Related papers: A "Proof" of $P\neq NP$
In this paper we present a short and elementary proof for the error in Simpson's rule.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
This article describes a formal strategy of geometric complexity theory (GCT) to resolve the {\em self referential paradox} in the $P$ vs. $NP$ and related problems. The strategy, called the {\em flip}, is to go for {\em explicit proofs} of…
In this article we show how any formula A with a proof in minimal implicational logic that is super-polynomially sized has a polynomially-sized proof in classical implicational propositional logic . This fact provides an argument in favor…
A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
Mathematical proofs should be paired with formal proofs, whenever feasible.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
In this document we define a method of proof that we call proof by dichotomy. Its field of application is any proposition on the set of natural numbers N. It consists in the repetition of a step. A step proves the proposition for half of…
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
We review Andr\'e Luiz Barbosa's paper "P != NP Proof," in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
Remarks on mathematical proof and the practice of mathematics.
We define several canonical problems related to contrastive explanations, each answering a question of the form ''Why P but not Q?''. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The purpose of the paper is to present an short proof of the Chuang's inequality.