It's true you may have set a low bar re: proofs, I just don't think any formal proofs are needed at the first step. Learning about numerical convergence and co

It's true you may have set a low bar re: proofs, I just don't think any formal proofs are needed at the first step. Learning about numerical convergence and computer arithmetic so you can understand why your MATLAB Linear Algebra program is not giving a useful result is far more valuable and doesn't need any proofs. It needs a knowledge of how to use theorems and results and what the conditions are for a result to be applicable. But there is no need to do the proof. Especially since many many proof sare quite idiosyncratic and give no help in suggesting how one thinks like that. Using the analogy of the car I am talking about teaching someone who rides a bike to drive a car. My explicit non-goal is being a mechanic of any kind. So your example of modifying your car is a strawman. That's exactly what I assert a student-driver doesn't need and *shouldn't have to do. It is going to be pretty much useless in actually learning how to steer and how to follow traffic rules. One is about proper usage, the other is about understanding internals. Sorry I still disagree and reassert that proofs are no use at all and a huge distraction for programmers trying to learn math. There is so much valuable and useful work a programmer can do even using existing mehods without ever modifying them. Especially with special purpose languages like R and MATLAB - the underlying algorithm are very mature and a first time user is not expected to modify them. Quite separately I think it's extremely valuable to learn/relearn the foundations of math but this is for anyone and not specific to what a programmer needs to do useful things with math. Yes and it should be taught in high school math. It's not taught bec the teachers didn't learn it that way and so it goes ...