The Math Problem With a $1 Million Prize for Solving
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- čas přidán 28. 07. 2021
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Video written by Ben Doyle
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Fun Fact: The man who solved the Poincaré Conjecture, Grigori Jakowlewitsch Perelman, rejected the prize money and told the congratulatory committee to get lost because he just wanted to be left alone.
I saw the video Count Dankula did on that
"It's a million dollars man! Just take the money!!" 😂
count dankula made a video on him
@@sabersz Some things in life are so unbelievable. That you deny them.
He returned the money because they didn't recognize another professor that did a lot of work in solving them.
@@lool12366 Why didn't he just give the money to that other professor, then?
me a computer science graduate: ah yes, my nightmares have returned
Yes, comp theory was my least favorite course in computer science. My running joke in the course was to ask if the person the theorem or proof was named after had gone insane (they pretty much all had). For example, Alan Turing, Kurt Gödel, etc.
It was a nightmare but at the same time pretty interesting, in particular the p=np problem. I don't know why there aren't more videos about this.
Lmao I was thinking the same
@@2011blueman I actually really enjoyed it but holy crap, those algorithm classes were some of the most difficult I took. I was always amazed by the solutions these people came up with and then I remember they did it decades ago... and now its taught in undergrad CS classes LOL. I was very fascinated by it all, but I could probably never come up with that stuff. the comp sci people of long ago were straight up geniuses and im here like...
@@Mathguy363 lol my analysis of algorithms course was basically straight up math. we didnt write a single line of code for that... unless you wanted to for fun, which I did because im a nerd lol
Just give me 3 flintstone gummies, I'll handle them.
You'll overdose.
You're a madman! You'll break yourself with that many flintstone gummies
@@Potatoinator but before they do they'll solve it nah I'm kidding they will just die
Nobody has ever survived that many before... are you sure you’re ready for this? To sacrifice your everyday life to fall into a flintstone gummy spiral? Sacrificing your life for a math problem, don’t get me wrong it’s brave, but your life will never be the same. Are you prepared for this?
Take 3 and eat all your vegetables
Yay, I'm about to become one million $ richer. I remember something about Paul having 10 apples and giving three of them to Mike, so I'll just take it from there and start working on this. Easy peasy!
That's not a math textbook problem. Paul needs at least 4 carts of 20 pineapples. Now Mike wants to trade 6 peaches for 1/4 pineapple each and 9 of his pubic hairs for 1 pineapple each.
How many Pineapples has Paul eaten in the meantime?
@@NuclearTopSpot 2 1/2 pineapples. Unless you count the one in his ass. Then 3 1/2.
I'll beat u to it
Tell us how it goes
@@notyourfriendlyneighbor2733 turns out p doesn't equal np 😤😅😭🤔🤣
The thing is: If you had the formula you would earn way more money by solving the problems selling your services to solve rather than selling the formula for a million USD.
You would have to play pretty stupid though, otherwise you would very likely give away how you proved it (or enough to deduce how to do so) and so you’d lose the advantage you have.
If you’re smart enough to know how to solve one of those problems, you would very likely get a lot more money from others as a result, either through jobs or otherwise.
But it's likely that the "formula" doesn't exist and a million dollars would be awarded to someone who proves that.
@@TheStrongestBaka There's also the case where the formula exists, but just proving its existence (without finding the formula itself) will also give 1 million.
@@TheStrongestBaka you cant prove a negative tho
@@TheStrongestBaka cirno
To be clear, even if we have a polynomial time algorithm which solves NP problems, it could still in practice be unhelpful, e.g. it could have constants greater than a googleplex or whatever and only be efficient for inconveniently large inputs.
" e.g. it could have constants greater than a googleplex or whatever and only be efficient for inconveniently large inputs."
*Googologists have entered the chat*
heh. years ago I remember working on a problem like that. we had two possible algorithms. I was working on one that starts off really well but got exponentially worse as the dataset got larger. there was another that had a high setup cost (and expletive ton of RAM), but once you got everything cooked (constant+linear) put into memory (linear), the solution also became linear.
