Algebraic curves and polynomial systems form a cornerstone of modern computational and theoretical mathematics. These structures are defined by polynomial equations and exhibit rich geometric and ...

Curved graphs can be used to solve equations. The points at which the curve crosses a particular line on the graph are the solutions to the equation. If we want to solve the equation ...

Since ancient Greece, researchers have tried to isolate special rational points on curves. Now they have the first ever formula that applies uniformly to all curves ...

In August, a pair of mathematicians discovered an exotic, record-breaking curve. In doing so, they tapped into a major open question about one of the oldest and most fundamental kinds of equations in ...

The Schrödinger equation rewrote the rules of matter and forever changed the field of chemistry. Donald Truhlar, a chemist at the University of Minnesota, calls it the “greatest advance of the 20th ...