3 ms·

A bit off topic to your question, but this reminds me. Where are we exactly progress wise with P vs. NP problem? I've not thought to track the millennium proble

A bit off topic to your question, but this reminds me. Where are we exactly progress wise with P vs. NP problem? I've not thought to track the millennium problems in a while. I'm sure I would have heard if something substantial had arisen though. I used to work with it at some point on specific variation of the problem with was the dorm room housing problem [1]. That particular scenario always stood out to me as something that should be relatively easy to solve and I worked on it for a few years. Anyways, I'm way off topic now. [1] http://www.claymath.org/millennium-problems/p-vs-np-problem http://www.claymath.org/millennium-problems/p-vs-np-problem

Aardwolf 9y ago
Every now and then there is a paper that attempts proving P=NP or attempts proving P!=NP, I've seen different papers on hacker news several times. The most interesting link someone posted was this one listing many such papers, nicely indicating [equal], [not equal], [undecidable] or [unprovable]: http://web.archive.org/web/20171006224902/https://www.win.tue.nl/~gwoegi/P-versus-NP.htm http://web.archive.org/web/20171006224902/https://www.win.tu... Archive link because original page has certificate error :(
- jdironman 9y ago
  I am especially intrigued by the argument made by Nicholas Argall. In that the question of whether P = NP or not is incomplete in and of itself.[1] I think this is very true on the basis that not all of these problems are the same or present the same criteria to solve. I think understanding these problems is going to require thinking from a different depth though. It's fun to me to think about and try to wrap my head around. I'm no expert but have a lot of fun with it. http://web.archive.org/web/20170817220728/http://www.win.tue.nl/~gwoegi/P-versus-NP/argall.txt http://web.archive.org/web/20170817220728/http://www.win.tue...
  - thethirdone 9y ago
    The argument put forward in the link misrepresents Godel's theorem. > 6) Therefore, no consistent and complete definition of the set NP is possible Rationale: If we accept that the set NP can only be rigorously defined via a language, this conclusion follows from the premises above. This doesn't even make sense. Definitions do not change a languages completeness or consistency; they simply relate a new concept to previously defined concepts. > 7) Therefore, no consistent and complete statement of the problem of P=NP is possible Comment: A conclusion which is not only proven in this paper, but supported by the years of argument between mathematicians regarding the relevance of proposed answers to the problem. This is not supported from Godel's theorem. The fact that you need a non-complete system to be able to reason about something does not mean the theorem you want to prove is not provable. The main problem with the argument is that it works for other theorems that have been formally proven.
- underwoodley 9y ago
  This seems to be mainly a collection of garbage papers and nonserious proofs by cranks and uninformed people. Not that it isn't interesting, but it doesn't seem to say anything about actual mathematical progress.
  - hexane360 9y ago
    Well it does seem to say something about the lack of actual mathematical progress -- or at least the lack of actual mathematical completion.

Aardwolf 9y ago

Every now and then there is a paper that attempts proving P=NP or attempts proving P!=NP, I've seen different papers on hacker news several times. The most interesting link someone posted was this one listing many such papers, nicely indicating [equal], [not equal], [undecidable] or [unprovable]: http://web.archive.org/web/20171006224902/https://www.win.tue.nl/~gwoegi/P-versus-NP.htm http://web.archive.org/web/20171006224902/https://www.win.tu... Archive link because original page has certificate error :(

jdironman 9y ago
I am especially intrigued by the argument made by Nicholas Argall. In that the question of whether P = NP or not is incomplete in and of itself.[1] I think this is very true on the basis that not all of these problems are the same or present the same criteria to solve. I think understanding these problems is going to require thinking from a different depth though. It's fun to me to think about and try to wrap my head around. I'm no expert but have a lot of fun with it. http://web.archive.org/web/20170817220728/http://www.win.tue.nl/~gwoegi/P-versus-NP/argall.txt http://web.archive.org/web/20170817220728/http://www.win.tue...
- thethirdone 9y ago
  The argument put forward in the link misrepresents Godel's theorem. > 6) Therefore, no consistent and complete definition of the set NP is possible Rationale: If we accept that the set NP can only be rigorously defined via a language, this conclusion follows from the premises above. This doesn't even make sense. Definitions do not change a languages completeness or consistency; they simply relate a new concept to previously defined concepts. > 7) Therefore, no consistent and complete statement of the problem of P=NP is possible Comment: A conclusion which is not only proven in this paper, but supported by the years of argument between mathematicians regarding the relevance of proposed answers to the problem. This is not supported from Godel's theorem. The fact that you need a non-complete system to be able to reason about something does not mean the theorem you want to prove is not provable. The main problem with the argument is that it works for other theorems that have been formally proven.
underwoodley 9y ago
This seems to be mainly a collection of garbage papers and nonserious proofs by cranks and uninformed people. Not that it isn't interesting, but it doesn't seem to say anything about actual mathematical progress.
- hexane360 9y ago
  Well it does seem to say something about the lack of actual mathematical progress -- or at least the lack of actual mathematical completion.