Think of C as analogous to Windows, and Python as analagous to MacOS. Everywhere you go you will encounter things written in C, and Python may be better depending on your personality but Python has in general less documentation and community support. C is ugly, Python is pretty. C is very fast, Python is almost as fast, with the tradeoff coming from intermediate virtual machine code (CPython, Jython) or interpretive compilation.
There are two cases, either speed and memory are important, or not. If you care about speed, then consider FORTRAN 77. This is the fastest 'high-level language', and although it has been supplanted by C, this is only because C traded performance for readibility, viz. the programming industry realized the enormity of the task of using old code, and suddenly readibility became a priority.
C was designed as a systems programming language (UNIX), but FORTRAN was designed as a scientific language. The only reason C is more readable (on an industrial scale) than FORTRAN is because it supports abstraction at a higher level. For the individual who is not designing a massive end-user program, FORTRAN is easier and faster to write then C.
In my work it is almost always the case that human time is more important than machine time, which is why I use and recommend Mathematica. Mathematica is a universal programming language, just like C or Python (although Mathematica is proprietary). The difference is that it contains, in an integrated way, the world's largest library for scientific computing, containing all the best of known algorithms as well as some that are not known outside of Wolfram Research. The other difference is that is 1000 times slower than C (not as bad as it sounds, because in fact the limiting factor always has to do with the size of the problem and multiplication by even such a large constant is not too terrible in most cases).
Unless your intended tasks are very basic to program (for example solving a particular differential equation for a variety of conditions using the same method ). If instead your work involves considerable variety, and in addition you want to consider visualizations of the data, Mathematica would be an excellent choice.
). I would also advise avoiding C++ as it introduced the object oriented paradigm, which is just another way to write code that is slow { for example, I was trying to find a solid random number generator for a stochastic simulator over the summer. I ran across the Mersenne twister in c++ and gave it a shot. With the number of random numbers I was generating (on the order of millions) the object oriented inheritance garbage was two orders of magnitude slower than the Miller-Parks bit shifting algorithm in straight C }.
