Type: Seminar

Distribution: World

Expiry: 18 Jul 2017

CalTitle1: MaPSS: Mathematical Postgraduate Seminar Series

Auth: casella@10.17.25.244 (acas5565) in SMS-WASM

Dear All, We are delighted to present the MaPSS Seminar topic of Monday 24/04; please see the abstract below. **This Semester the Seminar will always run on Monday, at 5:00pm in 535A** Following the talk, there will be pizza on offer. Speaker: Alexander Kerschl (Sydney University) Title: Solving polynomial equations with radicals or why there are no general solutions for polynomial equations of degree 5 and higher Abstract: The history of solving polynomial equations dates back to about 2000 BC for which we have written evidence that the old Babylonians already solved quadradic equations. Throughout the centuries people tried to formulize and solve these equations in general. Finally, in Italy during the 16th century scholars discovered the general solutions for cubic and quartic equations but the general quintic could not be solved. Nowadays we know that there is no solution using radicals for the general quintic and higher degree polynomial equations but historically it took until the early 19th century to give a proof for this fact. In 1799 Ruffini and GauÃŸ were the first to formulate that there is no general solution for degree 5 and higher. Following them Cauchy, Wantzel, and especially Abel worked to help to finish Ruffini’s first draft of a proof and led to the famous Abel-Ruffini Theorem in 1824. Independently and without knowing about Abel’s proof a young Frenchman named Ã‰variste Galois laid the groundwork of what is known today as Galois theory. Galois gave us a beautiful general approach to deal with solvability of polynomial equations of any kind and, moreover, his work led to solve two of the three classical problems of ancient mathematics. Unfortunately, he died way to young at the age of 20 after being severly injured in a duel. My talk will aim to lead throughout the centuries of the quest to solve polynomial equations and explain why there can’t be a solution for the general quintic. Supervisors, please encourage your students to attend. Thanks, MaPSS Organizers