Recent breakthroughs in artificial intelligence have uncovered surprising geometric structures within large language models (LLMs) like ChatGPT. These findings offer a new perspective on how these ...

In the 1980s, the US was constructing the Texas Superconducting Super Collider. It was designed to collide protons together so that scientists could study how gluons, which hold the quarks in protons ...

Recent advancements in thermodynamics have increasingly drawn on the language of differential geometry and systems control to reformulate classical principles. Geometric structures offer a rigorous ...

Conventional catalysts for hydrogen production via water electrolysis usually contain precious metals and are expensive. However, cheaper alternatives have been developed, for example cobalt–manganese ...

These are not the kinds of objects that concern Scott Sheffield. Sheffield, a professor of mathematics at the Massachusetts Institute of Technology, studies shapes that are constructed by random ...

The chirality lies in the geometry Scanning electron microscopy (SEM) image of nickel-based artificial chiral magnets fabricated at EPFL’s Center of MicroNanoTechnology. (Courtesy: Mingran Xu, Dirk ...

Using a sophisticated type of mathematics, scientists have uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain. This research has significant ...

The 2024 Nobel Prize in Chemistry was recently granted to David Baker, Demis Hassabis and John M. Jumper, renowned for their pioneering works in protein design. In addition, Nature has recently ...

This course presents the underlying mathematical connections between diverse geometric objects that exist in Euclidean Space (the 3-dimensional space we live in). We will reach a great understanding ...

Researchers have discovered geometric, hollow, ball-like structures in 80-million-year-old fossils of bizarre marine animals. Palaeobiologists Jennifer Hoyal Cuthill and Aaron Hunter identified the ...