Everything I do regularly in Mathematica can be done in Python. Even though Mathematica has a mind-boggling amount of functionality, I only use a tiny proportion of it. I skimmed through some of my Mathematica files to see what functions I use and then looked for Python counterparts. I found I use less of Mathematica than I imagined.
The core mathematical functions I need are in SciPy. The plotting features are in matplotlib. The SymPy library appears to have the symbolic functionality I need, though I’m as not sure about this one.
As I’ve blogged about before, I’d like to consolidate my tools. I started using Emacs again because I was frustrated with using a different editor for every kind of file. One of the things I find promising about Python is that I may be able to do more in Python and reduce the number of programming languages I use regularly.
I wrote this post years ago when I was just starting to move to the Python stack. Since that time I have used Python as my default programming environment, though I still use Mathematica as well. The number and quality of Python libraries for applied mathematics has increased greatly over that time.
Python has numerous advantages over Mathematica. It is open source, and so it is more transparent. When something goes wrong, you can dig in and debug it. It is of course free, so you don’t have to buy software licenses, saving not only money but administrative hassle. And perhaps more importantly, other people that you want to share code with don’t have to buy licenses; you might find a Mathematica license a good investment for your company, but you can’t expect everyone you work with to necessarily come to the same conclusion.
The disadvantage to Python relative to Mathematica is that it is less consistent and less integrated. The Python stack for applied math—SciPy, NumPy, Pandas, Matplotlib, etc.—is better integrated than it used to be, but it still remains a collection of separate libraries.