I’m sorry that it’s unrelated, but I couldn’t help but notice the lick
Also would the P=NP proof necessarily be constructive? If one could show that its possible to solve things in P time would it necessarily make it easier to find the algorithms? I understand that knowing that it's possible would be helpful but it wouldn't immediately resolve that issue.
Or it could have a complexity of O(n^100), which is polynomial but not practical.
> One of them has gotten significantly more attention and more failed attempts than the rest.
*The Riemann Hypothesis would like to know your location*
Thats what I thought too. Then I realized that the RH is probably not very suitable for HAI, since it might be difficult to explain in a simple way 😄
@@frederickm9823 Oh it is, you'd have to talk about convergence, complex numbers, applications to number theory and a whole bunch of stuff that's difficult for someone without a maths or physical sciences background.
@@stardestroyer19 Yeah. You can't really describe the "core problem" without explaining a lot of background stuff.
As somebody who wrote his bachelor thesis about elliptic curves, I am very interested in the Birch Swinnerton-Dyer hypothesis, but man, if I had to explain it with simple words, I would fail miserably 😄
I have been waiting for this comment
@@frederickm9823 I know how it be man! I'm a PhD student in theoretical physics and somethings could take a long time to explain if you want to make sure people get the core idea of something without watering it down so much it becomes too simplified.
Thanks for the callout... 0:08
hey but now you have keyboards 😦👍
lol nice
hipyo tf you doin here
A $3 million muffin is the exact opposite of a "very convoluted money laundering scheme".
In fact it might be the least convoluted money laundering scheme of all time.
Someone needs to try this and see if such a simple scheme can actually work.
oh so what if I create a company which concept is to give money to people which i obtain from other companies and the people that watch me launder money. why does i have the impression someone already did that before
Like a $1tn coin to avoid the debt ceiling simple.
@@vojtechstrnad1 it's called buying and selling art, they already do it. You ever hear of shitty paintings getting sold for millions of dollars? yeah...
Fun fact: The man who solved the first Millennium Prize Problem turned down the $1,000,000 as well as the award, and later a Fields Medal. He then quit his job and went into seclusion. When approached by a writer in 2012, he stated “You are disturbing me. I am picking mushrooms.”
Source: en.wikipedia.org/wiki/Grigori_Perelman
Why do I feel like half as interesting son will make a video in 2069 titled "why did they 2020 Olympics happen in 2021"
...Because Covid hadn't already killed enough people by the time 2021 came around. #FIFY
Kkkkkkkk true
@@dompedroii4656 Better not use the "brazilian laugh" in other languagues.
@ KKKKKKKKKKK
@@hipato6838 Not again.
“One of them has gotten significantly more attention and failed attempts to solve it than the rest - P vs NP”
*Riemann: Hold my hypothesis*
Well, I would say every math student was at one point trying to proof both, but at least p=np was also tried by some computer scientists^^
@@frankkobold "but at least p=np was also tried by some computer scientists"
guilty as charged
@@frankkobold I (a CS student) can confirm I've tried to proof that P=NP and P!=NP and failed at both. I don't even know what the Riemann hypothesis is though :D
Fedex: thx for solving the hardest problem in the world
Me: np
Gödelmmit
*slow claps*
This fkin guy right here.
@@imveryangryitsnotbutter Your reply is incomplete
I have a feeling that Sam wants us to solve this, so he can claim the money.
$1m isn't that much. It's a lot of playstations, but it's not a lot of years of salaries for well qualified people, buildings etc.
@@tomx641 if it’s not taxed, it will still give someone who makes 100k a year 10 years of salary considering their salaries are also not taxed
@@ethanl.1699 It all depends on contractual terms, but I'm talking about Universities in general.
@@tomx641 for a university professor, it’s still a few years of work saved, but yes, it’s nothing compared to a building lol
@@ethanl.1699 University professors get grants for millions all the time and it lasts them hardly any time at all. No idea where the money actually goes, just that it doesn't seem to last long.
Next video on Wendover Productions:
The Logistics of Why You Should’ve Paid Attention in Math Class
So, basically this video on how to survive The Cube
czcams.com/video/XkYvo6S82LE/video.html
It would make more sense if the promo code "half" gave 50% off...
missed opportunity to say 15% as interesting, tbh
Its supposed to make money not sense dear
After the intro I thought for SURE we'd be talking about the Riemann Hypothesis. Not sure if P=NP is more studied than RH.
