Earlier quoted context omitted.
All software used in science should be open source, because if it isn't, the science isn't repeatable.
Not true. For instance, if a report is originally typed in a closed-source, commercial text editor, that has no impact on the repeatability of the science. Similarly, Mathematica is (to my knowledge) a closed-source program, but calculations done by it can still be independently verified (so long as those calculations are made public). You're on the right track, but need to narrow down the wording some.
You're right. I was actually thinking that as I typed it.
How about this: when scientists take raw input data and use complex processes to convert it (by complex I mean more than you could do with a pocket calculator in a minute), then the programs doing the conversion must be open source, so that others may repeat the work done in processing.
I'm not familiar with Mathematica; how complex is the work that it does? And how easy is it to verify that its results are correct?