A principle for checking proofs with an application to the proof Vinay Deolalikar is standing by his $latex {\mathsf{P} \neq. Today I had planned not to discuss the proof, but I just received a note from Neil on Vinay Deolalikar “proof” that P {\neq} NP. Neil points out two. A few days ago, Vinay Deolalikar of HP Labs started circulating a claimed proof of P≠NP. As anyone could predict, the alleged proof has.


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Today I wish to talk about something other than the P NP proof. But it is hard to get back to other issues right now.

Deolalikar Responds To Issues About His P≠NP Proof | Gödel's Lost Letter and P=NP

I do agree with Tao that we need to move on to other topics, and let the proof checking continue at a more relaxed pace. I would like to share a proof searching trick that I have always used; it must be well known, but I do not know a name for it. Vinay deolalikar p np Principle Suppose that Alice is trying to provesome statement that Bob is interested in seeing proved.


Alice is working hard trying to understand the problem: Finally, after months of hard work, Alice has an outline of a proof. She has not checked all the details, but she is quite excited about the potential.

She thinks she has her proof.

Scientific proof of “P ≠ NP” math problem proposed by HP Labs’ Vinay Deolalikar

Imagine that she is about to go to explain the proof to Bob. Just before she does this, Alice notices the following. She notices vinay deolalikar p np the same proof—perhaps slightly changed—will also prove. In a sense she sees that where is a slight variation of her proof.


Here is the principle: Even if is an open problem, then this could be an issue. The reason is Alice felt she had a nice proofbut did not think her method was powerful enough to solve the hard open problem. I use this principle—unfortunately all too often—to shoot down my own proof attempts.

It vinay deolalikar p np either vinay deolalikar p np something dead-wrong or something that is way too hard for my weak method.

Math - Explain the proof by Vinay Deolalikar that P != NP - Stack Overflow

Here are two simple examples of this principle: Suppose Alice is working on the Riemann Hypothesis. This famous problem says that all the non-trivial zeroes of the zeta function must lie on the line.

The zeta function has so called trivial zeroes at She proves that all the vinay deolalikar p np zeroes of the zeta function must have a left-to-right symmetry about the line. She then uses this cool lemma to solve the Riemann Hypothesis.

But after checking her argument she discovers that her cool lemma never used vinay deolalikar p np fact that the zeroes were non-trivial.


Clearly, this is a problem, since it would imply that the zeta function has zeroes with real part greater than. This is false and so her lemma has to be re-thought Vinay deolalikar p np have worked on a much less important problembut one where the principle played a role.

I had an idea for proving a certain complexity theorem—nothing like P NP—but still an open vinay deolalikar p np. I was pretty excited and quickly thought I could generalize my trick to solve the full problem.

Alas, I saw that the principle applied here: The problem I worked on is still open. They do not state their concern in this way, but it is essentially a potential violation of the principle.

Deolalikar P vs NP paper - Polymath1Wiki

Of course, -SAT is long known to be in polynomial time, so if his proof does not have a critical step, lemma, or place where is used in an essential way, then it has problems.

Vinay deolalikar p np is that "intriguing structure in the solution space is not sufficient for NP hardness".

The second is that "intriguing structure is not necessary for NP hardness".