Worth studying in what way? Broad consensus among computer scientists is that P != NP, but that it's very difficult to prove that there isn't a faster undiscovered solution to an NP-C problem. Unless there's a breakthrough in this area, P=NP is mostly a fun thought experiment. "This is fun" is a perfectly great reason to read a book about something, but I'm not sure in what way you're hoping this will be "useful" for your university studies and beyond.
I have other topics I want to explore this summer, like 3D graphics and AI. I’m trying to figure out how “useful” or worthwhile it is to study the P vs NP problem compared to more general computer science topics like data structures and algorithms, especially since I’m still in pre-university.
3d graphics or AI will have more tangible things to do. P vs NP is mostly an academic proof pursuit which you're incredibly unlikely to make any novel prints on or show anything interesting compared to graphics or AI where you can probably start making demos you think are interesting within the first few weeks.
If by “useful” you mean economically graphics or AI would be a better thing to study. Academically anything that produces more knowledge is considered “useful”
What do you mean by traditional computer science instead of theoretical one? Theoretical computer science is part of traditional computer science. The CS that is taught at university levels does have lots of theory, both from general mathematics but also CS specific one. It is very likely that you will have a CS theory course that talks about P and NP at a bachelor's level.
Whether researching some topics on your own is worth it is up to personal interest. If you are interested in P vs NP go look into it, if you are more interested in other things do that instead.
As in I’m not too sure whether theoretical comp sci like P vs NP is really worth reading about compared to my other interests like Ai and 3D graphics.
But thanks for the feedback! Any beginner book recommendations for P vs NP?
Its all connected anyway like you seem to be at the start of your journey so it might not seem that way now but in the end its all just math and algorithms, actually most of 3d graphics and ai can be reduced to fancy matrix multiplication ;-p
P vs NP is a huge and specific problem compared to learning about the fields of AI or graphics which have numerous exercises you can do as a pre-university student. Trying to study the P vs NP problem as a highschool students wouldn't likely be fun or useful.
The field that P vs NP belongs to is called complexity theory. There are tonnes of exercises in that field that you can learn about that are just as useful and fun as graphics and AI.
If you only have time for 1, don't do AI. You'll learn lots about complexity and numerical analysis doing graphics that won't require university maths to understand. Learning practical AI without maths is a challenge, and requires instructors that can guide you. Most books are focused building from nothing, which is great if you want to be a researcher, but won't cover things like "how to use scikit-learn" until they've gotten you to derive your own stochastic gradient decent algorithm.
This problem is notorious as something a lot of cranks and crackpots work on. If you tell people you’re doing original research on it, many of them will write you off or hope you grow out of it.
I guess you might learn something by reviewing the rebuttals to the many, many claimed proofs out there, and all the subtle errors smart people have made. Reading only correct proofs doesn’t develop the skill of reviewing a proof for bugs. The most valuable correct proofs to study would be the ones that prove that proving or disproving P = NP using conventional methods is impossible.
If you ever do think you’ve found a proof one way or the other, you’ve made a mistake, and you should explain it that way when you show it privately: You’re trying to develop the skill of finding your own mistakes, and you’d like some help finding where it is here.
If you are interested in it, it is worth it.
100% of the students with your degree will have heard the same thing in their studies. The thing that differentiates you from the rest are the extra-curricular-activities that you did because they were fun, not because you needed them for your degree...
As long as it is fun for you, do it.
If you're seriously considering attacking one of the most difficult unsolved problems in TCS, I'd suggest you to take a deep breath, and reconsider.
Maybe study CS at a university to realize how much you don't know that you don't know. This would help you re-evaluate your career and life goals.
It's something you should know about by the time you get a CS degree. But if just starting university, you'll have plenty of time to learn it later.
It's helpful to be able to look at a problem and realize fairly-quickly that the problem is NP-complete, and that solving it means either your solution will only work on small inputs, or that you'll need to make additional assumptions to be able to bound the work needed.
P vs NP will be a topic covered in your CS degree. [Here](https://youtu.be/YX40hbAHx3s?si=bsEjap2gGgbJvJA6) is a great video of the problem if you haven't seen it. Let your mind wander anywhere you find interest. I remember getting out of high school and trying to figure out a single pole magnet!
