- As a grad student I used to read these until I found the mistake or until it was incomprehensible, which was the more common experience. Now I do not even bother going to the website that claims to have the proof.
- I do not believe that someone whose knowledge of math is not very deep could possibly prove P\ne NP. Actually I do not believe anyone right now can prove P\ne NP. Any paper claiming such would have to begin with the answer to What are you using to get around the known barriers?
- A proof that P=NP is more plausible now, except that I believe that P\ne NP.
- Our time is limited. For most people in the field, debunking proofs is not worth our time. Once you've debunked a few and gotten into arguments with the authors you will agree.
- My most recent debunking was actually okay. I got a paper that claimed that he MIGHT have a proof that P\ne NP (I like the humbleness) and it was reasonably well written. I told him that everything he wrote about Ham Cycle applies to Eulerian Cycle as well, and hence the proof cannot work. He accepted that but also said he may get me a better draft later. He has not.
- I have found that debunking a proof that P\ne NP is usually easy: like the above, Eulerian Cycle may be a counterexample to the usual You have to go through all possibilities argument. Debunking a proof that P=NP may be harder since they can be just code. But I would like commentary on this--- what have you debunked and what to you find easy or hard to debunk?
Monday, September 28, 2009
One of the comments of the last post asked my (or someones) opinion on the proofs floating around that P=NP or P\ne NP.