One journey has been finished. It's time to head into the next.
During the attempt of proving Statement T, I first-handedly experienced glimpses of real research on the forum Matheplanet.
We give the example of (affine) group schemes to demonstrate the importance of the Yoneda Lemma. In part 1, we discuss how basic matrix groups relate to algebras via representable functors.
A short essay about spending time with mathematics in places that you wouldn't expect at first.
What does it really mean to be Asian or American or German? Are you European-American? German-Asian?
A familiar functor from analysis, why rings should have a 1 and intuition on the equivalence of categories.
With the pandemic surrounding the Coronavirus going on, literally everything has been pulled from the ordinary. A small affected group would be the exchange students to whom I relate very dearly and so this essay is dedicated to everyone who ever was, is or will be an exchange student.
Still now, I am trying to optimize the ways to study mathematics. One things that has changed for me in recent days is that I'm trying to take up more challlenging books. Now, I occasionally need up to one hour to understand a single page. This blog entry is about some of my experiences with this and a little fact about finite fields.
Once upon a time, we studied finite Galois theory. Now is a time to advance to infinite Galois theory.
Hilbert's Theorem 90, a classical application on cyclic extensions and an unexpected application in number theory.