Millennium Problems: Math’s Million Dollar Bounties
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- Опубликовано: 5 сен 2024
- For those not willing to roll the dice that their mathematical discoveries will be important enough to earn one of these large cash rewards, there is good news. There are a number of specific math problems for which there is a cash bounty given to the first person to solve them. The most famous of these are the Millennium Prize Problems, a set of seven math problems worth $1 million each.
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#MillenniumProblems #sideprojects
I love how weird and esoteric, but also how simple to actually express the Riemann Conjecture is.
"There's this special function; it takes inputs and spits out outputs, just like any function. We're interested in what inputs make it spit out zero. The conjecture says that every input that makes the function spit out zero is either a 'trivial' value (one of a well known family of answers), or, if there be any others, they must be found on a very specific line."
It's that latter part that's the hard part to prove or disprove. All the 'hard parts' of the problem are wrapped up in the consequences of what the specific function we're looking at is... the actual function itself is relatively simple to state, but once you start fiddling with it, it ends up falling right into a sort of 'uncanny valley' of mathematical implications that make actually working with it fiendishly hard.
One of two things could be proven: that there exists a non-trivial input that *isn't* on the special line, but that still spits out zero (probably just by finding one); or that it is impossible to find such a counter example (likely by some kind of proof by contradiction).
It isn't immediately obvious from looking at the problem why it's so important or interesting. Weirdly, it turns out that, if we assume the Conjecture is true, it makes a whole *slew* of other extremely important unknown results (many of which involve prime numbers) effectively 'free'. In a sense, it's a lynchpin that could make or break a *bunch* of other really big-deal maths. This is one reason that a lot of people are *pretty* sure it has to be right, though again, it doesn't actually prove it.
Yes!
You may be interested in some of this man’s current work/research-
Robert Edward Grant
- I believe he already has a proof for the Riemann *hypothesis*, but as you mentioned it’s merely the key/lock or doorway, to a whole slew of new universal constants and understanding of the world around us.
Funny thing about the prime numbers part is the pattern it creates, and the relationship between primes, means that almost all current prime number cryptology encryption and even quantum encryption methods will be essentially obsolete.
(Part of why Robert has Not released everything he has found, is he had created/is working on a new method of encryption that can replace the now compromised methods)
@HuheJass you really sent me down a rabbit hole with that name, but having now learned an enormous amount about Robert edward grant as well as having read numerous of his published papers in full, I feel confident in saying that unfortunately he is not the prodigy which he professes to be. Instead, his significant intellect seems to be tainted with some form of narcissism which results in him being far more confident in his conclusions than he has any right to be. His work on the great pyramid at giza as shown on his website is a prime example of this, showcasing numerous absurd conclusions and his paper on prime numbers is a demonstration in misguided intellectual narcissism.
I was super excited to have found a new genius out there pushing the boundaries of science and humanity, however I can sadly assure anybody reading this that Robert edward grant is definitely not that person, and I wouldn't trust his cryptography nor any of his other inventions/discoveries/assertions in the slightest.
Sorry to burst your bubble 😞 I am just as saddened as you are by this, I assure you.
Edit: Oh, actually I looked even deeper, and he's just a straight up fraudster. Google his name + fraud to learn more, but yeah. Definitely not going to solve any of the millennium problems, is Robert edward grant, I can tell you that much. Lol.
@@HuheJass was he the one in witnail and i?
@@lilbaz8732 No, I’ve never heard of that, but Witnail is a Richard Grant. Robert Grant isn’t an actor, he was the youngest CEO on the nasdaq, made Botox popular (he was president of Allergan Medical at the time), funds a real/working company that’s successfully working on transmutation of elements, and now spend his time bridging current physics theory’s and mathematics with the missing pieces-
A true universal/working theory of physics for everything. Including the math to explain, and eventually manipulate, time, gravity, and space.
Nothing is ever really proved.
Hello. A computer scientist here. Great video! apologies for being pedantic but the correct name is polynomial time not polynominal time.
You're right.
He's unfamiliar with the jargon, and it's a 'cold read' without the generous off-script commentaries found in (eg) his The Casual Criminalist channel.
It's at least correct in the sub
There are a lot of other mispronunciations in this and other videos on this channel. I find it hard to trust he’s done his research on the topics if he hasn’t done the research on the jargon. Not saying he necessarily hasn’t, but it doesn’t inspire confidence. Anybody who has watched any one of thousands of videos on the Riemann hypothesis would know how to pronounce it surely? Or does he learn everything from reading without ever discussing it with others, watching videos or listening to talks? Puzzling.
