Zero-knowledge proofs (ZKPs) are cryptographic methods that let someone prove something is true without revealing the underlying data. A simple analogy: you can prove you’re over 18 without showing ...

NP-complete problems, including optimal routing, scheduling and network design, are foundational to essential tasks across various industries. However, they actually pose challenges for conventional ...

In 1990, Marilyn vos Savant riled up scores of mathematicians with her solution to the “Monty Hall Problem.” But she was right. The following is an excerpt from Proof: The Art and Science of Certainty ...

Abstract: Combinatorial problems-especially nondeterministic polynomial time (NP)-complete problems, poses a formidable challenge for efficient resolution within the constraints of conventional ...

A high-performance C# implementation of the classic NP-complete Subset Sum problem. Built as a research-driven exploration of computational complexity, this project applies advanced algorithmic ...

A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...

Electronic computers are extremely powerful at performing a high number of operations at very high speeds, sequentially. However, they struggle with combinatorial tasks that can be solved faster if ...

This is an edited transcript of an episode of “The Ezra Klein Show.” You can listen to the conversation by following or subscribing to the show on the NYT Audio App, Apple, Spotify, Amazon Music, ...

Light propagates in a three-dimensional photonic circuit to solve the subset sum problem. The image of the reconfigurable photonic processor is based on the research presented. Credit: Xu et al., doi ...

Traditional computers struggle with NP-complete problems, which grow exponentially in complexity. According to a study published in Advanced Photonics, a group of researchers from Shanghai Jiao Tong ...