I'd say P vs NP is the easiest, Riemann hypothesis is understandable in the sense that its statement is not too technical, but understanding why it is important is another matter. NS smoothness is probably understandable to the average math or physics nerd who has seen some PDE's. The rest require developing more machinery to even state the problems.
this post was submitted on 18 May 2025
28 points (96.7% liked)
No Stupid Questions
40895 readers
1002 users here now
No such thing. Ask away!
!nostupidquestions is a community dedicated to being helpful and answering each others' questions on various topics.
The rules for posting and commenting, besides the rules defined here for lemmy.world, are as follows:
Rules (interactive)
Rule 1- All posts must be legitimate questions. All post titles must include a question.
All posts must be legitimate questions, and all post titles must include a question. Questions that are joke or trolling questions, memes, song lyrics as title, etc. are not allowed here. See Rule 6 for all exceptions.
Rule 2- Your question subject cannot be illegal or NSFW material.
Your question subject cannot be illegal or NSFW material. You will be warned first, banned second.
Rule 3- Do not seek mental, medical and professional help here.
Do not seek mental, medical and professional help here. Breaking this rule will not get you or your post removed, but it will put you at risk, and possibly in danger.
Rule 4- No self promotion or upvote-farming of any kind.
That's it.
Rule 5- No baiting or sealioning or promoting an agenda.
Questions which, instead of being of an innocuous nature, are specifically intended (based on reports and in the opinion of our crack moderation team) to bait users into ideological wars on charged political topics will be removed and the authors warned - or banned - depending on severity.
Rule 6- Regarding META posts and joke questions.
Provided it is about the community itself, you may post non-question posts using the [META] tag on your post title.
On fridays, you are allowed to post meme and troll questions, on the condition that it's in text format only, and conforms with our other rules. These posts MUST include the [NSQ Friday] tag in their title.
If you post a serious question on friday and are looking only for legitimate answers, then please include the [Serious] tag on your post. Irrelevant replies will then be removed by moderators.
Rule 7- You can't intentionally annoy, mock, or harass other members.
If you intentionally annoy, mock, harass, or discriminate against any individual member, you will be removed.
Likewise, if you are a member, sympathiser or a resemblant of a movement that is known to largely hate, mock, discriminate against, and/or want to take lives of a group of people, and you were provably vocal about your hate, then you will be banned on sight.
Rule 8- All comments should try to stay relevant to their parent content.
Rule 9- Reposts from other platforms are not allowed.
Let everyone have their own content.
Rule 10- Majority of bots aren't allowed to participate here. This includes using AI responses and summaries.
Credits
Our breathtaking icon was bestowed upon us by @Cevilia!
The greatest banner of all time: by @TheOneWithTheHair!
founded 2 years ago
MODERATORS
Maybe easiest to wrap your head around but certainly the hardest. Heh
Navier–Stokes existence and smoothness
Is actually every easy to understand. NS is the basic fluid dynamics equation, it describes how fluids move.
Never mind the actual equation, you can think of it as "speed" depending on "pressure" and "inertia". We can use it in parts, in CFD, which is splitting the problem into very small pieces and calculating the pieces and then adding them up bit by bit. But that is super expensive to calculate, not as precise as we would like and difficult to understand.
We would really prefer an "analytical" equation like position = speed * time. The process to get there is usually the integral operation. That's what the problem is all about.
The problem with the equation we have, is that "pressure" and "inertia" variables are so mixed up in the equation, that we can't do that integral operation on the equation we have. You end up with something that's like
y/x = (y/(x-y)) + x
and
x/y = (x/(y-x)) + y
Idk if that explains anything if I put it like that... You can just look at the whole thing https://en.wikipedia.org/wiki/Millennium_Prize_Problems#Navier%E2%80%93Stokes_existence_and_smoothness
Both sides of that equation describe the same thing, one with forces and pressures, one with measures of speed and time. But BOTH sides contain both space and time parts.
The pieces are interlocked in a way, where we can't isolate variables, can't get an integral.
Understanding NS itself isn't that hard either, but I couldn't do it just from wikipedia, if you have a bit of help guiding you through it, it's not that complicated.
The problem is finding / proving that an integral exists and is smooth.
As for how hard it is and how useful it would be, the 1$ million are a joke. The solution is worth billions and billions.
And the problem is old.
The equations were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
Navier-Stokes
Just reading this gave me PTSD from my days in school