Mathematicians and astrophysicists recently discovered that work on the Fundamental Theorem of Algebra and gravitational lensing had a common answer.
The Fundamental Theorem of Algebra (FTA), proofs of which go back to the 18th century, is a bedrock mathematical truth, elegant in its simplicity: Every complex polynomial of degree n has n roots in the complex numbers.
In the 1990s, Terry Sheil-Small and Alan Wilmshurst explored the question of extending the FTA to harmonic polynomials. In a surprising twist in 2001, Khavinson, together with G. Swiatek, applied methods from complex dynamics to settle one of the cases of Wilmshurst's conjecture, showing that for a certain class of harmonic polynomials, the number of zeros is at most 3n - 2, where n is the degree of the polynomial.