Random polynomials, whose coefficients or zeros are drawn from probability distributions, provide a fertile ground for understanding complex systems and statistical behaviours. A central theme in this ...

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another. The equation x 2 – 5 = 0 is a bit trickier. The polynomial can’t be ...

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. Problems in ...