Now I know that none of those things were invented by Wolfram (the company or the man), but they were put into productive use, in a very slick and beautiful application with a slew of symbolic and numerical math libraries which were world class.
I guess to a large extent, you're not missing something, but the libraries are comprehensive, well designed, well documented, very consistent and reasonably intuitive.
I feel like I'm missing something because I read this a lot, but don't see it when I look at Mathematica. The language seems to be a higher-order, functional programming language with dynamic (?) typing. That part sounds like lisp, but syntactically it looks nothing like lisp to me. Is there a portion of the language that I'm overlooking?
It does naturally suit functional thinking, so that becomes the default 'best' way of engaging with it.
[1] http://en.wikipedia.org/wiki/Rewriting#Term_rewriting_system...
In[1]:= FullForm[a + b]
Out[1]= Plus[a, b]
In[2]:= a + b /. Plus -> Times
Out[2]= a b
Am I missing something? Is the point the quality/volume of the support libraries?