splitting field

[Liu]

Due to some personal affairs, I don't have much time to finish my plan
this week. I will try my best, though. I have just finished reading
the theory of splitting field, which is really beautiful. I find it is
always the case when a great mathematical theory comes out, that, we
must pretend first that something we don’t know in order to get a
deeper understanding of it. By something we already know, I mean
something like complex number field. By a deeper understanding of it,
I mean the field theory. We must think about a field such as the real
number field without the influence of the example of complex number
field. It is also the truth when we first met general topology. One
must throw away our original understanding of the familiar concept
such as “open sets”, “connected”, and so on.

Another point is that there are several structural theorems reminds of
the theorems in the “ergodic theory”. Terence Tao once said that he
sometimes can feel the inner connections between different
mathematical branches. It is the first time I have this feeling. It is
quite hard to write down explicitly several theorems in both fields to
compare. It is just a feeling. I guess you know what I mean.