As I mentioned, there is an accusation of malpractice in Jordi's rant. It is far more important than any source code though he doesn't seem to realise it. He wrote, "The modern tendency I see in mathematicians to tolerate this [lack of rigour] again gives me the impression of a regression to mathematical feudal middle ages". And yet, Jordi blames the tool rather than the malpractitioner! This is daft.

- what does it mean not to know how that tool works?

Take a look in any laboratory and you will see what it means when scientists don't know how their instruments work. (No single person or corporation knows how even any given mobile phone works.)

All scientists specialise lest they have nothing new to contribute.

- what does it mean for scientific results when their reproducibility depends on a closed tool?

It is a non-issue (neglecting that execution of software may itself be an experiment in computer science as I've discussed already).

Either the tool is understood or it isn't. If it is understood, then reproducing any result from that tool is possible. If the tool is not understood, then naturally it isn't relevant to the scientific process. Paranoid ranting notwithstanding, did anyone, anywhere, actually suggest that Mathematica output ought to be elevated to "assumed truth"?

(It must bother you that science rests ultimately on unprovable assertions. However, the problem for mathematicians is not the same.)

- what does it mean when, inevitably, that tool is no longer available?

It means nothing for science/math (in the absence of malpractice).

- what does it mean to put a paywall (Mathematica license) in front of scientific activity, access to data, methods, and results?

Again, it means nothing at all. Results are meaningless without documented method.

It is telling that the worst that your friend Quad can say against Mathematica is to complain, wouldn't it be great if the source code was verified via peer evaluation so you could say "Mathematica gives this result. QED."

Surely Quad does identify one of Mathematica's limitations, but apparently he doesn't suspect the gaping chasm that exists between formal proof of algorithm correctness and the typical open source code review process or the freedom for an end user to fix a bug!

And dare I raise the problem of proof of correctness of the hardware and software platform used to execute a hypothetically correct Mathematica algorithm?

If you still feel that I haven't addressed the questions you asked then I fear that I will not do so by typing more so hereendeththethread. Thanks for reading.