Calculus of variations establishes a framework to determine the extrema of functionals—mappings from functions to real numbers—which has been pivotal in elucidating natural principles such as the ...

Does string theory—the controversial “theory of everything” from physics—tell us anything about consciousness and the human ...

Recent decades have witnessed remarkable progress in establishing rigorous mathematical frameworks for quantum field theory (QFT), conformal field theory (CFT), quantum gravity and string theory.

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently ...

Researchers have demonstrated that self-organization of neurons as they 'learn' follows a mathematical theory called the free energy principle. The principle accurately predicted how real neural ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

Mathematics is one of the oldest disciplines of study. For all its antiquity, however, it is a modern, rapidly growing field. Only 70 years ago, mathematics might have been said to consist of algebra, ...

An illustration of two black holes about to merge and emitting copious gravitational waves. And as the numbers of gravitational-wave observations have increased, physicists’ careful modeling is ...

Breakthroughs, discoveries, and DIY tips sent six days a week. Terms of Service and Privacy Policy. In nature, patterns of chemical interactions between two different ...

An international collaboration between researchers at the RIKEN Center for Brain Science (CBS) in Japan, the University of Tokyo, and University College London has demonstrated that self-organization ...

Emily Riehl thinks hard about objects that don't exist in the material world yet mysteriously seem to underlie many things that do. These objects have no concrete existence of their own, but they do ...

Researchers are using chaos theory to 3D-print stunning pieces of jewelry. As Einstein himself said, "The greatest scientists are always artists as well." Monisha Ravisetti was a science writer at ...