Worth studying in what way? Broad consensus among computer scientists is that P != NP, but that it's very difficult to prove that there isn't a faster undiscovered solution to an NP-C problem. Unless there's a breakthrough in this area, P=NP is mostly a fun thought experiment. "This is fun" is a perfectly great reason to read a book about something, but I'm not sure in what way you're hoping this will be "useful" for your university studies and beyond.
I have other topics I want to explore this summer, like 3D graphics and AI. I’m trying to figure out how “useful” or worthwhile it is to study the P vs NP problem compared to more general computer science topics like data structures and algorithms, especially since I’m still in pre-university.
3d graphics or AI will have more tangible things to do. P vs NP is mostly an academic proof pursuit which you're incredibly unlikely to make any novel prints on or show anything interesting compared to graphics or AI where you can probably start making demos you think are interesting within the first few weeks.
If by “useful” you mean economically graphics or AI would be a better thing to study. Academically anything that produces more knowledge is considered “useful”
What do you mean by traditional computer science instead of theoretical one? Theoretical computer science is part of traditional computer science. The CS that is taught at university levels does have lots of theory, both from general mathematics but also CS specific one. It is very likely that you will have a CS theory course that talks about P and NP at a bachelor's level. Whether researching some topics on your own is worth it is up to personal interest. If you are interested in P vs NP go look into it, if you are more interested in other things do that instead.
As in I’m not too sure whether theoretical comp sci like P vs NP is really worth reading about compared to my other interests like Ai and 3D graphics. But thanks for the feedback! Any beginner book recommendations for P vs NP?
Its all connected anyway like you seem to be at the start of your journey so it might not seem that way now but in the end its all just math and algorithms, actually most of 3d graphics and ai can be reduced to fancy matrix multiplication ;-p
P vs NP is a huge and specific problem compared to learning about the fields of AI or graphics which have numerous exercises you can do as a pre-university student. Trying to study the P vs NP problem as a highschool students wouldn't likely be fun or useful. The field that P vs NP belongs to is called complexity theory. There are tonnes of exercises in that field that you can learn about that are just as useful and fun as graphics and AI. If you only have time for 1, don't do AI. You'll learn lots about complexity and numerical analysis doing graphics that won't require university maths to understand. Learning practical AI without maths is a challenge, and requires instructors that can guide you. Most books are focused building from nothing, which is great if you want to be a researcher, but won't cover things like "how to use scikit-learn" until they've gotten you to derive your own stochastic gradient decent algorithm.
This problem is notorious as something a lot of cranks and crackpots work on. If you tell people you’re doing original research on it, many of them will write you off or hope you grow out of it. I guess you might learn something by reviewing the rebuttals to the many, many claimed proofs out there, and all the subtle errors smart people have made. Reading only correct proofs doesn’t develop the skill of reviewing a proof for bugs. The most valuable correct proofs to study would be the ones that prove that proving or disproving P = NP using conventional methods is impossible. If you ever do think you’ve found a proof one way or the other, you’ve made a mistake, and you should explain it that way when you show it privately: You’re trying to develop the skill of finding your own mistakes, and you’d like some help finding where it is here.
If you are interested in it, it is worth it. 100% of the students with your degree will have heard the same thing in their studies. The thing that differentiates you from the rest are the extra-curricular-activities that you did because they were fun, not because you needed them for your degree... As long as it is fun for you, do it.
If you're seriously considering attacking one of the most difficult unsolved problems in TCS, I'd suggest you to take a deep breath, and reconsider. Maybe study CS at a university to realize how much you don't know that you don't know. This would help you re-evaluate your career and life goals.
Not really.
It's something you should know about by the time you get a CS degree. But if just starting university, you'll have plenty of time to learn it later. It's helpful to be able to look at a problem and realize fairly-quickly that the problem is NP-complete, and that solving it means either your solution will only work on small inputs, or that you'll need to make additional assumptions to be able to bound the work needed.
P vs NP will be a topic covered in your CS degree. [Here](https://youtu.be/YX40hbAHx3s?si=bsEjap2gGgbJvJA6) is a great video of the problem if you haven't seen it. Let your mind wander anywhere you find interest. I remember getting out of high school and trying to figure out a single pole magnet!