Henri Poincare, David Hilbert, and a Problem They Shared

Both well known mathematicians Henri Poincare and David Hilbert were leaders in their field.  Poincare, known as "the last universalist", and David Hilbert who gave the millennium address where he listed 23 problems that would guide mathematicians into the next century, were interested in periodic solutions to planar polynomial vector fields.   The 16th question from David Hilbert's list is precisely about this.   In this talk, I will present some historical facts about the lives of these two great mathematicians, and give an intuitive understanding of what the 16th questions asks.