>Mathematica is optimized for giving you results you need in undergrad classes
What makes you think this? Mathematica is used in all sorts research projects, technical fields, finance, and so on. I've seen Mathematica required or recommended in many, many job listings, especially for quants. I've never seen Sage there.
For evidence, here [1] is what you get for searching for Mathematica on Indeed.com. Note pretty much every one of those jobs lists several math related packages. Not one mentions Sage.
Unfortunately you cannot run the same search on Sage, since there is an ERP package that shows up instead. However, from browsing those listing again I find zero hits for the math package Sage.
What makes you think this? Mathematica is used in all sorts research projects, technical fields, finance, and so on. I've seen Mathematica required or recommended in many, many job listings, especially for quants. I've never seen Sage there.
For evidence, here [1] is what you get for searching for Mathematica on Indeed.com. Note pretty much every one of those jobs lists several math related packages. Not one mentions Sage.
Unfortunately you cannot run the same search on Sage, since there is an ERP package that shows up instead. However, from browsing those listing again I find zero hits for the math package Sage.
[1] https://www.indeed.com/jobs?q=Mathematica&l=
[1] https://www.indeed.com/jobs?q=Mathematica&l=