Definition
Plain language
A long-standing unsolved question in mathematics about how the roots of certain equations sit near each other.
As stated in the literature
A conjecture in complex analysis relating the zeros of a polynomial to the zeros of its derivative within the unit disk; included as a near-frontier problem in the dataset.
Also called: Sendov conjecture
Why it matters: Problems like this have resisted decades of serious effort, which makes them a good honesty check on any system claiming to produce new mathematics.
For example, it asks whether, whenever a polynomial's roots all sit inside a circle of radius one, each root has a nearby root of the derivative within distance one.