The two that I'm familiar with are mathematica and matlab.
Mathematica is a lisp for representing and manipulating mathematical expressions combined with an IDE that knows 2D layout (so you can write expressions like you would on paper) and a massive integrated library of mathematical routines. The "gateway drug" is its ability to symbolically integrate, differentiate, factor, simplify expressions, solve equations, interactively plot without explicitly sampling, etc. Then you discover that all it's "heavy lifting" capabilities are integrated with each other -- i.e. you could use a piece-wise implicit surface to define boundary conditions for a differential equation, solve it with finite element on 20 different tessellation levels, and compare the results using a norm built out of an interpolator and integrator to check for convergence. All in a handful of lines of code where you only have to worry about high-level details rather than dozens of for loops and hundreds of lines of glue. I really don't think there's anything comparable in the open source ecosystem yet, but I'd love to be wrong (yes, I know about SAGE).
Matlab is relatively unremarkable as a language -- it's not a lisp, it deals with matrices of floats not expressions, and its only competitive language feature is the eponymous set of linear algebra primitives that CS-trained language lawyers tend to roll their eyes at but that really do make a difference for the scientists and engineers who use it day-to-day. The killer value proposition, though, is its collection of libraries. They're not symbolic like what you would find in Mathematica but they're usually more extensive and relentlessly practical. Sometimes that means speed, sometimes that means features which cater to your particular obscure workflow, sometimes it means integration, but it always seems to result in a decision along the lines of "I could spend a day munging python libraries A, B, C, and D together, or I could open matlab which already has a package and a GUI for it."
Python, Julia, and R do many things very well. They can beat mathematica/matlab in a number of areas but there are still huge swaths of math/science/engineering where they're just not competitive. That goes double when you take into account legacy code. It's changing slowly, but science is a highly competitive environment which is not keen on rewarding contributions of this sort, so it could be quite a while before they catch up.
Mathematica is a lisp for representing and manipulating mathematical expressions combined with an IDE that knows 2D layout (so you can write expressions like you would on paper) and a massive integrated library of mathematical routines. The "gateway drug" is its ability to symbolically integrate, differentiate, factor, simplify expressions, solve equations, interactively plot without explicitly sampling, etc. Then you discover that all it's "heavy lifting" capabilities are integrated with each other -- i.e. you could use a piece-wise implicit surface to define boundary conditions for a differential equation, solve it with finite element on 20 different tessellation levels, and compare the results using a norm built out of an interpolator and integrator to check for convergence. All in a handful of lines of code where you only have to worry about high-level details rather than dozens of for loops and hundreds of lines of glue. I really don't think there's anything comparable in the open source ecosystem yet, but I'd love to be wrong (yes, I know about SAGE).
Matlab is relatively unremarkable as a language -- it's not a lisp, it deals with matrices of floats not expressions, and its only competitive language feature is the eponymous set of linear algebra primitives that CS-trained language lawyers tend to roll their eyes at but that really do make a difference for the scientists and engineers who use it day-to-day. The killer value proposition, though, is its collection of libraries. They're not symbolic like what you would find in Mathematica but they're usually more extensive and relentlessly practical. Sometimes that means speed, sometimes that means features which cater to your particular obscure workflow, sometimes it means integration, but it always seems to result in a decision along the lines of "I could spend a day munging python libraries A, B, C, and D together, or I could open matlab which already has a package and a GUI for it."
Python, Julia, and R do many things very well. They can beat mathematica/matlab in a number of areas but there are still huge swaths of math/science/engineering where they're just not competitive. That goes double when you take into account legacy code. It's changing slowly, but science is a highly competitive environment which is not keen on rewarding contributions of this sort, so it could be quite a while before they catch up.