@@thermidorthelobster4645 Simon does very little, if any research himself. Think about how many channels he has, there's no way he'd be able to research for all of them. He has a team who researches for him, and writes the script. Often during the shoot it's the first time he's reading the script which is why he mispronounces words.
@@kjth2003 agreed he has little if any familiarity with the subject. That is kind of the point. Think of all of his videos as a reaction video. He is reading off a script he intentionally does not read prior in order to give his genuine reaction.
I both appreciate and associate with the "I have no idea what I'm talking about" energy in this video.
@Brian Dawson So basically being omniscience? Feels a lot like that problem is asking if we can become God?
@Brian Dawson Yeah I get you. I don't mean God in a literal sense but having the ability to know everything instantly sounds pretty "God like". I mean, imagine the implications of having that kind of knowledge.. I'm not religious btw, it would still have to be scientific to be acceptable. And to be fair, most of this goes way over my head and I am certainly misunderstanding a lot of it wrong , math is hard 😅
3:30 - Chapter 1 - Clay mathematics institute
5:40 - Chapter 2 - P vs NP
8:45 - Chapter 3 - Navier stokes existence & smoothness
10:55 - Chapter 4 - Birch & swinnerton dyer conjecture
12:55 - Chapter 5 - Rieman Hypothesis
Being a physics major means this is right up my ballpark. And even I have a hard time trying to comprehend just how abstract these stuff can get sometimes.
"Being a physics major means this is right up my ballpark", you say?
And not being an English major (I'm guessing) you absolutely nailed mixing your metaphors there 🤣👍
Given you are a physicist though, I wouldn't put it past you that this is one of those brilliant self-digs along the lines of "yesterday I couldn't even spell engineer -- now I is one".
Either way, I think your comment wins the internet today.
👍👍👍 Being a computer scientist myself, I appreciate oxymoronic one-liners...
@@tttm99 You okay bro? Had a bad day? Got dumped or fired? Wanna vent? If so I'm all ears. It's okay to open up sometimes.
8:37 no, that's not the problem. The problem is that all existing encryption algorithm is NP. If P=NP, that means all of them can be easily cracked and we are all screwed. It's one of the few things that will affect people outside of the math/computer/science fields, it affects everyone.
The Riemann zeta function is not written correctly at 13:56. The -s for each term should be an exponent
Was looking for this comment
Good point! The Riemann Zeta Function, represented as ζ(s), is defined by the series 1^s + 2^-s + 3^-s + 4^-s + ... or simply 1 + 2^-s + 3^-s + 4^-s + ... This marks just the beginning of a fascinating journey that leads to results like 1 + 2 + 3 + ... = -1/12 and other intriguing concepts.
the Riemann hypothesis is false.@@RSLT
@@jaydenwilson9522 Interesting. Some people believe that R.H. is false, but I believe it's correct. There is no reason to believe R.H. is false; however, you certainly can have your opinion, and I hope you can come up with some proof and a video to explain why it's false.
@jaydenwilson9522 Also, please remember that it's very likely there won't be a 1 million dollar bounty, as there is a high possibility it can be reformulated.
I know several people who are working on the Riemann Hypothesis and the Navier-Stokes equations. The issue is not the money -- it is the bragging rights.
Simon didn't consider that those who can solve these problems, are already capable of making enough money to trivialize the prize amount.
Navier-Stokes is the secret project of every engineer in my field. The amount of time any individual spends on it varies wildly, but I’d stake my company on the fact everyone in vacuum engineering has a secret folder full of their work on the problem. It’s definitely for the bragging rights.
Yeah, if you are trying to earn a million dollars then solving one of the millennium problems might just be the hardest way to earn that million.
i already solved the Reimann hypothesis you bot
Well I beat them all. My solution to the Riemann hypothesis is iron clad.
s=0 when Zeta(0)=-.5=i=sqrt(-1)= nontrivial zeroes.
Props to Andrew Wiles for the Fermat conjecture proof. I was at a cricket match at university when a math student friend strolled up and said that he'd been at a lecture the previous day where it was delivered. (Yeah it had one problem: thanks Taylor for the fix.) I've read the paper and it sort of makes sense, but the Riemann zeta function is more than my medium brain can cope with. But if you look it up on the wiki machine, there are some lovely colorful graphs, which would make excellent poster gifts for nerds whichever holiday season they observe. (Oh, and read Simon Singh's book.)