Well arguably P vs NP is the most accessible of the problems, unlike RH which uses complex analysis and the other five which I barely know anything about. But yeah, if he ever makes a video on another one of the problems, it will be the Riemann hypothesis.
@@vojtechstrnad1 When he does I'll click on it so fast!
Me too.
The only ones I somewhat heard of was P vs NP, Navier Stokes and the RH
The proofs that P=NP (or P=/=NP) are appearing several times per month nowadays. It might be not studied more, but it certainly attracts a lot of attention.
The math problem my mom expects me to solve after watching the 3 minute video
The "Hey, you want to get rich quick" with the guy standing there with his finger at the beginning sounded like an advertisement for Honey.
I too assumed this would be about the Riemann Hypothesis. As a long-time computer nerd techie type I've followed P=NP for a long time.
We did it. The "Who Wants to Be A Millionaire?" in math is here.
Perelman clearly didn't want to.
@@GURken Perelman is a russian wizard. He has no need for earthly goods.
This isn't going to fix your dept greece.
(I'm greek myself so dont start ww3 here)
@@GURken "I'm gardening"
@@janno288 wow I'm not the only Greek youtuber...
Short addition: a problem in P does not have to be "easy" or solvable in a fast way. Let's say I would find an algorithm for the TSP problem with a constant runtime of hundred years. That would be O(1) and in P, but probably wouldn't help me to hack any bank account.
That is a very good point. I also find it strange that most videos on P=NP seem to equate proof that P=NP with breaking encryption. Proving that a solution exists does not necessarily lead you to that solution, or does it? So knowing that a polynomial solution exists may put the encryption on shaky grounds but it will not magically make it not work overnight. Someone still has to find that solution.
Also, one could have a proof that P = NP that is not constructive. So, contrary to what is said at 1:50, just proving equivalence does not necessarily lead to new algorithms. And, even if it did, it's entirely possible that an algorithm in P has such a huge overhead that it's slower than a corresponding algorithm in NP for any input we might be interested in.
This entire video is riddled with mistakes.
Yes, but the thing is: an actual algorithm would to some degree only be a side note. Breaking this exponential barrier is much more significant in itself. Any polynomial algorithm (even the one with a enormous exponent or huge constant inside the big-O) would still exploit some kind of non-trivial structure and would most likely mean there would be some insight into this class of problems. So very likely, even if that's the case, it's the crack in the problem that opens up a whole range of new research that will in all likelihood bring down the polynomial's constants and exponents.
But I also don't think you can find lots of experts that believe this would be the case. As far as I know, it is believed that it's much more likely that P != NP.
It might be a bit confusing to suggest there could exist a constant time algorithm for the TSP. Trivially it's at least O(n).
@@JanStrojil "Proving that a solution exists does not necessarily lead you to that solution, or does it?"
It doesn't, your understanding is certainly correct.
"So knowing that a polynomial solution exists may put the encryption on shaky grounds but it will not magically make it not work overnight"
Very well phrased. More to the point, simply knowing the answer(yes or no) to P=NP is not much better than pretending you know the answer, it would only tell you whether
or not your attempts at a proof for or against are futile or not.
Literal utopia, we all know it's too good to be possible, but good luck proving that as an abstract
Why can't math grow up so it could solve it's own problems?
0:56 Oh boy, I'm a math student and I seriously tought that when you said one has gotten more attention than the rest, that you were going to talk about the Riemann Hypothesis. Would have loved an episode about that but P vs. NP is also a good one.
The core of P=?=NP is way easier to explain in like 5 minutes than Riemann. :-)
The interesting thing is that the opposite hasn't been proved (although is the same question tho). We can't prove they're the same, but we can't prove they're different things either.
Yep. I'm pretty sure P != NP but don't know how to prove it. Maybe going over the axioms of the system questioning its provability incompleteness theorem style or something in that ballpark.
Does P = NP?
Only if P is equal to zero or if N is equal to one
Or P is 1 and N is also 1
I thought a way to solve the P-NP conjecture.
