>tfw you figured out why P=NP in a dream but then the alarm

>>8334580
You were wrong. Clearly, P = NP is not true for all N.

For example, consider N = 2. Then P = 2P, which implies 1 = 2, which is false. Therefore, P != NP.

Where is my million bucks?

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>>8334596

>it's another "anon intentionally treats P=NP as an algebra equation to try to be funny" episode

>>8334580
OK it seems like everyone is just making P=NP way more complicated than it needs to be. Like all it's saying is that any problem that can be verified quickly can also be solved quickly. But obviously that's true because how could you verify it if you hadn't already solved it? People just get too caught up in the obscure math hieroglyphics and lose sight of the bigger picture

>>8334580
>you figured out why P=NP
No you didnt, you had a very strong but false impression that you did

>>8334609

>Like all it's saying is that any problem that can be verified quickly can also be solved quickly. But obviously that's true because how could you verify it if you hadn't already solved it?

No, I don't think you really understand it unless this is an attempt at joking by intentionally misunderstanding it. The reason it's important is because if it's proven that for all NP problems there exists an algorithm that can be calculated in polynomial time rather than just exponential time then pretty much every single encryption / security measure in existence would be breakable without needing to have a supercomputer run for a million years to do so.

>>8334624
>muh encryption

>>8334642
Encryption is amazingly important

>>8334649
p=np has important consequences much beyond encryption

>>8334656

Encryption is bank accounts and there's literally nothing more important than your money.

>>8334658
>this is what capitalists actually believe

>>8334656
Its probably the most significant practical consequence though

>>8334609
>>8334624
>>8334642
Kids stop fighting, you're both awful popsci faggots who completely missed the point.

>>8334661

Money is literally the Platonic Form of Value itself you fool.

>>8334624
The trouble is that proving P=NP is an existence result, so unless it is a constructive proof, it doesn't mean we will have the algorithm. Most people just assume P≠NP in practice and move on. Besides, we have encryption that doesn't rely on polynomial-time checking algorithms which will not be affected by such an algorithm, so P=NP is more of a major theoretical tool than anything.

I'm not detracting its importance, as I am a pure mathfag anyways, but the consequences of P=NP are way overblown.

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>>8334668

>being too autistic to realize this was a meme thread from the very beginning

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>>8334580
>mfw I have an epiphany about the P=NP problem but don't have the time to explore the idea between work and trying to relax away from work

>>8334669
Stop, you're proving his point.

>>8334580

If you actually try to write down one of these dream-ideas, you'll find that it's often not going to work. It takes a lot of work to get the technical details to go through in this universe.

>>8334609
>OK it seems like everyone is just making P=NP way more complicated than it needs to be.
Yeah

>Like all it's saying is that any problem that can be verified quickly can also be solved quickly.
Right on

>But obviously that's true
Uh

>how could you verify it if you hadn't already solved it?
I don't think you quite get it. When it says "can be verified quickly" it means verified if someone gives you the solution.

So say you have a travelling salesman scenario and the question is if you if there is a cycle shorter than some given cycle X. If someone gives you a solution shorter than X then you can check that in polynomial time so the problem lies in NP. It's unknown whether the problem is also in P though.