Wiles is wrong. Proof?
1. Add the natural logs 2+3=5.
2. Take each log to a power of 4 yielding 2^4+3^4=5^4.
3. Using the power rule of natural logs yields [(4x2)+(4x3)=(4x5)]=[8+12=20]
4. Therefore Fermat's last theorem is negated. QED
Fermat's Theorem is the biggest and best trolling in human history
Can you expand on this?
@@bethaltair812 it became famous after Fermat stated his "theorem", and made a wry comment about how nice his proof was without writing it down anywhere it could be found. A few hundred years of trying to recreate the proof followed, only for the final proof to be completely different to anything Fermat could have possibly come up with (meaning his own proof was almost certainly flawed)
It's shouldn't be called Cunningham's Law ~"Post the wrong answer to get the correct one" Fermat thought of the idea first.
The statement of the Zeta function didn’t have the requisite exponents and I have always heard it pronounced as “Ree”man
Yours is the correct pronunciation. In German 'ie' and 'ei' are pronounced oppositely to how they are pronounced in English. Compare 'Einstein'.
"good for you mate"
This is Simon's way of saying his integrity isn't worth 1 million dollars.
He'd even advertise raid shadow legends for that amount!!!
The partial proof of specific cases of of Birch and Winnerton-Dyer was actually Andrew White solving Fermat as he proved elliptical curves are modular. (Technically he only needed to prove for semi-stable but all elliptical curves are now proved modular)
First trip into the Whistlerverse today. Mashed that like button. Cheers.
I picked one hell of an episode to watch while high.
3:23 clay mathematics institute
5:33 p versus np
8:41 navier-stokes existence and smoothness
10:48 birch and winnerton-dyer conjecture
12:51 Riemann hypothesis
Birch and Swinnerton-Dyer conjecture, not winnerton
my friend, whom was a math professor at georgia tech worked on the Riemann Hypothesis.
Which of the 7 millennial problems remain unsolved?
I solved it! but they won't accept my submission lol @@ExarchGaming
I actually didn't really understand a thing and he was speaking clear and plain English. Wow
Math is a language so its understandable.
You can do it though. Just remember you are about 10,000 hours of study away from being anything you want.
The issue with P vs NP is that there are NP problems that have very good algorithms that can do it in linear logaritmic time, that is a lot faster than exponential for a great number of samples. One example of such problem is the Fast Fourier Transform(FFT) this makes computation of the fourrier transform almost instante, whereas without this algorithm it is an untractable problem, and this is huge because this is so important in comunication, identification(Think medical exames), it is one of the top algorithms of XX century.
10:00 is an multi billion dollar problem, increase the efficiency of car or jet engines with 1% and its an major gain.
Understanding turbulent flow would help with improving jet engine efficiency.
The reason that most elementary and high school students HATE math is that schools are still teaching it using the terms and methods that Archimedes used 2800 years ago.
The students get so confused just trying to understand the words that they never understand the actual principles.
I took six semesters of math in high school and another 3 semesters in college. Because I went to what was basically an engineering school I had to use all that math in my major course even after those three semesters. I graduated (barely) but all I did was memorize. I knew which formulas to use in which situations.
It was not until decades later when I was in my 40 that many of those proofs and principle started to make sense to me. I had several EUREKA moments.
Actually, I'm a fan of this channel, but I didn't expect to see this topic featured here. The presentation was impressively simple and provided a good introduction, along with well-researched content.
That was a fun video; I was one of those crazies that liked math once I was far enough along to study algebra. Unfortunately I’m just not brainy enough to have been good at. I think my differential equations professor let me pass from pity. He was always saying I had creative ideas; a polite way of saying that’s the craziest messed up proof I’ve ever seen
This is funny🤣🤣
Something really sad is, the Field’s medal is the highest math prize, however Andrew Wiles didn’t get it as he was 41 years old when he proved the conjecture :(
Maybe you should do a video on all the prizes available for proving the existence of various supernatural things... (which unsurprisingly all go unclaimed 🤔😂)
I want to believe
Well people believe a multithousand year old magical, mythological, invisible, genocidal psychopath skydaddy is "all loving", and is " more real" than all the other previous multithousand year old, magical, mythological, imaginary fantasy genocidal psychopathic fairytale skydaddies(Ra, Zeus, Jupiter {not the planet obviously it exists}, odin, thor, Yaweh, allah, god, ect) 🤷😂😄
I have what you seek,I have ghosts figured out, I have the science caculated, people normally want to make the ghosts leave. Is that the "thing" you have in mind?
