When I was middle-aged, I did not know many young people working in the field of computational mathematics. The symbolic computation community, in the late 1980ies was dominated by middle-aged professors, as well as numerics was. No computational mathematics hackers around.
The field was dominated by the objective to replicate mathematics in computers AND influence programming by mathematical concepts.
When working in factory automation (dealing with geometry, kinematics and dynamics of controlled mechanisms), I felt how important this will become.
And after having met Stephen Wolfram (1990) personally, I knew this will dominate my future technical and business life. Mathematica as the system on the intersection point of mathematics and computer science. Then on version 1 now on version 7 (close to ..).
But conceptual revolutions seem to take longer: I am still astonished about discussions like, why do quants love C++ , or MatLab versus Mathematica?
One of the outcomes of computational mathematics thinking is the distinction between the language of mathematics and its operational semantics. You can wrap any algorithmic representation, implemented in almost any of the major languages with Mathematica and deal with it like it was an original construct in the Mathematica kernel (you extend the language and provide your own operational semantics - in Mathematica, C++, Java, ... and yes, MatLab).
So it needs some patience to convince a broader community that Mathematica is not just another tool set. It is a concept and an integrated approach for accelerate the innovative spiral.
Maybe too much patience for the very young? I am over 60 now, BTW.