More and more people are switching to Python for scientific purposes (look at this list to see some of the possible uses).
Why would you use Python in science?
First of all, Python is free, which is often not the case with other software. For personal use, the prices are not that steep, especially for students, but if you want to use it professionally, the price quickly becomes big enough that smaller businesses or startups just cannot afford it (for instance, Mathematica "home" edition is 295€, the "Standard" edition is 3.185€ and the "Enterprise" edition is 8.920€ at the time of writing1)
Readability was a primary consideration when Python's syntax was designed. You can often hear the joke that turning pseudo-code into Python code is just a matter of correct indentation. This is very important in collaboration, as it is much easier for other people (especially beginners) to understand your code and contribute to it if they don't first need to take a few days off to understand what it does.
Python is often used to glue other languages together and this can really come in handy. For instance, let's say you already have some code that will solve this particular part of the problem really fast, but it's written in FORTRAN, and R would be perfect to then parse that data easily and quickly.
If you're using something besides Python, you will need to re-create those functions / tools in the language you're using, or come up with a different way. In Python however, you can simply use F2PY and RPY2 and use the scripts you already have.
Balancing high level and low level coding
As Python is a high-level programming language it often times means that some
things will naturally be slower then when written in a low-level language such
as C. There are many way around that - for instance, you could use
Cython to statically type variables (you do something
cdef int x to declare
x as an integer), which gives massive speed-ups,
as typed variables are treated using low-level types rather then Python
Python has some great libraries that are great when using Python in science. To list just a few them that I've personally used:
A pair of amazing libraries for working with arrays, matrix structures, linear algebra, numerical optimisation, random number generation, Fourier transforms, image processing and many many more.
As mentioned before, it allows you to make parts of your program faster. Used it very little apart from testing it out myself.
Essentially a wrapper around an SQL database, it makes working with databases a breeze with a set of intuitive query operators, especially if you aren't used to pure SQL commands. Combine it with sqlite (which is embedded in Python's standard library) and you can leverage databases for scientific work easily.
I've used it when working witk Kotti.
IPython is basically an enhanced Python shell, but it has grown to be much much more. The IPython notebook is seeing more and more use in scientific circles, as it allows you to easily make interactive presentations that can be exported to many formats such as HTML, stripped down HTML (for using it in blogs etc.), presentations (using reveal.js), PDF and many more. It's easy to write your own rules for exporting, so new formats can be added if you wish to. There are even whole webpages build using only IPython notebook with a customised HTML export (had a link here but I cannot find it again :( ).
The tutorials on this site are actually made in the notebook - they are exported to stripped down HTML and used as the base for "tutorial posts".