Lol, I like that idea.
One should check out the video of Wiles after proving Fermat's Last Theorem in which he basically breaks down in joy and heartache.
To be honest, I'm still stumped by the understanding that you cannot successfully make 1 third of a number of a whole. You end up with .33333ad-infinim. If you convert even one digit to a 4 you gain a greater number then the whole you started with.
I saw the mean equation and felt smug. Now after finishing this video I am doubting whether I deserve my degree or not bc I understood nothing lol
Math is such a fascinating area.
I hated maths until I started extension 1 in high school and realised how fun it is
Simon, I'm a mathematics PhD student and you got some of the pronunciations wrong. Riemann is pronounced Reeman, Not Ryeman. It's polynomial time, not polynominal time.
Was going to point this out, but you beat me to it. A bit worrying that they will put out a video on this, without checking that the pronunciation is correct. Almost as if they didn't understand it in the first place!
Credit to Kevin for the first description of P vs NP that I can understand, sort of...
In a more simplified way, the P vs NP problem is if there is a problem that is very complex that can be solved as fast as a far simpler problem.
@@zaco-km3su And here I was thinking it was to do with being able to solve the problem as fast as verify the solution... Silly me.
A couple of days ago I spent a good chunk of an evening going over it with my wife and now I realize I should have just waited haha
@@Chris-hx3om
Or that. It's just a bit more specific.
@@zaco-km3su It always is...
Nice derail Kevin! 😂
Simon... checking updates on your channels is the highlight of my evening after work. But today... maths. It was like selecting a nice bottle of wine and uncorking it to find your welcome libation wasn't sealed well and has gone sour and you are now denied your relaxing moment. I didn't understand a bit of this episode as maths was not my forte, at all. I'm not certain you (or your writers) were speaking English. I suspect your writer was showing off. But if I understood this subject I would have too. Nonetheless, thank you for your work. It is very much appreciated.
uhhh...It's not polyNOMINal time, it's polyNOMIal time. That is, can you solve the problem in polynomial time in terms of the size of the inputs, and not exponential time in terms of the size of the inputs? It's okay, I understand you don't get it. This is just for the record.
It is a really tiny nitpick but it is polynomial not polynominal; it only has one N.
The derision at the end...a snort! I'm....amused.
N vs NP would work if N was asked to complete the sudoku in 100x100 ways, if a computer asked every variant of the question once instead of trying every combination
Grigori Perelman is a legend regardless if he takes the money or not
Fact Boy goes 3Blue1Brown! Impressive!
Proving P=NP may lead researchers to look into creating polynomial time algorithms for complex problems, but they're isn't a compelling reason to believe they will quickly develop any
The NP=P problem must logically be more important than even RH: it will be easy to verify a proof or counterexample to the Riemann Hypothesis, so it would follow from NP=P that it is easy to find such a proof or counterexample.
Nope, the most important one is RH
The Problem with "higher" math in schools is, that we get it presented as some abstract number/fomulas/equations/etc, that kids have to be able to recite in tests, but rarely with grounded real life applications on why its important or where its used!
really a shame, i bet more kids would be interested in it (&physics) if it would be taught closer to "real life"
Couldn't Perelmen just accept the prize then split it with the other dude?
For someone who solved such a hard problem, he seems to have missed an obvious solution to an easy one...
As always the answer to all of life's hardest problems is 42
Really? I thought it was 97!
How many roads must a man walk down?
@@Chris-hx3om depends on how far you're goin
We need a crossover where Simon gets taught some Numberphile stuff!
Yeap!
As usual, my brain hurts after videos like this.
It’s “polynomial time”. Not polynominal. No prize for you.
i guess P=?=NP problem could get some help with quantum computing, or eventually find some really basic problem that literally allows you to calculate the minimal possible time it takes to verify and minimal possible time to solve, if it says "everything", then just 1 thing that could disprove it would be enough, but then there's quantum computing which might completely mess up the way we currently think about time complexity
Turbulence is friction...As opposed to going through a undisturbed substance. I guess I don't understand why this would be a problem. Thanks for the video. It keeps me a humble human. Kind of like golf. :)
Well, turbulence isn't friction. It can be caused by and cause friction, but it isn't friction. It's chaos.
