MaPSS: Mathematical Postgraduate Seminar Series: Alexander Kerschl (Sydney University) -- Solving polynomial equations with radicals or why there are no general solutions for polynomial equations of degree 5 and higher

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 Gauß 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 Évariste 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