From John von Neumann’s universal machine to John Nash’s insight into computation, this video explores how computer scientists began measuring problems by the number of steps a machine must take as ...

AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we can't verify them. How will we know if they're right?

\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 ...

This essay offers an epistemological reinterpretation of the foundational divide between matrix mechanics and wave mechanics. Though formally equivalent, the two theories embody distinct modes of ...

This repository presents a novel framework for reenvisioning the P vs NP problem through the synthesis of computational phase transitions, knowledge accumulation dynamics, and thermodynamic principles ...

NEW YORK — Jalen Brunson cut the tension. Not long after Cameron Payne signed with the New York Knicks last summer, the team gathered for a pickup run at its practice facility. This was Payne’s first ...

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 ...