First, consider written language.
If you are going to publish an academic paper for an international readership, what language will you use? You won’t use Russian, Mandarin, French, Spanish, in spite of their huge numbers of native speakers: you will write in English. This is simply because English has become the dominant language of international communication. Every now and then you may find some author writing a windy expostulation as to why English is “better” than other languages: it will be rubbish, because English is demonstrably no better than any other language. In fact in many ways it’s a terrible language: maddenly inconsistent, impossible spelling, grammar that no two people can agree on – it’s simply an historical accident that it has its current position as the world’s most popular second language. After all, only a few hundred years ago, at least in the Western world, Latin was the dominant common language, so who knows – maybe English will in its turn be supplanted by something else.
Note that only in 2011, in their Melbourne meeting, the International Association of Plant Taxonomy decreed that English was an acceptable alternative to Latin for the formal description of a new species.
Just recently I was looking at a international conference to be held in France, where the main language was to be English, but the organizers have planned for a bilingual conference, the other language being of course French. Even so: “We aim that at most 30% of the contributions … will be in French.”
Next, back to software.
More and more papers in mathematics and mathematics education now include computer code: a few lines, or indeed entire programs, written either to accompany the paper, or as a major part of it. This is a trend I really like; I believe that there are huge changes to the way in which mathematics is done and perceived, and computer-based experimental or experiential mathematics is fast becoming mainstream.
What happens if a paper is written in which the code is in Mathematica, or Maple? This means that readers who don’t use that software are unable to experiment with the code, or to get to grips with the full material of the paper. I have found this very frustrating time and again. Sometimes the authors give pseudocode, but not always. And sometimes the code given is simple and clear enough that it is almost pseudocode itself, and such easily translatable into another language. But again, not always. Mathematica writers in particular have a tendency to produce obscure code, and such code can look like the offspring of an unholy coupling between BASIC and Befunge:
colSeq[x_] := NestWhileList[ Which[ EvenQ[#], #/2, True, 3*# + 1] &, x, # \[NotEqual] 1 &]
But of course each language has its own quirks and peccadilloes, and even with the best will in the world a writer who has been used to one language for years may write what appears to be simple and clear – which it may be – but only to users of that language. The trouble is that as far as commerical systems go, hardly anybody is proficient in more than one, and hardly anybody has access to both: an institution may standardize on one or the other, but very rarely both. So if you use Maple or Mathematica, users of the other system will be left out.
I am guilty of this myself, I have published papers which use Maple.
I think that there should be a common “second language” in which all authors publish. For symbolic algebra alone there’s a lot to choose from: Maxima, Sage, Reduce, Axiom, SymPy to name but five. Note that SageMathCloud allows users to collaborate, share LaTeX papers, and experiment with such software all for the cost of creating a free account. (It’s worth noting, though, that the free accounts have certain space and computational restrictions; to obtain more space or less restrictions you have to pay for it.)
It seems to me that writers of mathematical papers which include computing should very seriously think about the use of such open systems, and editors of journals should be more proactive in encouraging authors. If you write a paper which is heavily based around Mathematica (for example), and is not easily translatable to another language, then its rightful place is not in a mathematics journal, but a trade magazine such as the Mathematica Journal. After all, published mathematics is available for averybody, anyhere, to use withough restrictions; a theorem is available to all. But locking up material in commercial software flies in the face of openness in mathematics publishing: it makes it harder for readers, and harder for other researchers to check your work. Don’t do it.
When you write your paper which uses your favorite commercial computing platform, ask yourself: am I happy to alienate all readers who use other systems? Am I happy to halve my readership?