Fermat's Last Theorem

The content in today's blog is taken from Jean-Pierre Tignol's Galois' Theory of Algebraic Equations . Although Albert Girard ...

Leopold Kronecker was born on December 7, 1823 in the city of Liegnitz which is today part of Poland. At the time of his birth, it was part...

In a previous entry , I posted the proof of Sturm's Theorem. This is a method for determining the number of real roots in a given inter...

In a previous blog entry , I talked about the properties of Sturm Chains . In today's blog entry, I will show how they can be used to es...

Augustin-Louis Cauchy came up with a useful bound for real roots in a polynomial equation. This works well with Sturm's Theorem. Theor...

Before proceeding to Sturm's Theorem, let's talk about Sturm Chains. Definition 1: Sturm Chain A Sturm Chain is a series of polyno...

Here's a major problem that Jacques Charles Francois Sturm solved: Find the number of real roots of an algebraic equation with real coe...

Jacques Charles Francois Sturm was born on September 29, 1803 in Geneva, Switzerland. His father was a math teacher. When Sturm was 16, hi...

In today's blog, I will present Paolo Ruffini's proof that if n ≥ 5 and F is a splitting field, then F/k is not a radical tower....