I am a little bit of a mathematician and I am just starting to learn music. The problem with me being a mathematician is that I question everything. I am learning about scales and whatnot, and I just don't get something.

Somewhere western music was decided to have twelve notes. And for some reason, someone decided that those notes should be named, and he/she named them with the beginning of our alphabet. But why did the person choose that there should be no sharp or flat between B and C (and E and F)?

I mean, why not make notes be:
A Bb B Cb C Db D Eb E Fb F Ab

Or even easier
A B C D E F G H I J K L

What made this musical inventor choose the naming scheme that he/she chose??