Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

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 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 ...

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, ...

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 ...

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 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 ...

Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

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 ...