I added mysql with homebrew. I try create a table using
$ mysql -uroot
then
mysql> create database test;
I get
ERROR 3680 (HY000): Failed to create schema directory 'test' (errno: 13 - Permission denied)
Edit

Most likely the permissions in your MySQL data directory are wrong.
Look into your data directory and make sure, that it is owned by the use MySQL is running as.
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