What if, no matter how strong your password was, a hacker could crack it just as easily as you can type it? In fact, what if all sorts of puzzles we thought were hard turned out to be easy?

\begin{abstract} We present a locality--audit framework for proving circuit lower bounds for NP languages. We define an explicit NP--complete language equipped with structural invariances (``audits'') ...

Source: Darren Edwards What if one of the biggest unsolved problems in mathematics is not just about numbers or computers, but about observers like you and me? This isn’t a proposed solution to P vs ...

Complexity theory remains one of the great unsolved mathematical puzzles. Kenneth Regan is trying to figure it out. Kenneth Regan paused at lunch in New York to glance at incoming texts from top ...

The distinction between problems whose solutions can be quickly verified (NP) and quickly solved (P) is a foundational question in computer science and mathematics. The mainstream assumption is P≠NP.

When one thinks of mathematics, the thought that comes to most peoples’ heads is solving an equation and getting a correct answer. That is the case with many mathematical theorems, including one of ...

ABSTRACT: We present a new perspective on the P vs NP problem by demonstrating that its answer is inherently observer-dependent in curved spacetime, revealing an oversight in the classical formulation ...