In an editorial published by the American Mathematical Society, mathematicians from the US Naval Academy and the University of Washington noted that, because so much mathematical research is now conducted using proprietary software like Mathematica, much of the ability to meaningfully review such research is being lost. As the authors point out,
There is a proof in the article by Campbell et al. in The Atlas of Finite Groups—Ten Years On (1998) that describes how many separate software packages were “easily used” to deduce various mathematical facts—no code is given, and some of the programs are proprietary software that runs only on hardware many years out of date. Such proofs may become increasingly common in mathematics if something isn’t done to reverse this trend.
...suppose now Jane [an imaginary mathematician] says a theorem is true based partly on the results of software. The closest we can reasonably hope to get to a rigorous proof (without new ideas) is the open inspection and ability to use all the computer code on which the result depends. If the program is proprietary, this is not possible...To quote J. Neubüser, “with this situation two of the most basic rules of conduct in mathematics are violated: In mathematics information is passed on free of charge and everything is laid open for checking.”
Their solution, of course, is open source alternatives to proprietary software like Mathematica, Maple, and SAS.