100 thoughts on “P vs. NP and the Computational Complexity Zoo

  • July 17, 2019 at 12:07 pm
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    Okay seriously this was the best video I have seen in my entire life. You got all of my appreciation!

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  • July 17, 2019 at 3:41 pm
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    please consider not using background music

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  • July 17, 2019 at 10:42 pm
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    if u find out, dont tell anyone because it cost less to kill you than it is to pay for the damages of encryption.

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  • July 18, 2019 at 6:58 pm
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    1:30 interested in that statement. Has it been 'proved' that there is no fast algorithm for the best chess move?

    Also, if someone proved P = NP, would that automatically provide a way to crack encryption? Wouldn't the proof just being saying "There exists a way…" rather than "I have the way for every problem ever"?

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  • July 19, 2019 at 2:18 am
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    I wish the Clay Institute would add the Twin Prime Conjecture to the list. Very easy to understand the question but very difficult to prove. It's also a very interesting problem indeed.

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  • July 19, 2019 at 3:17 am
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    I hardly understand but I feel motivated to crack it for humanity!

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  • July 19, 2019 at 11:27 pm
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    #Chromium nobel metal's reflections.

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  • July 20, 2019 at 8:15 pm
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    make more videos

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  • July 21, 2019 at 12:20 am
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    Haha. I was going to ask who would "thumbs down" this video, but see that is a major topic of discussion. (48K likes and 622 dislikes as of 7/20/2019.)

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  • July 23, 2019 at 2:58 am
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    Not as hard as it seems if you smoke weed. Individuals like me who are psychological adventurers tend to understand very complex questions. I know the answer, but who do I submit it to?

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  • July 23, 2019 at 4:23 am
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    What was the definition of NP again? Seemed unclear to me. Wikipedia mentions something called a non-deterministic Turing machine. A TRUE random generator? Are there really such things? Even quantum mechanics may be deterministic Stephen Hawking wrote and the pilot interpretation of QM is deterministic, so then what is true randomness?

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  • July 23, 2019 at 5:43 am
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    Still waiting for a new video

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  • July 24, 2019 at 4:06 am
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    Please come back from retirement!

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  • July 24, 2019 at 8:37 am
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    Outside of all these problems is figuring out the best thing to say to a girl you like.

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  • July 24, 2019 at 9:07 am
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    Amazing video. But I REALLY wish you could clean your blackboard.

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  • July 24, 2019 at 5:10 pm
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    where are you man !!!!!! come back we need you !!!

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  • July 25, 2019 at 6:07 am
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    can't reinforcement learning help in solving n-p problems?

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  • July 25, 2019 at 8:45 pm
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    P=NP if P=0 or N=1, otherwise P=/=NP. There, I solved it

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  • July 26, 2019 at 7:40 am
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    Is it wrong to see it as representing P as a single demonstration of a small piece or the fundamental rule the computer follows and NP as the computer having to perform P many many times in order to represent what we need it to show? And in that case wouldn’t P still equal NP? And the bottom line is that we just simply need a faster computer at some point?

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  • July 29, 2019 at 10:21 pm
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    wow for gibberish he spent 8min last min was informative

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  • July 30, 2019 at 1:39 am
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    the answer seems to be deep learning?

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  • July 30, 2019 at 9:11 am
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    yeah fuck pentium 4

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  • July 30, 2019 at 8:10 pm
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    This is trippy

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  • July 31, 2019 at 11:10 pm
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    So I have long believed that P is a strict sub-set of NP. There is no solution, but it isn't possible to prove or disprove it. Think Godel's theorem of Incompleteness. Has anyone proposed that yet? Like within the cutting edge theoretical CS circuit? Is that argument taken seriously by experts who spend most of their time on the NP/P sub-expertise?

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  • August 2, 2019 at 5:18 am
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    If P=NP life is Heaven …..
    Everyone is a Scientist …Einstein

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  • August 3, 2019 at 4:26 am
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    7:08 women doing the dishes meanwhile men are playing… LOL

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  • August 5, 2019 at 8:18 pm
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    – Ty
    – Np 🙂

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  • August 6, 2019 at 4:47 pm
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    Thank you for showing others how to connect the Love of Wisdom with modern terminologies!!!

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  • August 7, 2019 at 8:31 pm
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    It would be a fun world if p=np

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  • August 9, 2019 at 7:11 am
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    One of the most inspiring and delightful videos I've ever seen on YouTube in a long time. Thank you!

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  • August 10, 2019 at 11:00 pm
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    music is fine

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  • August 13, 2019 at 12:30 pm
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    I don’t think this is very hard to understand, as is everything for me, for I am an extraordinary genius who solves any sudoku puzzle in less than 2 seconds. I believe N=NP, but that must be because I’m an incredible intellectual with huge amounts of terabytes of brain power and cognitive prowess. The mere thought of a problem to hard to solve is a joke to me, one I frequently make with my friends on Fortnite. I would help humanity solve all its problems, but sorry kids, it’s way more fun pwning you on fortnite.

