Solving the unsolvable

When you first learnt the “quadratic formula”, you may have wondered if there were similar algorithmic methods for solving higher-degree polynomial equations. This question was investigated over many centuries, leading from geometric origins to the development of modern abstract algebra. In this seminar we shall find exact solutions to some cubic equations and see why you might not want to memorise a “cubic formula”. We shall also see how the interplay between algebra and geometry is used to prove the impossibility of certain constructions, such as trisecting an angle.