I would highly recommend using the anaconda distribution, in particular miniconda.
For OSX Yosemite, this is a link to the Python 3.4 64-bit installer.
After downloading the application, open a terminal window, navigate to where you downloaded the app (e.g. cd ~/Downloads) and type:
bash Miniconda-latest-MacOSX-x86_64.sh
Now close and re-open your terminal window for the changes to take effect.
To test your installation, enter the command conda list
from the terminal. If installed correctly, you will see a list of packages that were installed.
From here, you should be able to follow the on-screen instructions. If you get lost, you can refer to their installation guide.
After installing conda, you need to create an environment. To install an new environment named py3
with Python 3:
conda create --name py3 python=3
To activate this environment:
source activate py3
Here, I normally install iPython, iPython notebook and pyqt:
conda install ipython, ipython-notebook, pyqt
Now, to activate an ipython shell from within your environment:
ipython qtconsole
Although this reply does not attempt fix the homebrew issue, it answers the question of how to install Python3 on Mac OS X Yosemite.