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Terminology of mathematics by computer

Posted 8 years ago
4 Replies

It's always been a jungle. There has never been a single 'best language'. My coding experience predates c, and there are few languages in existence then that are still in use. What languages survive does not always depend on quality. For example, in the clinical chemistry (and related fields) business, MUMPS is still used, even though it is a truly wretched language.

For most people's needs, Wolfram|Alpha is great. Certainly, one can get through high school maths using it. It also serves as a gateway to Wolfram's other products. If someone needs to write code for their job, the choice is often determined by the traditions of the job. In my case, I never needed javascript or HTML, so I never learned it. However, I did have to be able to read FORTRAN, Pascal, and a few other languages well enough to translate that code into c, and later into Wolfram Language.

As for CAS, it is easy enough to translate MathCad or Maple into Wolfram Language code, since Wolfram Language supports multi-paradigm coding.

Having multiple choices can be a problem for students, professors and textbook writers, to be sure. I see the issue myself when I take MIT Open courseware for maths, most of which seems to use MathCad. It is easy enough for me to do the translation, and I think that anyone who is seriously entering a field where they need to use a CAS will need to have some experience with more than one of these languages. Fortunately, must universities have site licenses, so the cost is acceptable for students.

Another issue regarding language is the almost exclusive use of English. I may be wrong, but Mathematica is one of the few software systems that addresses this: they have what are essentially subtitles for their code. You still have to type the commands in something English-like, but you can see the meaning in French, German, Chinese, etc.

Ultimately, things will settle out. We live in interesting times. We cannot go back to the days where all you needed was a yellow pad and #2 pencil (plus access to a whole lot of books, plus a mentor or two), and the future is not happening soon enough. For myself, I do not see things falling out to one CAS, any more than there is only one operating system, although it might have appeared to be the case in the late 1990s.

If you think about it, there have always been different ways of doing things in maths: different approaches, different metaphors. This may be poorly taught at present, but diversity is a good thing.

Posted 4 years ago

Another issue regarding language is the almost exclusive use of English. I may be wrong, but Mathematica is one of the few software systems that addresses this: they have what are essentially subtitles for their code. You still have to type the commands in something English-like, but you can see the meaning in French, German, Chinese, etc.

I think the EXCEL table functions (not the VBA macro language) are a well-known example of a multilingual programming language.

I am German, but I don't like this. It produces a host of problems for code readability and documentation and even more if you have to work on the same code on systems with different installation languages.

Since English is such a widely used language, it is much better to write the code completely in English, at most commenting in e.g., German.

POSTED BY: Werner Geiger

I tend to agree with you on all these points. Observe though: (1) While a student license certainly compares to other popular expenses by students, a teacher who wants to work on the class screen will still need a school license. It takes two to tango. (2) While Mathematica is a most agreeable language to work with, since it takes its structure from mathematics itself, combined with Wolfram's innovations on patterns in input (and perhaps other elements but let us not start a discussion on that), we still see that other computer algebra systems do not adopt the same language. See the new Babel at https://en.wikipedia.org/wiki/List-of-computer-algebra-systems (underscores). Is it really so that mathematics by nature invites a new Babel, merely because such programmers want to impress the world with their own way of putting the same ? Isn't it the truth that mathematics already developed quite a uniform way to state issues, and that Wolfram had the wisdom to adopt the language of his intended users ? PM. Google translate helps for English versus French, but not between Mathematica, Maple, R, SageMath, and what have you, so that programming is always for smaller communities instead of the whole world. The present situation goes fundamentally against the notion of Leibniz of letting mathematics be the universal language. It are people who create the present situation, and it ought to be possible to talk some sense into this. As an economist my diagnosis is that we don't have a market but a jungle, and that regulation is required to create a proper market.

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