How to install an homebrew formula without updating homebrew itself?
According to this github issue and to the man page, the environment variable HOMEBREW_NO_AUTO_UPDATE can be set to 1.
HOMEBREW_NO_AUTO_UPDATE=1 brew install &lt;formula&gt;

This will stop the homebrew update for this command. If you want to prevent auto update for your shell session, use:
export HOMEBREW_NO_AUTO_UPDATE=1

to set it permanently, add it to your ~/.bash_profile. Note that changing this permanently is discouraged by the developers.