Nowadays, the Mathematica Notebook is probably Mathematica's biggest brake. For me the GUI feels slow on any computer. However, as already mentioned in the othe

Nowadays, the Mathematica Notebook is probably Mathematica's biggest brake. For me the GUI feels slow on any computer. However, as already mentioned in the other posts, under the hood Mathematica has not yet been beaten for it's LISP attemp of computer algebra. The biggest contrahent in the Julia/SciPy environment is probably the SAGEmath computer algebra system, however it follows more the route of Maple which is more natural to the employed Python host/meta/binding language but (for me) does not feel as powerful as Mathematica when it comes to symbolic computing. I think the big advantage of Julia against Mathematica is the modern software stack and the bleeding edge technology they can embed very quickly, such as d3js, WebGL, etc.. The web world is moving quickly and the scientific python community can keep up while Mathematica moves only very slowly -- note they started their web interface (cloud version) only a few years ago.