Unfortunately, this comment bar is to small for writing it in.
Fermat, is this you?
Classic Fermat😂
Whose Fermat?
At 1:26 I took my TI-84 plus into my hand and silently whispered "He didn't mean it!"
The whole calculator part is exactly what I have to go through when I tell my students about these problems. One of my students was convinced that they found a counterexample to Goldbach's conjecture (not one of these, but still an open problen) when I couldn't immediately tell them 2 primes that sum to 1,000,000.
You get the reward for settling the P =?= NP problem; winning it doesn't have to mean that P = NP. Furthermore, even if you prove that P = NP doesn't imply you have a non-exponential algorithm for NP problem. (Having such an algorithm of course means P = NP, but the reverse doesn't). (Also, an algorithm which takes n^1000000 steps technically is in P, but in practice, that won't give us efficient algorithms)
How again does P=NP not imply a polynomial algorithm for all NP problems?
I mean of course there may be non-constructive proofs but in theory there should be algorithms.
@@Caesim9 I think Abi's saying that it's possible to prove that P = NP without actually coming up with a formula for an NP problem
@@NerdTheBox indeed, a --"nonconstructive proof" would be accepted-- just noticed the first reply literally said non-constructive proof oopsie
Actually, I see we're all latched onto that idea of non-constructive proofs being a thing.
I think @Caesim9 is saying, regarding the statement: "Having such an algorithm of course means P = NP, but the reverse doesn't"
he interpreted it to imply "even if P=NP that doesn't mean a non-exponential algorithm exists", which would be wrong,
its definitely the case that if P=NP then such an algorithm does indeed exist.
Imma pretend I understand that.
2:51 this graph also applies to other activities
i watch these when im high and it always fades into commercial in a very sneaky way.. i kinda love it
0:25 I think you forgot the part about having no skills attatched to your degree
Therapist: "Stock Footage Anonymous Hacker Guy can't hurt you"
Stock Footage Anonymous Hacker Guy: 4:04
3:20 Unfortunately the problem described here is not equivalent to the traveling salesman problem, and actually could be solved with a greedy algorithm within polynomial time. The mistake in the video is that the points are labeled in a particular order and the difficulty is being described as finding the streets to take to traverse them in that order. This is equivalent to graph traversal and can be solved in linear time using the A* search algorithm. The key point that makes traveling salesman an NP-hard problem is that you're not given a particular order to traverse the nodes. Checking every possible permutation of the nodes is what makes it explode into factorial time.
Your promo code “HALF” doesn’t work. The checkout process says “The provided code is invalid.”
Incidentally it's because the encryption was longer to solve that to verify
maybe it applied automatically and now you try to apply the second time, MAYBE
Does not work for me either and no there is no discount already applied
Try using the code WHOLE
I don't fail to appreciate the smug humour that this has generated, but it's also a quiet scandal and merits some sort of response. Presumably Sam can be bothered to give a shit when his promo codes don't work, but ... it would sure be nice to know for sure.
2:18
It's Actually all the problems that can be solved in polynomial time, not those whose solution time is not exponential. If the time complexity of a problem were say 2^sqrt(n), then it would satisfy your definition because it grows slower than all exponentials. But it would still not be in P since it grows faster than all polynomials.
Finally a topic I knew about before an HAI video! Also, in case anyone is wondering why the problems are so difficult to discuss - I'm a senior in a Math/CS double major, and I can only fully understand what 2 of the 7 problems are even asking. I'd bet a lot that the majority of math *professors* can't understand more than 4 of the statements.
5:30 swiss army pocket knife : amateurs
Genuinely thought you were gonna talk about the Riemann Hypothesis since that problem is even more studied than P vs NP.
I really like that right after you note about people catching all the mistakes you are about to make, you say that P is things which can be solved in time which is not exponential. But this isn't the same as being polynomial. There are things which have time complexity which is worse than polynomial but still not exponential. For example, the best known algorithm for solving graph isomorphism has this level of intermediate complexity time. But well done video anyways!
(Also we do have algorithms for traveling salesperson problem that are better than brute force checking everything. But the savings for it aren't that great.)
