I agree. How an algorithm "actually behaves" depends on the implementation details of the language interpreter or compiler; open source or not, there are complex transformations leading to running code, that it might as well be a black box.
From the article calling for open-source mathematical software (my emphasis):
> ..we need a symbolic standard to make computer manipulations easier to document and verify.
> ..perhaps we should not be dependent on commercial software here. An open source project could..find better answers to the obvious problems such as availability, bugs, backward compatibility, platform independence, standard libraries, etc.
> Increasingly, proprietary software and the algorithms used are an essential part of mathematical proofs.
> ..with this situation two of the most basic rules of conduct in mathematics are violated: information is passed on free of charge and everything is laid open for checking.
If Mathematica were to be open-sourced one day, I suppose that would cover most of this wish list, with improved availability/reproducibility and verifiability. Tough to imagine without significant funding, collaboration, and communal agreement.
