RecursionError when installing SageMath 8.2

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As some other answers pointed out, the problem is that the first time that sage is called, the script relocate-once.py is executed. Since in that file, the shebang line reads /usr/bin/env python, the system calls the default python interpreter. The simplest solution is to have python 2.7 installed and change that line to /usr/bin/env python2.7 or directly the path of a python 2.7 interpreter.

On the off-chance you're using Anaconda, try commenting out the export PATH="/anaconda/bin:$PATH" line in the .bash_profile file (and restarting your terminal) before you run Sage for the first time.

You can uncomment it again after sage successfully runs (until you have to rebuild or upgrade Sage).

You need to copy the SageMath directory to somewhere on your hard drive – you can't just run ./sage from within the directory in the virtual drive that you get when you open up the dmg file. Once you've copied it somewhere and run ./sage, you should see

Rewriting paths for your new installation directory
===================================================

This might take a few minutes but only has to be done once.

followed by lots of messages like

patching /Users/palmieri/Desktop/SageMath/build/make/Makefile-auto
patching /Users/palmieri/Desktop/SageMath/config.status
  (etc.)

At this point, you won't be able to move the SageMath folder – its location has been burned in during the patching process – so pick a good location. (You can always copy a fresh SageMath folder from the dmg file, if you want to start over.)