I installed MySQL on Mac OS X Mountain Lion with homebrew install mysql, but when I tried mysql -u root I got the following error:
homebrew install mysql
mysql -u root
Ough, that took me a while to figure out. I saw it in a comment. After installing mysql using brew, and starting the service (perhaps using sudo brew services start mysql) then run:
sudo brew services start mysql
$ mysqld
And MySQL should be running for your thereafter.