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  • August 13, 2019 at 7:53 pm
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    5:30 Bullshit. A lot of maths terminology is very helpful.

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  • August 13, 2019 at 9:46 pm
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    Can anyone tell me why or how finding prime numbers is under P?

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  • August 14, 2019 at 11:03 am
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    Did anyone notice at 4:09 he classified the question in "P" and "NP" where P has "a quick wat to find them" and NP has "being able to quickly recognise correct answers"

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  • August 14, 2019 at 1:49 pm
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    5:29 "Polynomial" is a terrific word. It refers to the level of terms, or addition and subtraction, which, if you remember, are operations allowable only between identically named terms. Or are you just virtue signalling by dissing our ancestors?

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  • August 16, 2019 at 2:24 am
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    You are WRONG. You claim that mathematically proving things is NP, when it is in fact undecidable, because verifying a mathematical proof is isomorphic to the halting problem. The proof ends with "QED" instead of "end program", that's kind of the only difference. Just because verifying a mathematical proof the sort of mathematical proofs YOU are used to seeing is EASIER than actually proving it, doesn't mean the act of verifying a mathematical proof is polynomial-time in worst case. It is NOT. "Easier to verify than solve" is a vague human subjective description, but easier isn't the same as "polynomial time in worst case". Thus proving math theorems is NOT NP, and in fact a polynomial time NP solver would NOT lead to a magic mathematical proof generator program that can prove anything that can be proved quickly because that WOULD NOT APPLY. And things don't get much worse than "polynomial time" than "undecidable".

    Also, there are actually very few things that a p-time NP solver would actually allow that is useful. Breaking cryptography is pretty much all it would result in. The key is, that in every actual practical problem that is NP complete, first of all, you can find the solution pretty quickly MOST of the time, just not in worst case, and secondly, generally finding an exact solution isn't necessary, but a "good enough" solution that doesn't quite optimize it is often all you care about. For instance, suppose you wanted to fill a disk to capacity and you wanted to pick and choose a combination of files to put on it that would most fully utilize its free space (i.e. the knapsack problem), it's OK if you don't fill it PERFECTLY to capacity, it may be ok if you leave 0.000000002% free space on the disk. And the protein folding thing is misunderstood by the way, it's one of those often-requoted things that is not understood by those quoting it and isn't really what you think it is. Really, destroying public key cryptography is the ONLY important thing that would come about from a P time NP solver.

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  • August 16, 2019 at 4:49 am
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    Nice!!

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  • August 16, 2019 at 10:47 am
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    what do you think about 656 people that Dislike this beautiful video ?
    why ?? 🙂

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  • August 16, 2019 at 3:44 pm
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    Many people just came for the 1M prize

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  • August 18, 2019 at 5:22 am
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    gg best explanation ever fk lectures

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  • August 21, 2019 at 11:39 pm
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    Guys, can we agree that math is not the longest thing to solve. This blackboard is.

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  • August 22, 2019 at 3:48 am
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    Algum brasileiro por aqui?

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  • August 23, 2019 at 3:09 pm
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    I feel very strongly inclined to trust someone with that perfect giant number typography

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  • August 23, 2019 at 8:48 pm
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    Thank you so much for this!!!

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  • August 25, 2019 at 11:49 am
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    I wish this channel would produce more videos, the world (and YouTube) needs this type of highly valuable (and also enjoyable) content among these rubbish science-y pile of clutter that seems be more like entertainment minus the science.
    JUST PLEASE MAKE MORE VIDEOS

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  • August 25, 2019 at 5:46 pm
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    Is this how mining crypto works?

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  • August 25, 2019 at 8:01 pm
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    why aren't there any more videos from this channel? Educational channel such as these shouldn't stop existing. We need them.

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  • August 26, 2019 at 4:21 am
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    If P=NP then
    Cure for cancer would be easy to find.
    But online banking would be easy to crack.

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  • August 28, 2019 at 2:50 am
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    And now I want to play Sodoku

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  • August 28, 2019 at 10:39 pm
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    Von Neumann and Gödel corresponded on the p vs np problem in the early 1950s.

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  • August 29, 2019 at 1:06 am
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    Now, that's simplicity! Cheers.

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  • August 29, 2019 at 1:21 am
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    P = NP
    N = 1
    there you go

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  • September 2, 2019 at 12:17 pm
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    Just say Traveling Salesman. Defining a problem is not the same as solving a problem, and P vs NP just means there is no solution. There's only a best guess, based on math. Most people can understand this as "Good Enough". There. I explained it for you. You're welcome.

