This picture thing turned out to be a pain. Maybe there was some easy fix, like, I don’t know, clicking “Use your old picture,” but that didn’t seem to work. So then I just tried re-uploading it, but the size was too big. Then no matter how I shrunk the size and dimensions, when I would re-upload it would just blow it back up to the original size. Thus, I had to change the picture to one in which I was further away from the camera in order to have a head small enough so that after cropping you could see more than just a single eye.

I have this nice post all typed up on every finite group arising as the Galois group of number fields, but there is some weird LaTeX bug that is cutting out some sentences. I also have a square bracket problem, which I think I’ve narrowed down to: you cannot start your LaTeX code with “[“. The other weird thing might be that you cannot end with “!”?

Both of these are bad considering I’m dealing with the group , so it has order n!, and I’m dealing with field extensions which means I need [K : F], but I’ve subscripted, so I need it inside of LaTeX code…

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You mean that for any finite group , there is an extension of , such that there exists an extension of with , right? Otherwise, my understanding is that you’d have solved the inverse Galois problem, which would get you a Fields Medal…

Yes. That is precisely what I mean when I say “Galois group number fields,” though a fields medal would be nice…

Ahh, gotcha. I’ve always heard people refer to the Galois group of a field, with no other qualification, to mean over or .

And well…everyone I know secretly has a big problem like this that they work on. Keep it in the back of your head and play with it whenever you have some time, see if you CAN solve it.

In order to start a LaTeX expression with square brackets, enclose it in curly braces. EG

was created by typing {[L:K]}. This is a bug somewhere in wordpress, but at least it isn’t too hard to work around.

Thank you so much! This problem has been annoying me for months!