You make this comparison between programmers and mathematicians, but perhaps the more apt analogy is programming language designers vs mathematicians and programmers vs engineers/scientists? I would say that most engineers and scientists learn a couple of mathematical models in class and then go off and do stuff in R or Matlab. What the average engineer/scientist can model presently is now far greater than even the very best could model in the past. And they don’t need to know which of the 11 methods of approximation is going on under the hood of the program.
Then the different abstractions are things like ODE models, finite element analysis, dynamical systems (eg stability), monte carlo, eigenvalue analysis, graph theory stuff, statistical significance tests, etc
You make this comparison between programmers and mathematicians, but perhaps the more apt analogy is programming language designers vs mathematicians and programmers vs engineers/scientists? I would say that most engineers and scientists learn a couple of mathematical models in class and then go off and do stuff in R or Matlab. What the average engineer/scientist can model presently is now far greater than even the very best could model in the past. And they don’t need to know which of the 11 methods of approximation is going on under the hood of the program.
Then the different abstractions are things like ODE models, finite element analysis, dynamical systems (eg stability), monte carlo, eigenvalue analysis, graph theory stuff, statistical significance tests, etc