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  • September 2, 2019 at 1:08 pm
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    If you give me a map, three salesmen in Dallas and three destinations, I can mark the correct / shortest routes every time without even thinking about it. Give me 30 salespersons, I can still do it – but it's going to take longer. And I'd be correct in both cases. The first case would be obvious. The second, not so much. But even with 30 I could eventually calculate them all and prove I was right (given a finite number of roads and conditions). But it still falls in the NP domain because I can't give the mathematical proof – because I don't understand how something that was easy for my brain could be virtually impossible to solve with a computer – and prove mathematically. IF we can solve this, then AI will actually work (what we have now is not true AI). And if AI works, human brains will indeed be obsolete. Not sure why everyone is rushing toward this proof – because like Elon said, it will probably spell our demise.

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  • September 2, 2019 at 3:09 pm
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    The solution to P v NP. Please, take a look:
    https://justme12345678.livejournal.com/21661.html

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  • September 4, 2019 at 3:21 am
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    so good!

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  • September 4, 2019 at 3:39 am
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    Crumpleaz

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  • September 4, 2019 at 1:48 pm
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    Only thing I understood is there is a zoo for dragons which is the hardest.

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  • September 4, 2019 at 11:03 pm
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    Nice najdorf

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  • September 5, 2019 at 8:31 am
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    Well, remember that silicon based computer chipsets are limited on how fast they can do calculations. Even if you used GPU cores it would still lack behind on calculations. So, the fact of silicon computers solving ultra hard NP problems isn't a reality unless you had some sort of miracle chip. Sorting out small list is common sense because it take litterly no time to calculate. The larger the caluation the slower. What we have now can only solve a problem one by one causing limitations.

    Quantum computing is to be designed to where it'll layout all possible solutions at once and pick the best solution in a matter of seconds. So maybe our answers to complicated NP won't exist until we have quantum computing and the advancement of A.i and when we have quantum computers, we will unlock way more than what we have. Qubits are much better and faster at solving than bits. that's just my opinion.

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  • September 5, 2019 at 8:47 am
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    The only way to solve NP is in quantum computing.

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  • September 6, 2019 at 11:52 am
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    Could machine learning play a role in figuring these things out?

    I'm thinking about these two quotes from the video.
    "Even classic video games as Super Mario and Metroid turns out to be connected to NP complete level traversal problems"
    "A fast program to solve any NP-complete problem could be used to solve any problem in NP"

    Seth Bling made a program using machine learning that (after it had been trained) could breeze through randomly generated Super Mario-levels. Now these where straight levels without any path splits if I recall correctly. But we have search algorithms for that, like path finding in mazes which is P.
    I don't know if game speed factors into this as well? Old school games do run in emulators where one could increase the emulated speed, making it possible for a program to complete the levels at it's own limits. There is probably something I am missing as I assume this video present a somewhat simplified version of the problems, or that there was something I missed in the video.

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  • September 6, 2019 at 8:02 pm
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    Thanks for a great explanation! Clear and with good style.

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  • September 7, 2019 at 10:43 pm
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    I think that quantum computing might make p=np, but that making quantum programs is an NP problem that can’t be solved in P time without a quantum computer, which means that without quantum computers, p is not np, but once we have them, P=NP.

    I think, maybe.

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  • September 8, 2019 at 12:13 am
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    Great video. One should point out, though, that the internet security apocalypse is not going to happen, not even if P=NP AND a good general algorithm can be found. The conclusion by Scott Aaronson is also completely false.

    Writing music is not an algorithmic problem. For one thing, nobody has found an algorithm that can even write a melody as simple as "Greensleeves", yet, which I would call a much bigger failure of computer science than the P=NP problem. That is truly embarrassing, folks! For another, any and all attempts to set rules for music have to fail as the interesting part about music is the breaking of rules. What each new generation does is to get used to their parents' music to the point that it becomes utterly boring. Then they take what they know and they grind it to pieces and create something new out of it. No algorithm will ever be able to foresee the future taste of people.

    That mathematical proofs like that of Gauss are outside of the algorithmic realm is being taught by mathematicians in an introductory class about mathematical logic. Do I really have to mention Goedel? Jeez, guys, take a break. NP contains a few interesting problems for CS and mathematicians, but pretty much the entire universe that's fun and important for everybody else lives in exp or way, way beyond.

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  • September 8, 2019 at 5:02 am
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    What if you had a problem that generated solutions.

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  • September 8, 2019 at 9:48 pm
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    and u disappeared 🙁

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  • September 11, 2019 at 1:00 pm
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    "I'm gonna start an educational YouTube channel… Nope. Changed my mind."

