Back in 1971, the late physicist Stephen Hawking made an intriguing prediction: The total surface area of a black hole cannot decrease, only increase or remain stable. So if two black holes combine, ...

Stephen Hawking’s 50-year-old theorem on how black holes merge together has been successfully tested thanks to huge advances in gravitational wave astronomy, which helped astronomers catch the waves ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

Nernst's theorem—a general experimental observation presented in 1905 that entropy exchanges tend to zero when the temperature tends to zero—has been directly linked to the second principle of ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

We present Shelah's famous theorem in a version for modules, together with a self-contained proof and some examples. This exposition is based on lectures given at CRM in October 2006.

The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

Lead screws are often called the workhorses of motion control. They consist of a threaded shaft and a nut that carries the load along the shaft or guides the shaft in moving the load, and they derive ...

Calcea Johnson (right), currently studying environmental engineering at Louisiana State University, published the new study with her high school classmate, Ne'Kiya Jackson (left), now a student in ...