[reikonomusha]

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization.

Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use.

I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathematica, including its documentation and interface.

I definitely don't agree with you that everyone should use or learn Mathematica though to learn it. As a student of computer algebra, I'd have to contend that Mathematica actually does computer algebra remotely correctly. A much more beautiful system for doing computer algebra was Axiom [0].

[0] http://www.axiom-developer.org/

[judk]

I am worried that Sage will get stuck in the mud as its Python code base grows, without a powerful expressive functional core like Mathematica's Lisp-ish core language. For example, see the discussion in this page about simple association lists vs what Mathematica 10 just launched

[reikonomusha]

Have you noticed that in Mathematica you're not even able to make your own opaque data types? Only Wolfram has that ability.

Python is usable for actually writing software systems and algorithms. When a Mathematica code base grows over 10 lines, it becomes virtually unmaintainable in my experience.

[taliesinb]

You can make your own opaque data objects, quite easily, thanks to HoldAll, UpValues, and Internal`SetNoEntry (the nuclear option).

What precisely becomes unmaintainable about Mathematica/Wolfram Language code after 10 lines? You could just be bad at programming in WL.

[reikonomusha]

Name[Field1, Field2, ...] is not an opaque data type. Maybe you can give me an idiomatic example of how to build a binary tree, for example? Or maybe something more complicated like a doubly linked list?

I do not write Mathematica code, but most code I've seen usually ends up being this mess of functions. I'll give you that maybe the code I've seen has just been bad, so we can ignore my point there.

[programnature]

People into traditional programming languages look at Mathematica and see abstractions for which they see no purpose.

People into PL research look at Mathematica and scoff at its low-brow, for-the-masses term rewriting, lacking whatever theoretical property deemed "essential" that week.

Yet somehow the language has formalized and made more computable and consistent more domains of math, science, and increasingly data than any other.

There is no honor or glory in purposeful ignorance.

[reikonomusha]

I disagree that it has made more domains of math computable and consistent. It's syntax is consistent, but it's evaluation semantics is wildly inconsistent. This is noticeable when you use some of their internal simplification algorithms on non-trivial problem.

I think Axiom covered more surface area in terms of mathematics than Mathematica. Mathematica is mostly good at performing over reals and complexes and doing term-rewriting algebra. Axiom supported arbitrary algebraic structures.