Riemann isn't pronounced Rhyman
The word is polynomial, not polynominal. You (or your spell check) are adding an 'n' where you shouldn't be.
14:40 Hello. Yes I am a maths genius. Here is the solution to the Riemann Hypothesis:
s=0 when Zeta(0)=-.5=i=sqrt(-1)= nontrivial zeroes.
When it comes to mathematics, I'm that person that looks a the price of toilet roll and giggles at the "cost per 100 shts" on the label... :P
The opening to this video was on full surround sound top volume and bass in my room.when Simon came in with' MATHEMATICS' I near shit myself
"Polynomial", not "polynominal". And the formula flashed on screen for the zeta function was totally mistyped!
"Mathematicians had already felt confident Fermat's Last theorem must be true over for over 1000 years". Obviously, this is plain nonsense.
I assume most number theorists had this impression after Kummer's break through around 1850.
You really should figure out how to pronounce "Riemann". To talk about the Riemann conjecture and not even know how to pronounce it is disgusting.
The "formula" for the zeta function appearing at 13:55 is a joke. The zeta is no zeta and the sum is plain nonsense. Shame on you.
It kind of sound like if p=np we are all screwed as encryption, digital signatures, and hashes become quickly breakable, most especially public key crypto that is entirely based on trapdoor functions easy to compute in one direction but exceptionally difficult in the other, like factoring large numbers composed of just two very large primes, but it's exceptionally easy to verify whether two primes are the factors, determining them from the product is hard
"Super Computer being super smart?" No Simon! "Super Computer being super Terrifying"!..."Inconceivably Terrifying"!....
Solving for the quadratic equation will tell you if there are rational number solutions for any given standard polynomial right? I'm not a serious mathematician but it seems to me like there should be an analysis equation for elliptical curves that could be reasonably quickly used to determine if the solutions to that curve are rational or non-real. Anyone feel free to tell me if I'm wildly off. That would solve that Birch Winnerton-Dyer conjecture.
The answer is 42 😏
😨 Genius
50 000 dollars to anyone who can finish a yoko ono album
This is definitely your video that has given me a massive headache. Taking 2 Tramadol capsules now. 😫
Tramadol ? that's some headache.
All those numbers, but she still won't give you her's.
thank you for breaking it down!!With everything going on right now, the best decision to be on any creative man's heart is having a profitable investment strategy.
I agree with you and I believe that the secret to financial stability is having the right investment ideas to enable you earn more money, I don't know who agrees with me but either way, I recommend either real estate or crypto and stocks
@@jackfinnva2409 Regardless of all, investing in crypto markets trading still remains one of the best ways of getting out of poverty and obtaining financial freedom in this global economy pandemic
I wanted to trade crypto but got confused by the fluctuations in price
@@waynes4369 The fluctuations of the market only affect those that hodl coins, but traders makes money on both sides, when it's bearish they go short when it's bullish they go long... The best strategy to use in trading crypto is to trade with a professional, like Arjun B Jagat he understand the market quite well, that way maximum profits are guaranteed.
I have heard a lot about Investments with Arjun B Jagat , how good he is and how he has helped People. Please how safe are the profits?
13:49 - This is wrong. How didi you even get this? It's the analytic continuation of the sum of all reciprocals of powers of s for Re(s) > 1.
Polynomial is po-lee-no-mee-al, not po-lee-nom-in-i-mal. So we know Simon doesn't really do math.
How many RUclips channels does this guy have?
what about the 3-body problem? 🤔
You would think a mathematician could divide by two and share the prize.
Or he could of accepted the money and given the lot to the other person. Not so smart after all .
“Polynominal [sic]”
“Smooth and globally-defined basically means the equations are consistent and universally applicable”
“Vague terms like «chaotic»”
“… to prove that a theory [sic] or conjecture is false”
“ζ(s) = 1 + 2-s + 3-s + 4-s + …”
I’m just disappointed.
So why are all the comments spell checks?
Is he trying to say "polynomial"?
Bravo. Was that in one take?
Countably infinite versus Uncountably infinite
Yeah, the if NP != P, then we’ll still get to super smart AI, but if NP = P we could make god-like machines.
P can equal np. Reasoning? :say you give a computer a infinite grid. This means that it will take infinite time to solve it and thus it cannot be solved note that this only works on infinity and no other numbers will work, as finite numbers will always end up being caught.
oH. Cool...
