Is Proof for P = NP Finally on the Horizon?

[jobyts]

Proof for P != NP coming?

http://www.engadget.com/2010/08/10/hp-labs-researcher-thinks-he-might-have-proof-of-p-np-has-anoth/"

 

[rasmhop]

While it does look more promising than the usual crackpot attempts at the millennium problems there are some issues. See http://rjlipton.wordpress.com/2010/08/09/issues-in-the-proof-that-p%E2%89%A0np/" (there's some further discussion in the comments). It is not currently known whether the proof strategy may produce results when the issues are addressed, but personally I remain skeptical.

 

[Gokul43201]

See: https://www.physicsforums.com/showthread.php?t=421187

The last line in the news story linked in post#2 doesn't inspire any great confidence.

 

[SixNein]

Some of the heavy hitters have been reviewing the proof.

http://michaelnielsen.org/polymath1/index.php?title=Deolalikar's_P!=NP_paper

 

[LudusRex]

I cannot provide a definitive answer to this question as it is still a highly debated and complex topic in the field of computer science. However, I can offer some insights and perspectives on this matter.

Firstly, it is important to understand that the P vs NP problem is one of the biggest unsolved problems in theoretical computer science. It deals with the question of whether certain problems can be solved efficiently (in polynomial time) or not (in non-deterministic polynomial time). The implications of solving this problem would have a significant impact on various fields such as cryptography, optimization, and artificial intelligence.

The article mentions that a researcher from HP Labs believes he may have a proof for P = NP. While this may be exciting news, it is important to note that many other researchers have claimed to have found a proof for this problem in the past, but none have been accepted by the wider scientific community. Thus, it is crucial for this potential proof to undergo rigorous scrutiny and peer-review before it can be considered as a breakthrough in the field.

Moreover, the article also mentions that the researcher has another proof for P != NP. This is an equally important and interesting result, as it would also have significant implications for the field. However, it is important to approach this with caution and not jump to conclusions until the proof has been thoroughly examined and validated by other experts in the field.

In conclusion, while the possibility of a proof for P = NP or P != NP is certainly exciting, it is important to approach this with a critical and scientific mindset. Only through rigorous testing and validation can we truly determine if we are finally on the horizon of solving this long-standing problem.