In these talks we started with polynomial equations in one variable, and moved from degree one (like 2x+1=5) and quadratic (with the well-known formula that so many students have been taught to memorize), to cubic, quartic and quintic. The point was to make them realize that before “solving” an equation we need to decide in what set will we seek for solutions (be it the natural numbers, the rationals, the reals,…) and what kind of answer do we look for. Changing these parameters can turn the problem from “trivial” to “impossible”, and the different choices are applied in different situations. The second part of the talk was on equations in two variables (still polynomial) and how the problems here are much harder. We ended with results that have been proven during the 20th century, and with problems that are still open nowadays.