The ad that played before the video just fit perfect
My brother was working on this problem back in high school (~2005). He had his work copy written so as to date it. I have no idea how close he came to solving, because none of us knew what tf he was talking about lol. Will have to bring it up with him the next time we’re together
Spoiler alert: not close at all. Still, it’s nice to have a crack at problems even if they are famously unsolved by the greatest minds in the field of maths, it can still be an interesting experience and you’ll learn something probably
@@henryginn7490 We don't really know, I mean the great minds were not able to solve Poincare conjecture as well, but now it is solved. But yeah, the chances that he wasn't able to solve it are higher.
Expected a Navier-Stokes rundown and got an N = NP instead
Still loved it nonetheless
I expected Reimann Zeta, that's the millennium problem that seems to get the most attention
Man, I'd be shocked if HAI could figure out the question. Not because I think he's stupid - I'm a senior in a Math/CS double major, and I can't figure out the question.
2:06 Called me out lol
I was gonna quote that super long sentence at the beginning of the video and then make fun of it.
But it’s literally so long to quote. I just can’t. 😂
_Hey, psst-do you want to get rich quick? Have you exhausted all the other get-rich-quick schemes on the internet?_
_Do you have absolutely no marketable skills because you pursued a degree that became obsolete shortly after graduation due to an unstable and rapidly shifting job market, which then ironically drove you into crushing student-loan debt that compounded with the pressures of late-stage capitalism to create a predatory cycle of poverty that has ultimately forced you to desperately scrape the internet for schemes to support yourself financially?_
This is amazing.
This is amazing.
@@kkmac7247 you are amazing
Will you marry me ?
Please
Smells like desperation in here
Hardest problems to solve
When will be another bricks video
As a computer science student i have to complimet you! Awsome 6 minute summary of a topic, i would regard as one of my hardest during my bachlelor degree!
I feel called out (2:09)
But I did not notice any mistakes at all, good job on this one :)
"Half" should be a 50% off promo code, change my mind.
Am I the only one who actually doesn't want to join my friends at the "P" party....? That's just nasty....
"-------, Found out why the box has a band-aid,"
lol
2:52 they definitely knew what they were doing with the labels on that graph
Even this knife you will replace after a year. Learn how to sharpen one, and your 20 dollar knife will last a long time
Sam: Are you in crushing student debt due to a predatory poverty cycle brought on by late-stage capitalism?
Also Sam: Use this code to get 15% off expensive cookware
Me, a millennial: He gets us 🥰 take my money
Wasn't expecting to see Barcelona appear on minute 3:10. Especially just the place where I used to live. Thanks for the surprise, HaI!
I like the knife segment...thanks.
As well great video
I would like to get rich quick, this is why I chose to become a painting major. Never mind u said math.
No. Please go into German politics.
@hi there What happing in German politics, aren’t y’all rank high for the least corrupt governments
@@youngrex7694 The joke is a reference to the fact that Hitler wanted to become a professional artist but he failed the entrance exams to some art institution.
Sam sounds like he solved this equation.
Now I have context for that one Elementary episode.
I knew what the video was going to be about just from the title, and I STILL don't fully understand it... but you certainly helped make it easier.
P loses because he's alone and NP is two so basically its a 1v2.
It's been a while where my 1 million?
But what if P is Dream?
@@NoodleProductions He wins for a while then people finds out he used pvp cheats so he loses. Wins at the start but at the long run he losses.
So
P would be a 20% tip
NP would be a 20% that took the tip into account of the total so it would keep increasing,?
I'll try to explain it - HAI didn't do that well. In these examples, I'll call the number of items X.
P would be "I ordered these specific X items in the menu. How much is a 15% tip?".
NP would be "My bill from yesterday had the total of $123.45, but that seems high. I forgot what items I ordered, but I know the menu has X items and I ordered 5. Are there any 5 items from the menu add to $123.45?"
The first problem requires adding X numbers - you can do that in X time units. The second problem doesn't have a "easy" solution - the best known solution takes 2^(XK) time units. K is a constant number you shouldn't care about here - the point is that each time you put another item on the menu, the number of units goes up a bunch more than it does in the first case.
