Quadratic equations are polynomials, meaning strings of math terms. An expression like “x + 4” is a polynomial. They can have ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

In this paper we consider symmetric noncommutative polynomials and call one "matrix-positive", if whenever matrices of any size are substituted for the variables in the polynomial the matrix value ...

How can the tiniest particles and the vast structure of the universe be explained using the same kind of mathematics? This puzzle is the focus of recent research by mathematicians Claudia Fevola ...

An algorithm that provably finds the ground state of any one-dimensional quantum system is presented, providing a promising alternative to the widely used, but heuristic, density matrix ...

Mathematicians use algebraic and positive geometry to link particle physics and cosmology, offering new tools beyond Feynman ...