I don't think that's really the answer --- e.g. Matlab has all of those (and the open source things are YMMV). The reason I've seen people prefer Mathematica i

I don't think that's really the answer --- e.g. Matlab has all of those (and the open source things are YMMV). The reason I've seen people prefer Mathematica is because its symbolic computation and visualization capabilities are both powerful and easy to use for basic things. Here, it is just very good, as to be expected from popular software with a long history with significant resources spent on its development. (The open source alternatives for symbolic computation may be as good in some applications for experts in some mathematical fields, but the general purpose user experience is not as good. As an alternative to Mathematica, I'm currently using Sagemath, and while it's perfectly OK for many things, the polish is often lacking.)