Polynomial optimization concerns the problem of finding global minima or maxima of multivariate polynomial functions subject to polynomial constraints. Such problems are inherently nonconvex and often ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

Polynomial math often appears in college algebra and trigonometry courses, and many students have wondered whether they will ever have a need for such math after college. You may have never come ...

Algebraic geometry and differential geometry form two pillars of modern geometry, each providing its own language and techniques to study shapes and spaces. Algebraic geometry examines solution sets ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says ...

In new research, mathematicians have narrowed down one of the biggest outstanding problems in math. Huge breakthroughs in math and science are usually the work of many people over many years. Seven ...