Everybody gansgsta till Sam raps the terms and conditions
Wasn't expecting that opening, but y'know I'll take it
The only video without shilling in the first 10 seconds has a 20 second long rant written by a redditor
Holy hell! That 4 knives set costs same as my monthly salary here in India 😂
You've got a better shot at winning the lottery than cracking these maths puzzles.
The ad in the end was like "and here is the base for trying to crack down this world class math problem, and here's a knife". I honestly thought the knife was for protecting yourself from criminals trying to steal your prize money in case you got it.
Your traveling salesman example is incorrect. That's an NP-Hard problem, not NP.
I was going to say that the explanation didn’t make sense to me!
His formulation was a decisional problem so it's NP. Also, "your"
To clarify, the P versus NP problem is a computer science problem, not a mathematical problem.
Well, it's theoretical computer science which is pretty much just a branch of mathematics.
P vs NP is a problem in theoretical computer science, which can be viewed both as a subset of computer science and mathematics.
@@1vader "Pretty much". That's right. In another words, "very nearly". The P vs NP problem is not an entirely mathematical problem. It's close, but it doesn't cut it. That honor belongs to the Riemann Hypothesis.
@@ultraviolet.catastrophe A solution to P=NP would be a mathematical proof. I don't see why it wouldn't count as an entirely mathematical problem.
@@Vaaaaadim If P=NP will be a mathematical solution, what about P!=NP?
Good job Sam and crew!
5:19 I gotta be honest, that's the smoothest progression I've ever heard.
I know the scriptwriter wrote this by creating their own ELI5 for themselves, but much of the language used in this video is extremely misleading and wrought with technicalities.
2:08, they knew we'd come and point out mistakes LOLOL
Today I learned: The probability of a blue lobster existing is widely touted as being one in two million.
The prize isn’t for solving that P=NP it’s for solving P=NP. Slight difference, the first is asking to show it to be true, the last is asking to show if it is true or false.
P=NP probably isn’t true so my point is that if you get the million dollars you’ll be able to put it in your bank.
Got nothing better to do this Sunday so might try it
Crazy Fact: In 2006, a Coca-Cola employee offered to sell Coca-Cola secrets to Pepsi. Pepsi responded by notifying Coca-Cola.
Teacher: the test will be easy
The test:
It's nice you used a map of Barcelona and marked the route from my home to the comic shop
Alright. I need a lot and I mean A *LOT* of pens and paper. Oh, and also like maybe 4000 pieces of mango flavored jelly?
One of the best moments in my cs class was when our lecturer showed how you can change one NP problem into another (reduction). it's basically saying you show that problem X is at least as hard as problem Y (which you know is NP) so X is at least NP. Iirc he showed 3 SAT (NP problem) and reduced to Traveling salesman
Sudoku is a great example of a problem that’s easy to check but hard to solve.
Woah, just a few days ago I was browsing Wikipedia and got to the article about this. I didn’t totally understand it so, thanks for this video
Lol, the ad I got before the video sounded exactly the same as the intro.
0:01 man went rapping 😂
I propose a drinking game. In which the player has to take a sip of their preferred drink, whenever sam says the word problem.
"Thanks for solving the hardest problem in the world."
Me : *No need to Thank me*
Ok let's see how well he really does when trying to describe this
Sam, I don't have any expectations in you
Me who fell asleep in the middle of the video then woke up in 5:00 : how tf did math problem became cooking problem
And that was a half semester of Computer Science condensed into 5 minutes.
Does anyone know what he was talking about for the solving of primes being a p function? What is the name of the method used to solve them?
The algorithm is the Agrawal-Kayal-Saxena (or AKS) primality test (otherwise known as the cyclotomic AKS test). I'll avoid another direct citation since they apparently get me flagged as spam here, but Wikipedia has a decent article explaining it (wiki/AKS_primality_test).
@UCjsL3qY34qXo-efewPwNkcA thank you
That intro about crippling student loan debt hit me in the feels
Imma go ask my math teacher to solve this right now
5:22 "Found out why the box includes a bandaid"
Wow, Sam *really* likes that knife.
You should talk about the Collatz Conjecture.
Thought I recognised the map at 3:15, a restaurant I used to enjoy going to that sold massive platters of meat and potatoes was there, but apparently it's permanently closed now :(