8275 well you have none

[@jacobwilson8275]

@@paolarei4418 someone feels mad about being corrected. Get a life

[@logicmass621]

It would be nice to incorporate more storytelling, although perhaps you just value conciseness.

[@lepidoptera9337]

If I had to tell a story about this, then it would go like this: "Dude who doesn't understand math made a math video. Dude might have been an AI. The whole thing sounds like a hallucination."

[@tkz4_on_osu295]

@@lepidoptera9337it’s an AI video.

[@lepidoptera9337]

@@tkz4_on_osu295 It probably is. There is so much AI nonsense on the internet now it's not even funny. I keep testing AI but it's not getting better. I think we have reached peak stochastic bullshitter and there is no there, there.