Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

A ripple tells you something happened, but not exactly what. That is the core problem behind a hard class of equations that scientists use when they try to work backward from what they can measure to ...

Scientists have developed a new AI method that can work backward from patterns to uncover the hidden processes driving them.

We find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in ...

Then it’s kind of a mystery to try to figure out why and how they’re related.” The Riemann hypothesis has proved to be a font ...

An equation is a mathematical statement showing that two expressions are equal. The two expressions are linked with an equals symbol (=). The unknown variable (often the letter \(x\)) can take any ...

An equation with brackets must be expanded before it is solved. An understanding of expanding brackets is essential when solving equations with brackets. Some equations include a set of brackets. When ...

Fields medalist Terence Tao is part of Team ALPHA, which aims to develop artificial intelligence tools to transform how ...

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT ...

THIS book gives a thorough introductory study of the properties of ordinary points in the differential geometry of curves and surfaces in 3-space. Chapter 1 gives an account of twisted curves, Chapter ...

This research involving human participants complies with all relevant ethical regulations, including obtaining informed consent from all participants through the recruitment sites. Ethical review and ...