I think it’s fair to say that the documentation system of Mathematica is the best documentation for any software language anywhere in the world at any time. Not exaggerating one bit.
There are not only practical example snippets for every language function but also tutorials and technical deep dives on related topic areas such as signal processing, video analysis, partial differential equations such as the heat equation and wave equations with rich 2D and 3D visualizing s of potentials and flows over surfaces.
It’s very powerful for exploratory research that involves deep math and nothing else comes anywhere close.
The fact that it’s a functional language makes it much easier to compose functions while just trying out new ideas but it’s not really a general purpose programming language as much as it is a mathematical computation system.
And the huge bonus is that you never ever have to import anything or worry that a new version of a critical lib will topple your version dependency house of cards. All subsystems and libraries are internally consistent and always available, without need to import and with context sensitive help.
(Former Wolfram employee)
Glad you like the documentation system, there is a lot of hard work going into making the examples in that documentation, and making sure they are linked to other relevant areas.
Matlab is focused on a) Matrix manipulation but builds a lot on top of that such as Signal Processing, differential equations etc. and b) But at the end of the day it is a numeric evaluation language. Whereas in Mathematica everything is an expression and so it does most of its work doing symbolic manipulation until at the end you may or may not choose to evaluate an expression numerically. This allows it to have a whole other capability doing Symbolic Integration and Differentiation of very complicated expressions, Mathematical Logic, Abstract Algebra and IIRC Category Theory and such like. Don’t mean to be a hater but the MATLAB language and default environment feels clunky in comparison.
An analogy I use often is that Python, MATLAB and Mathematica are respectively like Linux, Windows and the Mac, aesthetically and functionally.
I have used MATLAB as well and their docs are good no question. But the native notebook interface and the “built in everything” environment means you can explore rapidly and run the example code without having to know which other packages you need to buy. So I would put the development experience with Mathematica a couple of notches above that of MATLAB. BUT in the engineering domain especially at Univs MATLAB is king. This is a flaw of Wolfram marketing and pricing not of the underlying product.
