Soon, I am going to write my master thesis in theoretical physics. I assume there, and later on in my career, I will have to do more serious numerics than I did up to this point. That's why I want to find out:
What programming languages are available for doing numerics in theoretical physics? What are their relative strengths/weaknesses? How do their speeds compare?
The programming language should be able to do top performance (in the first place) and at the same time be reasonable fun to programm in. Considering the first criterion, I assume there will be a mostly not opinion-based answer to my question.
So far, for most calculations in physics, I have been using Maple and Mathematica, with which I am fairly familliar with but which do not seem to provide the performance for more serious stuff. Furthermore I know Matlab, which I am using now for a year but only for a lecture of numerics thus far (so purely for elementary problems).
Then of course I know C++, where there is a numerics package called GSL. This does not seem very handy to me on the first glance.
I never worked with python but fear, it will not provide the needed performance and will be rather a drastic change from what I used so far.
So are there other options, which I oversaw? And what is the way to go for "modern numerics in physics"? What does the answer depend on?