The question seems a bit backwards to me (who come to programming from maths). I am more familiar with the opposite question "how much, if any, programming do

The question seems a bit backwards to me (who come to programming from maths). I am more familiar with the opposite question "how much, if any, programming do you need for math?" Every year I meet lots of math students who love math but hate the very idea of programming, as if it was a dirty and unnoble thing to do. I have to convince them that sometimes it may be useful for them. The best course of action is to start by offering the game: "you don't need any programming for math, except in very particular cases". This gives them a clear starting point where they feel safe. Then we work from there, showing them inductive experiments that would be impossible without computing. For example, it is well known that Gauss would check, by hand computation, many theorems about prime numbers before attempting to prove them. This entailed many days of tedious hand computation that he was very proficient at. Today, most of these experiments can be programmed in a handful lines of code and the computer verifies them in a second. Then some students are eager to actually see these lines of code, but more importantly, to see their result.