[cdavid]

I cannot speak for mathematic, I have barely used it. For stats, R is hard to beat, it has a lot of "cutting edged" toolboxes through CRAN (CPAN for R), and that's what uses most academics in statistics - most leading academics in statistics use it.

Now, its heritage shows quite a bit, and the language is not always nice to play with. It has great plotting facilities ala ggplot: http://had.co.nz/ggplot, which is a very interesting way to look at data visualizaton in a principled way.

There are also quite a few things available in scipy if python is your thing. If you just want to do stats and are not familiar with python nor want to deal with a general programming languge, R is better I think. If you want to make full-fledged applis with a web-fronted, R will not be pleasant :) {usual disclaimer: I am a numpy/scipy contributor).