I would recommend especially Mathematica and using Wolfram resources (Mathworld [1]) so you can randomly browse through different ideas and play with them in Ma

I would recommend especially Mathematica and using Wolfram resources (Mathworld [1]) so you can randomly browse through different ideas and play with them in Mathematica code. It's great fun if you like both math and programming. Mathematica can understand and process mathematical notation and has high level of expression allowing you to build an abstraction on top of other abstractions (Prolog like). [This high level of expression of Mathematica is sort of disadvantage as far as programming languages go because you can easily end up with a code that works but is completely unreadable even to you without wrapping your head around it - same like elegant mathematical formula that needs complex proof] Matlab is more for modelling and applied math (it is really good at that). [1] http://mathworld.wolfram.com/RiemannHypothesis.html http://mathworld.wolfram.com/RiemannHypothesis.html