Why can't I execute mysql without the full path? At my terminal, I can't cd to the folder containing mysql and call it. 

TimsMacBookAir:/ tim$ cd /Applications/MAMP/Library/bin/
TimsMacBookAir:bin tim$ mysql
-bash: mysql: command not found


If I execute the file by using the whole path, it works

TimsMacBookAir:bin tim$ /Applications/MAMP/Library/bin/mysql
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 7
Server version: 5.5.38 Source distribution


Why is that?
The current directory is usually not in the PATH variable (the variable contains all the directories where to look for an executable).

If you type echo $PATH you will see that . is not in the semicolon separated list of directories.