Tao: Today there are a lot of very tedious types of mathematics that we don’t like doing, so we look for clever ways to get ...

Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the University of Waterloo suggests that more than creativity ...

A recursive language model framework enhanced with φ-Separation Mathematics, featuring streaming responses, document analysis, REST API, and parallel processing. phi-enhanced-rlm/ ├── README.md # This ...

Low-rank data analysis has emerged as a powerful paradigm across applied mathematics, statistics, and data science. With the rapid growth of modern datasets in size, dimensionality, and complexity, ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

You chose selected. Each dot here represents a single video about selected. While you’re on the app, TikTok tracks how you interact with videos. It monitors your watch time, the videos you like, the ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. Non-Commercial (NC): Only non-commercial uses of the work are permitted. No ...

When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture ...

The original version of this story appeared in Quanta Magazine. One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling ...

A new technical paper titled “Scanning electron microscopy-based automatic defect inspection for semiconductor manufacturing: a systematic review” was published by researchers at KU Leuven and imec.

MicroAlgo Inc. announced its research on the Quantum Information Recursive Optimization (QIRO) algorithm, which aims to address complex combinatorial optimization problems using quantum computing.