Hichem Ben-El-Mechaiekh in Department of Mathematics presented the first keynote address at the 10th United Arab Emirates Mathematics Day held at the American University of Sharjah on April 14. His talk, entitled The Poincaré Intermediate Value Theorem on Non Smooth Domains, surveyed the old and new about the most generic solvability theorems for nonlinear systems in arbitrary dimensions and its applications to the existence of viable solutions to dynamical systems.