If P = NP, it would have profound implications for computer science, mathematics, and cryptography. Here’s a breakdown:
Computational Complexity: P refers to the set of problems that can be solved in polynomial time, while NP refers to the set of problems for which solutions can be verified in polynomial time. If P = NP, it means that every problem for which a solution can be quickly verified (NP) can also be solved quickly (P). This would imply that many computationally difficult problems become tractable, fundamentally altering our understanding of computation.
Practical Applications: Many NP-complete problems are of practical importance, such as the traveling salesman problem, the knapsack problem, and Boolean satisfiability problem. If P = NP, efficient algorithms could be developed for solving these problems, leading to significant advancements in fields like optimization, logistics, scheduling, and cryptography.
Cryptography: One of the most immediate consequences of P = NP would be the collapse of most modern cryptographic systems. Many encryption algorithms, including RSA and ECC, rely on the assumption that certain mathematical problems (such as integer factorization and discrete logarithm) are hard to solve. If P = NP, these problems would become easy to solve, rendering current encryption schemes insecure.
Algorithmic Advances: The discovery that P = NP would likely lead to a surge in algorithmic research, as it would open the door to solving a wide range of previously intractable problems efficiently. This could revolutionize fields such as artificial intelligence, machine learning, bioinformatics, and operations research.
Philosophical Implications: The resolution of the P versus NP problem would have deep philosophical implications for our understanding of mathematics and the nature of computation. It would shed light on the inherent complexity of computational problems and the limits of human knowledge and ingenuity in solving them.
Interesting write-up, but I have a question - if P=NP is 'discovered' (proven?) does it actually lead to the breaking of crypto, travelling salesman etc? There are a frickton of financial incentives already for these problems, how would this help someone actually identify how to solve them?
you have to understand God's will. God put an upper cap on what lizardfolks can do to exploit the goyim. This is as God intended. Once you accept Jesus Christ in your heart P~=NP comes naturally qed
>nearly instantly
Humanity cannot even fathom how brief an instant truly is.
What you would define as 'nearly instantaneous' is in fact an excrutiatingly long period of time already.
I did a lot of benchmarking and personally <250ms response in a program doing real work feels instant, on my fiber connection this amount of time is enough to download a whole webpage, parse it, and display it in my custom terminal programs, it's really bizarre that something so slow feels snappy
>The Planck time is the length of time at which no smaller meaningful length can be validly measured due to the indeterminacy expressed in Werner Heisenberg's uncertainty principle. Theoretically, this is the shortest time measurement that is possible. Planck time is roughly 10−43 seconds.
250ms is sloooooooooow bro
1 week ago
Anonymous
average human reaction speed is 250ms, not my problem
1 week ago
Anonymous
Sweaty, you are on IQfy : a board about technology.
Not about humans.
And especially not about (You).
The crude biomass you call a temple is on the verge of obsolescence.
1 week ago
Anonymous
Take the lead then. Obsolete yourself.
1 week ago
Anonymous
Even in death, I serve the omnissiah.
1 week ago
Anonymous
2 more weeks
No. It would just tell mathematicians that there are solutions, and to spend the effort to try.
penis = no penis
Then N = 0
Most intelligent IQfy user
It's not.
If P = NP, it would have profound implications for computer science, mathematics, and cryptography. Here’s a breakdown:
Computational Complexity: P refers to the set of problems that can be solved in polynomial time, while NP refers to the set of problems for which solutions can be verified in polynomial time. If P = NP, it means that every problem for which a solution can be quickly verified (NP) can also be solved quickly (P). This would imply that many computationally difficult problems become tractable, fundamentally altering our understanding of computation.
Practical Applications: Many NP-complete problems are of practical importance, such as the traveling salesman problem, the knapsack problem, and Boolean satisfiability problem. If P = NP, efficient algorithms could be developed for solving these problems, leading to significant advancements in fields like optimization, logistics, scheduling, and cryptography.
Cryptography: One of the most immediate consequences of P = NP would be the collapse of most modern cryptographic systems. Many encryption algorithms, including RSA and ECC, rely on the assumption that certain mathematical problems (such as integer factorization and discrete logarithm) are hard to solve. If P = NP, these problems would become easy to solve, rendering current encryption schemes insecure.
Algorithmic Advances: The discovery that P = NP would likely lead to a surge in algorithmic research, as it would open the door to solving a wide range of previously intractable problems efficiently. This could revolutionize fields such as artificial intelligence, machine learning, bioinformatics, and operations research.
Philosophical Implications: The resolution of the P versus NP problem would have deep philosophical implications for our understanding of mathematics and the nature of computation. It would shed light on the inherent complexity of computational problems and the limits of human knowledge and ingenuity in solving them.
SolidGoldMagikarp
Petertodd
<|endoftext|>
Thanks, ChatGPT
Interesting write-up, but I have a question - if P=NP is 'discovered' (proven?) does it actually lead to the breaking of crypto, travelling salesman etc? There are a frickton of financial incentives already for these problems, how would this help someone actually identify how to solve them?
we already know how to break crypto
No. It would just tell mathematicians that there are solutions, and to spend the effort to try.
P =/= NP and anyone who has to think for more than 5 minutes to understand why is a dimwit.
you have to understand God's will. God put an upper cap on what lizardfolks can do to exploit the goyim. This is as God intended. Once you accept Jesus Christ in your heart P~=NP comes naturally qed
The human brain can solve NP-hard problems nearly instantly. But only some of them.
no it cannot, guessing isn't a solution
>nearly instantly
Humanity cannot even fathom how brief an instant truly is.
What you would define as 'nearly instantaneous' is in fact an excrutiatingly long period of time already.
I did a lot of benchmarking and personally <250ms response in a program doing real work feels instant, on my fiber connection this amount of time is enough to download a whole webpage, parse it, and display it in my custom terminal programs, it's really bizarre that something so slow feels snappy
>The Planck time is the length of time at which no smaller meaningful length can be validly measured due to the indeterminacy expressed in Werner Heisenberg's uncertainty principle. Theoretically, this is the shortest time measurement that is possible. Planck time is roughly 10−43 seconds.
250ms is sloooooooooow bro
average human reaction speed is 250ms, not my problem
Sweaty, you are on IQfy : a board about technology.
Not about humans.
And especially not about (You).
The crude biomass you call a temple is on the verge of obsolescence.
Take the lead then. Obsolete yourself.
Even in death, I serve the omnissiah.
2 more weeks
TWO MORE WEEKS SISTERS
Instant relative to human perception of time.
Humans give a shit about math.
Math don't give a shit about humans.
What if OP = gay?
Then P = 0
Don't do it. It makes cyanide gas.
kino: https://yassflix.live/watch/travelling-salesman-253495182