What worked for me was removing all files (but not directories) in the mysql dir.
Edit #2 As per answers below, you only need to delete the log files: [ib_logfile0, ib_logfile1]
So quit MAMP and then in the terminal:
rm /Applications/MAMP/db/mysql/ib_logfile* #(or wherever your MAMP is installed)
Edit!: A few people have mentioned that you may want to back up these files first in case anything goes wrong, so maybe just use mv instead:
mv /Applications/MAMP/db/mysql/* /tmp/.
If this doesn’t work go back and kill all processes:
sudo killall -9 mysqld
This is also duplicated here:
mysql server won’t start MAMP