Mathematica, in essence, is a very high-level language (as called by its founders as “knowledge-based”), and intend to provide an intuitive programming interface for, I guess, students and researchers, or anyone who is interested to explore math and programming.
One of the key feature of Mathematica is that, it has utilized the concept of List Comprehension（which I borrowed from Python), to the core of its interface. Both Table and Manipulate are using the same kind of nesting syntax to iterate values through its list.
Apart from the list comprehension, another cool part is its variety of objects provided for computing. So far, not long into learning Mathematica, I have experiences working with,
- Graphics & Graphics3D
- Array (halfway in)
There is a really cool feature where you can do a text analysis with just one line of code, such as this wordcloud on the wikipedia entry about “Computers”,
And its code is just as simple as this,
There are really some interesting features over Mathematica and I think it is probably very worth it to have this tool at hand. After all, a mathematical exploration tool (as provided with Manipulate), is just what everyone needs right?