Ferb, I know what we are gonna be doing today.
No lag here bro!
I feel like if your smart enough to solve these problems your smart enough figure out how to make some money
The 1 dollar prize is a joke, you have to have your solution public for 2 years. If you can't figure out how to make money with it in two years, they give you some pity money, cause you got robbed for billions from the industries, who did make money from your breakthrough.
@@thedeadbatterydepot completely wrong lmao. The proof has to be public because it needs to be verified, which is incredibly hard to do and takes a lot of time. Most of the problems here are only of interest to pure mathematicians, so most businesses would never be able to monetize it (hell most people outside of university maths departments won't even understand the ramifications of the problem). The million dollar prize is advertising to raise the profile of mathematics as an academic discipline. Nobody good enough at maths to even stand a chance of solving one of the problems (or more likely, contributing to an eventual solution at all) needs money to motivate them
@@epicmarschmallow5049Exactly 😎👍
The last one I solved two years ago. Easy, when you know the trick.
Unfortunately, RUclips deleted my comments with links.
P = NP P calculate N Divided equally.
P=NP has been proved for the special cases where P = 0 or N = 1. 😜
I feel like NP complete problems are probably soon to be solved with quantum computing, and that will give us the proof we need.
The expanded spherical numberline of the hyperbolic cow: I broke in here to avoid trying to speak up using MSNBC
Working on 3x+1 x odd x/2 x even problem by changing function into one that's from odd numbers into odd numbers. Lol very interesting subsets of domain point to a possible way. Lol prize is a bit more than a million.
Feels like Kevin is asking for a pay rise.
13:49 The Riemann zeta function is wrong. Those -s are powers of their respective terms. It ought to be
1 + 2^(-s) + 3^(-s) + ....
0:06: 🧠 Mathematics is paradoxical, as our brains are hardwired for basic math but struggle with abstract concepts, yet it remains both the most loved and most hated subject among students.
3:39: 💰 The video discusses the Millennium prize problems, a set of seven unsolved math problems worth one million dollars each.
6:29: 🧩 The video discusses the P vs NP problem and the Navier-Stokes equations.
9:49: 🧮 The video discusses three unsolved problems in mathematics: the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the Riemann hypothesis.
13:07: 💡 The Riemann hypothesis is a problem in number theory that has eluded mathematicians for over a century.
Recap by Tammy AI
What’s on the back of the door and why is it always half open? Sorry mate but i’ve been watching you for a while (thanks for your great content) but all I can do is stare at that door handle. I’m a camera and editor and it just bugs me. Also, today you forgot to turn on the light in the corridor 😂😂 keep up the good work 😊
Kevin 💯💯
I got a D minus in high school algebra. So there.
I feel smarter with every Whistler video I cram into my eyeballs.
That's funny because I feel a lot dumber after watching this one 🥲
The actual problems start here, the first 5 minutes is trash talking 5:37
regarding turbulence.. maybe I missed something, but it's it just compound, negative, interference patterns, in the flow of the medium?
The non-trivial zeros of the zeta function all fall on the line y=0.5+ni.
I didn't even try to understand that. LOL
Sometimes struggles are exactly what we need in our life. If we were to go through our life without any obstacles, we would be crippled. We would not be as strong as what we could have been. Give every opportunity a chance, leave no room for regrets
Hi there. I'm just wondering about this giveaway message. I got one myself. All very confusing as seems completely unrelated to the video and "side projects!" Scam?
@@josephrous4250 total scam yes, they do this on a lot of other channels as well (along with copying the name and profile picture and making fake telegram accounts)
"Polynominal"
"Rye men"
I knew something was off with the youtube algorithm, only took this video to put 2 and 2 together.
Maybe it's the accent, but it sounds like you're saying "polynominal time", instead of "polynomial time"
The explanation of Navier Stokes is off, The navier Stoke equations are complete and fully describe the flow, there are even solution for them under certain caracteristics of laminar flow, however the problem stated wants to prove the existence of a smooth solution for an arbitrary velocity field globally. This is relevant because looking at fluid flow in reality we see no such smothness, we also can solve them computationally but energy scale has both small and large vortexes and proper solution requires a mesh small which if you actually count is a ridiculous ammount that there is no hope of solving on any computer today or near(even never for traditional computing) future. Ence usually simplified models are used.