Thanks for the advice. There are multiple versions of instructions to build Sagemath from source, and some are clearer than others. I am trying to work through it, but am running into problems. When I try to install gfortran using brew, it doesn't work, and spits out a whole bunch of "No such file or directory" messages ending with "Permission denied." Also, the GCC version on my computer is 14.0.0, but the instructions say it needs to be between 8.0.0 and 12.0.0.

The instructions at https://doc.sagemath.org/html/en/inst... should work. If not, look at https://stackoverflow.com/questions/1.... If that doesn't help, maybe completely remove homebrew and start over? If that still doesn't work, you can install Sagemath without any homebrew packages, it will just take longer: just try ./configure; make. First you could do export MAKE="make -j4" to speed up the compilation process because it will try to build using 4 parallel processes. You could replace 4 with other higher numbers if your machine is capable of it.

I just got done removing files from a conflicting admin account on the computer, and I'm trying the instructions at https://doc.sagemath.org/html/en/inst...

I am stuck on the step source SAGE_ROOT/.homebrew-build-env (replacing SAGE_ROOT by Sage’s home directory)

These instructions leave it up to my discretion what to put in for Sage's home directory, but I don't know what to put in because SAGE has not been installed yet.

Can you please help me understand what I am supposed to put in the place of SAGE_ROOT to make this work?

You will have to decide where to install Sage. Once you compile it, you cannot move it or else it won't work; if you decide on a different location, you will need to build it again. On my machine I use my own home directory, but I suppose some people might use /usr/local or some other location. Once you decide, then download a tar file or clone the GitHub distribution in your desired spot. Eventually, you will want to add the location to your PATH variable (in .zshrc if you are using the default zsh) to make sure that you can run sage without specifying the full path. You can also create a symbolic link to SAGE_ROOT/sage in a convenient spot. (See instruction #19 in SAGE_ROOT/README.md. Indeed, look at that file for more installation instructions and advice.)