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  • September 12, 2019 at 3:49 am
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    P is not equal to NP, take chess for instance you can teach a computer to make moves in chess based on what the best probable defensive and offensive move would be, but you would never be able to teach a computer to make a move based on the most intuitive defense or offense, given human intuition being the standard. If you look at the complexity of this part problem, it all rests on the inability of the person to mathematically define human intuition.

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  • September 12, 2019 at 6:57 pm
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    No text explanation would make me understand this compared to watching this video.

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  • September 13, 2019 at 11:57 am
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    I'm not good at sudoku but this might help. Assume P=/= NP = (NP)^N=P^N=1… sry if it's a bit underwhelming.

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  • September 13, 2019 at 4:41 pm
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    great video, it's a shame us nerds are in the minority because this should have a lot of views

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  • September 14, 2019 at 9:11 pm
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    Why in the world did you stop making videos dude!

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  • September 15, 2019 at 1:37 am
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    9:17

    I got the refference in the bottom left corner.

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  • September 15, 2019 at 12:20 pm
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    Millennial problems: Math is really really hard.
    P vs NP problem: No it's not.

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  • September 15, 2019 at 10:43 pm
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    Thank You!

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  • September 17, 2019 at 2:09 pm
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    "Here there be dragons ?" … it just killed me hahahaha

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  • September 17, 2019 at 10:16 pm
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    Awesome content!
    Thanks!

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  • September 18, 2019 at 6:48 am
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    I’ve actually proved that P=NP and won a million dollars for solving that millennium problem!

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  • September 18, 2019 at 10:01 pm
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    why is P vs NP considered a problem?from what the narator presented it looks more like a preference rather then something that needed to be demonstrated mzthematically

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  • September 23, 2019 at 2:15 pm
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    Why take 5 minutes and 20 seconds to state what P stands for?! Infuriating!!

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  • September 26, 2019 at 5:03 am
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    Amazing video. Well done! Just one correction. Determining the best move from any state in chess is actually in p-space, which is probably not exp. I'd also mention that solving a rubik's cube is polynomial like you said, but solving it in as few twists as possible isn't.

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  • September 27, 2019 at 12:01 pm
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    Getting likes on my comments is an NP-Problem

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  • September 28, 2019 at 2:59 pm
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    I felt pretty good about my understanding of this topic and then the last two minutes hit me

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  • September 29, 2019 at 11:43 pm
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    non sense no explanation

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  • September 30, 2019 at 6:57 am
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    I have tackled this equation in a more Spiritual way. Paradox =(is, is not, both, and neither) Like a shadow a paradox is the nature of that shadow. It exists and does not exist at the same time. Paradox is full of NP. What happened, Will happen, Never happened ar all true or P and our very perception of this sides change. In -paradox yes and no are both right answers, logic becomes perception and consciences is made. Basically it's not real until you hear it; Like the proverbial tree in the woods. did it fall. Paradox is the answer. When you Identify it you give it a name and nomenclature or a judgement. The first judgement might answer the problem but it may not turn out to be the ultimate solution but the questions exist like shadows and we observe and verify all things together, With our Culture being each of our bios or Cognitive Dissonance= NP.

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  • October 1, 2019 at 1:13 am
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    Wow great video!!! So clear, so focused…so powerful in informing. Thank you!

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  • October 2, 2019 at 11:03 pm
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    God, everytime I feel down and depressed, I visit this video and it breaks my heart because it is such an achingly BEAUTIFUL video … Thank you Mister Hackerdashery … 😥

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  • October 4, 2019 at 3:57 am
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    If I had to take a guess about how these work, I’d say that every problem has some best solution of with a fixed solution time, and P problems are just ones we guess or figure out the best solutions the first time, and there’s less of a difference between these problems then we think. But I doubt this is correct

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  • October 4, 2019 at 10:17 am
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    The hardest mathematical equation in the universe:
    Just because one can, does that mean one should?
    An Egyptian predicted writing should not be done just because we can, that it would lead to self destruction.

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  • October 5, 2019 at 5:18 am
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    Don't commit Sudoku.

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  • October 6, 2019 at 8:25 am
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    WHY WOULD YOU PUT ME IN A ZOO???????

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  • October 7, 2019 at 9:47 am
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    This video is so fucking cool … please keep making more

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  • October 12, 2019 at 3:56 pm
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    I never comment on a video. But the sheer depth and amazing complexity explained in such a simple way was something I never expected to see in a video. Thank you very much!

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  • October 14, 2019 at 4:52 am
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    poly – nomial
    – nomial: from νομός (nomos) – in Greek, meaning portion, part; not from name.

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  • October 14, 2019 at 8:47 am
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    p=np

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  • October 14, 2019 at 5:31 pm
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    Excellent primer.

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  • October 17, 2019 at 11:44 pm
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    This seems more like philosophy than math tbqh.

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  • October 18, 2019 at 7:15 pm
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    Watching this almost every week

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